From 292f3541112775e6bcc0e31ee62aab620883e6d3 Mon Sep 17 00:00:00 2001
From: ivan <ivan.li@practiceinsight.io>
Date: Thu, 20 Dec 2018 10:53:16 +0800
Subject: [PATCH 01/24] refine bubble sort

---
 scala/src/main/scala/ch11_sorts/Sorts.scala   | 53 +++++++++----------
 .../src/test/scala/ch11_sorts/SortsTest.scala | 19 +++++++
 2 files changed, 43 insertions(+), 29 deletions(-)
 create mode 100644 scala/src/test/scala/ch11_sorts/SortsTest.scala

diff --git a/scala/src/main/scala/ch11_sorts/Sorts.scala b/scala/src/main/scala/ch11_sorts/Sorts.scala
index bf110d3..9062989 100644
--- a/scala/src/main/scala/ch11_sorts/Sorts.scala
+++ b/scala/src/main/scala/ch11_sorts/Sorts.scala
@@ -8,42 +8,37 @@ import scala.util.control.Breaks.{break, breakable}
   * Author: yangchuz
   */
 object Sorts {
-  def main(args: Array[String]): Unit ={
-//    println(bubbleSort(Array(0, 6, 2, 3, 8, 5, 6, 7), 8).mkString(", "))
-//    println(insertSort(Array(0, 6, 2, 3, 8, 5, 6, 7), 8).mkString(", "))
-    println(selectionSort(Array(0, 6, 2, 3, 8, 5, 6, 7), 8).mkString(", "))
-  }
 
-  def bubbleSort(arr: Array[Int], n:Int): Array[Int] = {
-    val n = arr.length
+  def bubbleSort(items: Array[Int]): Array[Int] = {
+    val length = items.length
     breakable {
-      for(i <- (n-1) to (1, -1)){
-        var flag = false
-        for(j <- 0 until i){
-          if(arr(j) > arr(j+1)){
-            val tmp = arr(j)
-            arr(j) = arr(j+1)
-            arr(j+1) = tmp
-            flag = true
+      for (i <- Range(0, length)) {
+        var exit = true
+        for (j <- Range(0, length - i - 1)) {
+          if (items(j + 1) < items(j)) {
+            val temp = items(j + 1)
+            items(j + 1) = items(j)
+            items(j) = temp
+            exit = false
           }
         }
-        if(!flag){
+        if (exit) {
           break
         }
       }
     }
-    arr
+    items
   }
 
-  def insertSort(arr: Array[Int], n:Int): Array[Int] = {
-    for(i <- 1 until n){
+  def insertSort(arr: Array[Int], n: Int): Array[Int] = {
+    for (i <- 1 until n) {
       val tmp = arr(i)
-      breakable{
-        for(j <- (i-1) to (0, -1)){
-          if(tmp < arr(j)){
-            arr(j+1) = arr(j)
-          }else{
-            arr(j+1) = tmp
+      breakable {
+        for (j <- (i - 1) to(0, -1)) {
+          if (tmp < arr(j)) {
+            arr(j + 1) = arr(j)
+          } else {
+            arr(j + 1) = tmp
             break
           }
         }
@@ -52,11 +47,11 @@ object Sorts {
     arr
   }
 
-  def selectionSort(arr: Array[Int], n:Int): Array[Int] = {
-    for(i <- 0 until n){
+  def selectionSort(arr: Array[Int], n: Int): Array[Int] = {
+    for (i <- 0 until n) {
       var min = i
-      for(j <- (i + 1) until n){
-        if(arr(j) < arr(min)){
+      for (j <- (i + 1) until n) {
+        if (arr(j) < arr(min)) {
           min = j
         }
       }
diff --git a/scala/src/test/scala/ch11_sorts/SortsTest.scala b/scala/src/test/scala/ch11_sorts/SortsTest.scala
new file mode 100644
index 0000000..3fc2d79
--- /dev/null
+++ b/scala/src/test/scala/ch11_sorts/SortsTest.scala
@@ -0,0 +1,19 @@
+package ch11_sorts
+
+import org.scalatest.{FlatSpec, Matchers}
+
+class SortsTest extends FlatSpec with Matchers {
+
+  behavior of "SortsTest"
+
+  it should "bubbleSort int arrays" in {
+    var array = Array(4,5,6,3,2,1)
+    array = Sorts.bubbleSort(array)
+    array.mkString("") should equal ("123456")
+
+    array = Array(4)
+    array = Sorts.bubbleSort(array)
+    array.mkString("") should equal ("4")
+  }
+
+}

From 3e5fb582817c7c6b27a5171281cc7d711bea9905 Mon Sep 17 00:00:00 2001
From: crazyang <yang3781590@163.com>
Date: Sun, 23 Dec 2018 00:36:32 +0800
Subject: [PATCH 02/24] Update counting_sort.py
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

之前代码有错误，第26行已修改
---
 python/14_sorts/counting_sort.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/python/14_sorts/counting_sort.py b/python/14_sorts/counting_sort.py
index 1bdcd8b..41a32ab 100644
--- a/python/14_sorts/counting_sort.py
+++ b/python/14_sorts/counting_sort.py
@@ -23,7 +23,7 @@ def counting_sort(a: List[int]):
         a_sorted[index] = num
         counts[num] -= 1
     
-    a = a_sorted
+    a[:] = a_sorted
 
 
 if __name__ == "__main__":
@@ -37,4 +37,4 @@ if __name__ == "__main__":
 
     a3 = [4, 5, 0, 9, 3, 3, 1, 9, 8, 7]
     counting_sort(a3)
-    print(a3)
\ No newline at end of file
+    print(a3)

From 1f66f823bcbc67a932d2198396548fbec4207ece Mon Sep 17 00:00:00 2001
From: unknown <gz1301@4399HOUTAI.COM>
Date: Mon, 24 Dec 2018 18:35:12 +0800
Subject: [PATCH 03/24] divide and conquer applications

---
 .../merge_sort_counting.py                    | 51 +++++++++++++++++++
 1 file changed, 51 insertions(+)
 create mode 100644 python/38_divide_and_conquer/merge_sort_counting.py

diff --git a/python/38_divide_and_conquer/merge_sort_counting.py b/python/38_divide_and_conquer/merge_sort_counting.py
new file mode 100644
index 0000000..b036746
--- /dev/null
+++ b/python/38_divide_and_conquer/merge_sort_counting.py
@@ -0,0 +1,51 @@
+#!/usr/bin/python
+# -*- coding: UTF-8 -*-
+
+inversion_num = 0
+
+
+def merge_sort_counting(nums, start, end):
+    if start >= end:
+        return
+
+    mid = (start + end)//2
+    merge_sort_counting(nums, start, mid)
+    merge_sort_counting(nums, mid+1, end)
+    merge(nums, start, mid, end)
+
+
+def merge(nums, start, mid, end):
+    global inversion_num
+    i = start
+    j = mid+1
+    tmp = []
+    while i <= mid and j <= end:
+        if nums[i] <= nums[j]:
+            inversion_num += j - mid - 1
+            tmp.append(nums[i])
+            i += 1
+        else:
+            tmp.append(nums[j])
+            j += 1
+
+    while i <= mid:
+        # 这时nums[i]的逆序数是整个nums[mid+1: end+1]的长度
+        inversion_num += end - mid
+        tmp.append(nums[i])
+        i += 1
+
+    while j <= end:
+        tmp.append(nums[j])
+        j += 1
+
+    nums[start: end+1] = tmp
+
+
+if __name__ == '__main__':
+    print('--- count inversion number using merge sort ---')
+    # nums = [5, 0, 4, 2, 3, 1, 6, 8, 7]
+    nums = [5, 0, 4, 2, 3, 1, 3, 3, 3, 6, 8, 7]
+    print('nums  : {}'.format(nums))
+    merge_sort_counting(nums, 0, len(nums)-1)
+    print('sorted: {}'.format(nums))
+    print('inversion number: {}'.format(inversion_num))

From ec99c673b0c6cef49784db0d0d1271051b0ea1d9 Mon Sep 17 00:00:00 2001
From: unknown <gz1301@4399HOUTAI.COM>
Date: Mon, 24 Dec 2018 18:46:33 +0800
Subject: [PATCH 04/24] backtrack applications

---
 python/39_back_track/01_bag.py       | 59 ++++++++++++++++++++++++++++
 python/39_back_track/eight_queens.py | 57 +++++++++++++++++++++++++++
 python/39_back_track/permutations.py | 42 ++++++++++++++++++++
 python/39_back_track/regex.py        | 35 +++++++++++++++++
 4 files changed, 193 insertions(+)
 create mode 100644 python/39_back_track/01_bag.py
 create mode 100644 python/39_back_track/eight_queens.py
 create mode 100644 python/39_back_track/permutations.py
 create mode 100644 python/39_back_track/regex.py

diff --git a/python/39_back_track/01_bag.py b/python/39_back_track/01_bag.py
new file mode 100644
index 0000000..53c7731
--- /dev/null
+++ b/python/39_back_track/01_bag.py
@@ -0,0 +1,59 @@
+#!/usr/bin/python
+# -*- coding: UTF-8 -*-
+
+from typing import List
+
+# 背包选取的物品列表
+picks = []
+picks_with_max_value = []
+
+
+def bag(capacity: int, cur_weight: int, items_info: List, pick_idx: int):
+    """
+    回溯法解01背包，穷举
+    :param capacity: 背包容量
+    :param cur_weight: 背包当前重量
+    :param items_info: 物品的重量和价值信息
+    :param pick_idx: 当前物品的索引
+    :return:
+    """
+    # 考察完所有物品，或者在中途已经装满
+    if pick_idx >= len(items_info) or cur_weight == capacity:
+        global picks_with_max_value
+        if get_value(items_info, picks) > \
+                get_value(items_info, picks_with_max_value):
+            picks_with_max_value = picks.copy()
+    else:
+        item_weight = items_info[pick_idx][0]
+        if cur_weight + item_weight <= capacity:    # 选
+            picks[pick_idx] = 1
+            bag(capacity, cur_weight + item_weight, items_info, pick_idx + 1)
+
+        picks[pick_idx] = 0                         # 不选
+        bag(capacity, cur_weight, items_info, pick_idx + 1)
+
+
+def get_value(items_info: List, pick_items: List):
+    values = [_[1] for _ in items_info]
+    return sum([a*b for a, b in zip(values, pick_items)])
+
+
+if __name__ == '__main__':
+    # [(weight, value), ...]
+    items_info = [(3, 5), (2, 2), (1, 4), (1, 2), (4, 10)]
+    capacity = 8
+
+    print('--- items info ---')
+    print(items_info)
+
+    print('\n--- capacity ---')
+    print(capacity)
+
+    picks = [0] * len(items_info)
+    bag(capacity, 0, items_info, 0)
+
+    print('\n--- picks ---')
+    print(picks_with_max_value)
+
+    print('\n--- value ---')
+    print(get_value(items_info, picks_with_max_value))
diff --git a/python/39_back_track/eight_queens.py b/python/39_back_track/eight_queens.py
new file mode 100644
index 0000000..a25b728
--- /dev/null
+++ b/python/39_back_track/eight_queens.py
@@ -0,0 +1,57 @@
+#!/usr/bin/python
+# -*- coding: UTF-8 -*-
+
+# 棋盘尺寸
+BOARD_SIZE = 8
+
+solution_count = 0
+queen_list = [0] * BOARD_SIZE
+
+
+def eight_queens(cur_column: int):
+    """
+    输出所有符合要求的八皇后序列
+    用一个长度为8的数组代表棋盘的列，数组的数字则为当前列上皇后所在的行数
+    :return:
+    """
+    if cur_column >= BOARD_SIZE:
+        global solution_count
+        solution_count += 1
+        # 解
+        print(queen_list)
+    else:
+        for i in range(BOARD_SIZE):
+            if is_valid_pos(cur_column, i):
+                queen_list[cur_column] = i
+                eight_queens(cur_column + 1)
+
+
+def is_valid_pos(cur_column: int, pos: int) -> bool:
+    """
+    因为采取的是每列放置1个皇后的做法
+    所以检查的时候不必检查列的合法性，只需要检查行和对角
+    1. 行：检查数组在下标为cur_column之前的元素是否已存在pos
+    2. 对角：检查数组在下标为cur_column之前的元素，其行的间距pos - QUEEN_LIST[i]
+       和列的间距cur_column - i是否一致
+    :param cur_column:
+    :param pos:
+    :return:
+    """
+    i = 0
+    while i < cur_column:
+        # 同行
+        if queen_list[i] == pos:
+            return False
+        # 对角线
+        if cur_column - i == abs(pos - queen_list[i]):
+            return False
+        i += 1
+    return True
+
+
+if __name__ == '__main__':
+    print('--- eight queens sequence ---')
+    eight_queens(0)
+
+    print('\n--- solution count ---')
+    print(solution_count)
diff --git a/python/39_back_track/permutations.py b/python/39_back_track/permutations.py
new file mode 100644
index 0000000..b02a876
--- /dev/null
+++ b/python/39_back_track/permutations.py
@@ -0,0 +1,42 @@
+#!/usr/bin/python
+# -*- coding: UTF-8 -*-
+
+from typing import List
+
+permutations_list = []  # 全局变量，用于记录每个输出
+
+
+def permutations(nums: List, n: int, pick_count: int):
+    """
+    从nums选取n个数的全排列
+
+    回溯法，用一个栈记录当前路径信息
+    当满足n==0时，说明栈中的数已足够，输出并终止遍历
+    :param nums:
+    :param n:
+    :param pick_count:
+    :return:
+    """
+    if n == 0:
+        print(permutations_list)
+    else:
+        for i in range(len(nums) - pick_count):
+            permutations_list[pick_count] = nums[i]
+            nums[i], nums[len(nums) - pick_count - 1] = nums[len(nums) - pick_count - 1], nums[i]
+            permutations(nums, n-1, pick_count+1)
+            nums[i], nums[len(nums) - pick_count - 1] = nums[len(nums) - pick_count - 1], nums[i]
+
+
+if __name__ == '__main__':
+    nums = [1, 2, 3, 4]
+    n = 3
+    print('--- list ---')
+    print(nums)
+
+    print('\n--- pick num ---')
+    print(n)
+
+    print('\n--- permutation list ---')
+    permutations_list = [0] * n
+    permutations(nums, n, 0)
+
diff --git a/python/39_back_track/regex.py b/python/39_back_track/regex.py
new file mode 100644
index 0000000..001cac7
--- /dev/null
+++ b/python/39_back_track/regex.py
@@ -0,0 +1,35 @@
+#!/usr/bin/python
+# -*- coding: UTF-8 -*-
+
+is_match = False
+
+
+def rmatch(r_idx: int, m_idx: int, regex: str, main: str):
+    global is_match
+    if is_match:
+        return
+
+    if r_idx >= len(regex):     # 正则串全部匹配好了
+        is_match = True
+        return
+
+    if m_idx >= len(main) and r_idx < len(regex):   # 正则串没匹配完，但是主串已经没得匹配了
+        is_match = False
+        return
+
+    if regex[r_idx] == '*':     # * 匹配1个或多个任意字符，递归搜索每一种情况
+        for i in range(m_idx, len(main)):
+            rmatch(r_idx+1, i+1, regex, main)
+    elif regex[r_idx] == '?':   # ? 匹配0个或1个任意字符，两种情况
+        rmatch(r_idx+1, m_idx+1, regex, main)
+        rmatch(r_idx+1, m_idx, regex, main)
+    else:                       # 非特殊字符需要精确匹配
+        if regex[r_idx] == main[m_idx]:
+            rmatch(r_idx+1, m_idx+1, regex, main)
+
+
+if __name__ == '__main__':
+    regex = 'ab*eee?d'
+    main = 'abcdsadfkjlekjoiwjiojieeecd'
+    rmatch(0, 0, regex, main)
+    print(is_match)

From 04158f29476106fbea6f28b1cea5a8406fddc6a9 Mon Sep 17 00:00:00 2001
From: Wenru Dong <dongwenru.aaron.shenyang@gmail.com>
Date: Mon, 24 Dec 2018 12:55:22 +0000
Subject: [PATCH 05/24] backtracking 8 queens problem in python

---
 python/39_backtracking/backtracking.py | 25 +++++++++++++++++++++++++
 1 file changed, 25 insertions(+)
 create mode 100644 python/39_backtracking/backtracking.py

diff --git a/python/39_backtracking/backtracking.py b/python/39_backtracking/backtracking.py
new file mode 100644
index 0000000..6f3059a
--- /dev/null
+++ b/python/39_backtracking/backtracking.py
@@ -0,0 +1,25 @@
+"""
+    Author: Wenru Dong
+"""
+
+from typing import List
+
+def eight_queens() -> None:
+    solutions = []
+
+    def backtracking(queens_at_column: List[int], index_sums: List[int], index_diffs: List[int]) -> None:
+        row = len(queens_at_column)
+        if row == 8:
+            solutions.append(queens_at_column)
+            return
+        for col in range(8):
+            if col in queens_at_column or row + col in index_sums or row - col in index_diffs: continue
+            backtracking(queens_at_column + [col], index_sums + [row + col], index_diffs + [row - col])
+    
+    backtracking([], [], [])
+    print(*(" " + " ".join("*" * i + "Q" + "*" * (8 - i - 1) + "\n" for i in solution) for solution in solutions), sep="\n")
+
+
+if __name__ == "__main__":
+
+    eight_queens()

From 0ff4d661f736f2524ede916d650b53a19389c58b Mon Sep 17 00:00:00 2001
From: hjlarry <hjlarry@163.com>
Date: Tue, 25 Dec 2018 15:29:22 +0800
Subject: [PATCH 06/24] fix array

---
 python/05_array/myarray.py | 135 ++++++++++---------------------------
 1 file changed, 36 insertions(+), 99 deletions(-)

diff --git a/python/05_array/myarray.py b/python/05_array/myarray.py
index f85a33b..e7fa40e 100644
--- a/python/05_array/myarray.py
+++ b/python/05_array/myarray.py
@@ -1,133 +1,70 @@
-from typing import Optional
-
-
 #
 # 1) Insertion, deletion and random access of array
 # 2) Assumes int for element type
 #
 # Author: Wenru
 #
+
+
 class MyArray:
     """A simple wrapper around List.
     You cannot have -1 in the array.
     """
 
     def __init__(self, capacity: int):
-
         self._data = []
-        self._count = 0
         self._capacity = capacity
 
-    def __getitem__(self, position: int) -> int:
-
-        """Support for subscript.
-        Perhaps better than the find() method below.
-        """
+    def __getitem__(self, position: int) -> object:
         return self._data[position]
 
-    def find(self, index: int) -> Optional[int]:
+    def __setitem__(self, index: int, value: object):
+        self._data[index] = value
 
-        if index >= self._count or index <= -self._count:
+    def __len__(self) -> int:
+        return len(self._data)
+
+    def __iter__(self):
+        for item in self._data:
+            yield item
+
+    def find(self, index: int) -> object:
+        try:
+            return self._data[index]
+        except IndexError:
             return None
-        return self._data[index]
 
     def delete(self, index: int) -> bool:
-
-        if index >= self._count or index <= -self._count:
+        try:
+            self._data.pop(index)
+            return True
+        except IndexError:
             return False
 
-        self._data[index:-1] = self._data[index + 1:]
-        self._count -= 1
-        # 真正将数据删除并覆盖原来的数据 ，这个需要增加
-        self._data = self._data[0:self._count]
-        print('delete function', self._data)
-        return True
-
     def insert(self, index: int, value: int) -> bool:
-
-        # if index >= self._count or index <= -self._count: return False
-        if self._capacity == self._count:
+        if len(self) >= self._capacity:
             return False
-        # 如果还有空间，那么插入位置大于当前的元素个数，可以插入最后的位置
-        if index >= self._count:
-            self._data.append(value)
-        # 同上，如果位置小于0 可以插入第０个位置.
-        if index < 0:
-            print(index)
-            self._data.insert(0, value)
-
-        self._count += 1
-        return True
-
-    def insert_v2(self, index: int, value: int) -> bool:
-        """
-        支持任意位置插入
-        :param index:
-        :param value:
-        :return:
-        """
-        # 数组空间已满
-        if self._capacity == self._count:
-            return False
-
-        # 插入位置大于当前的元素个数，可以插入最后的位置
-        if index >= self._count:
-            self._data.append(value)
-        elif index < 0:
-            # 位置小于 0 可以插入第 ０ 个位置
-            self._data.insert(0, value)
         else:
-            # 挪动 index 至 _count 位到 index+1 至 _count+1 位
-            # 插入第 index
-            self._data[index+1:self._count+1] = self._data[index:self._count]
-            self._data[index] = value
-
-        self._count += 1
-        return True
-
-    def insert_to_tail(self, value: int) -> bool:
-
-        if self._count == self._capacity:
-            return False
-        if self._count == len(self._data):
-            self._data.append(value)
-        else:
-            self._data[self._count] = value
-        self._count += 1
-        return True
-
-    def __repr__(self) -> str:
-
-        return " ".join(str(num) for num in self._data[:self._count])
+            return self._data.insert(index, value)
 
     def print_all(self):
-
-        for num in self._data[:self._count]:
-            print(f"{num}", end=" ")
-        print("\n", flush=True)
+        for item in self:
+            print(item)
 
 
 def test_myarray():
-    array_a = MyArray(6)
-    for num in range(6):
-        array_a.insert_to_tail(num)
-    assert array_a.find(0) == 0
-    assert array_a[0] == 0
-    array_a.delete(0)
-    assert array_a[0] == 1
+    array = MyArray(5)
+    array.insert(0, 3)
+    array.insert(0, 4)
+    array.insert(1, 5)
+    array.insert(3, 9)
+    array.insert(3, 10)
+    assert array.insert(0, 100) is False
+    assert len(array) == 5
+    assert array.find(1) == 5
+    assert array.delete(4) is True
+    array.print_all()
 
 
 if __name__ == "__main__":
-    a = MyArray(6)
-    for i in range(6):
-        a.insert_to_tail(i)
-    a.delete(2)
-    print(a)
-    a.insert_to_tail(7)
-    print(a)
-    print('origin', a)
-    a.delete(4)
-    print('delete ', a)
-
-    a.insert(100, 10000)
-    print(a)
+    test_myarray()

From ec602f96fd8e7854af570e9dc27f13bcea93acc8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=9D=8E=E8=B6=85?= <lichao@910app.com>
Date: Wed, 26 Dec 2018 16:39:44 +0800
Subject: [PATCH 07/24] =?UTF-8?q?=E4=BF=AE=E6=94=B9=E5=88=9B=E5=BB=BA?=
 =?UTF-8?q?=E5=B8=A6=E7=8E=AF=E9=93=BE=E8=A1=A8=E7=9A=84=E4=B8=80=E4=B8=AA?=
 =?UTF-8?q?=E9=97=AE=E9=A2=98?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 c-cpp/07_linkedlist/LinkedListAlgo.c | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/c-cpp/07_linkedlist/LinkedListAlgo.c b/c-cpp/07_linkedlist/LinkedListAlgo.c
index 159522f..b326ee3 100644
--- a/c-cpp/07_linkedlist/LinkedListAlgo.c
+++ b/c-cpp/07_linkedlist/LinkedListAlgo.c
@@ -79,6 +79,8 @@ void test_checkCircle() {
         SinglyLinkedNode* node = malloc(sizeof(SinglyLinkedNode));
         node->data = i;
         current->next = node;
+        //reset current node
+        current = node;
     }
     current->next = h;
     

From 336394dc90810fe31c940c7c84de507eaa7c30d8 Mon Sep 17 00:00:00 2001
From: Wenru Dong <dongwenru.aaron.shenyang@gmail.com>
Date: Wed, 26 Dec 2018 13:26:22 +0000
Subject: [PATCH 08/24] 0/1 knapsack problem in python

---
 python/40_dynamic_programming/knapsack.py | 30 +++++++++++++++++++++++
 1 file changed, 30 insertions(+)
 create mode 100644 python/40_dynamic_programming/knapsack.py

diff --git a/python/40_dynamic_programming/knapsack.py b/python/40_dynamic_programming/knapsack.py
new file mode 100644
index 0000000..7a71272
--- /dev/null
+++ b/python/40_dynamic_programming/knapsack.py
@@ -0,0 +1,30 @@
+"""
+    Author: Wenru Dong
+"""
+
+from typing import List
+
+def knapsack01(weights: List[int], values: List[int], capacity: int) -> int:
+    # Denote the state as (i, c), where i is the stage number,
+    # and c is the capacity available. Denote f(i, c) to be the
+    # maximum value when the capacity available is c, and Item 0
+    # to Item i-1 are to be packed.
+    # The goal is to find f(n-1, W), where W is the total capacity.
+    # Then the DP functional equation is:
+    #   f(i, c) = max(xᵢvᵢ + f(i-1, c-xᵢwᵢ)), xᵢ ∈ D, i ≥ 0,
+    #   f(-1, c) = 0, 0 ≤ c ≤ W,
+    # where
+    #                  /  {0},    if wᵢ > c
+    #   D = D(i, c) = 
+    #                  \  {0, 1}, if wᵢ ≤ c
+
+    prev = [0] * (capacity + 1)
+    for w, v in zip(weights, values):
+        prev = [c >= w and max(prev[c], prev[c-w] + v) for c in range(capacity + 1)]
+    return prev[-1]
+
+
+if __name__ == "__main__":
+    # To find the maximum weight that can be packed,
+    # set values equal to the weights
+    print(knapsack01([2, 2, 4, 6, 3], [2, 2, 4, 6, 3], 9))

From dfc4d967dcbbd75739c6273bb56f02e24ee158d2 Mon Sep 17 00:00:00 2001
From: KP <109694228@qq.com>
Date: Wed, 26 Dec 2018 14:26:44 +0800
Subject: [PATCH 09/24] dynamic programming applications

---
 python/40_dynamic_programming/01_bag.py      | 66 ++++++++++++++++++++
 python/40_dynamic_programming/yh_triangle.py | 64 +++++++++++++++++++
 2 files changed, 130 insertions(+)
 create mode 100644 python/40_dynamic_programming/01_bag.py
 create mode 100644 python/40_dynamic_programming/yh_triangle.py

diff --git a/python/40_dynamic_programming/01_bag.py b/python/40_dynamic_programming/01_bag.py
new file mode 100644
index 0000000..4c5d1b3
--- /dev/null
+++ b/python/40_dynamic_programming/01_bag.py
@@ -0,0 +1,66 @@
+#!/usr/bin/python
+# -*- coding: UTF-8 -*-
+
+from typing import List, Tuple
+
+
+def bag(items_info: List[int], capacity: int) -> int:
+    """
+    固定容量的背包，计算能装进背包的物品组合的最大重量
+
+    :param items_info: 每个物品的重量
+    :param capacity: 背包容量
+    :return: 最大装载重量
+    """
+    n = len(items_info)
+    memo = [[-1]*(capacity+1) for i in range(n)]
+    memo[0][0] = 1
+    if items_info[0] <= capacity:
+        memo[0][items_info[0]] = 1
+
+    for i in range(1, n):
+        for cur_weight in range(capacity+1):
+            if memo[i-1][cur_weight] != -1:
+                memo[i][cur_weight] = memo[i-1][cur_weight]   # 不选
+                if cur_weight + items_info[i] <= capacity:    # 选
+                    memo[i][cur_weight + items_info[i]] = 1
+
+    for w in range(capacity, -1, -1):
+        if memo[-1][w] != -1:
+            return w
+
+
+def bag_with_max_value(items_info: List[Tuple[int, int]], capacity: int) -> int:
+    """
+    固定容量的背包，计算能装进背包的物品组合的最大价值
+
+    :param items_info: 物品的重量和价值
+    :param capacity: 背包容量
+    :return: 最大装载价值
+    """
+    n = len(items_info)
+    memo = [[-1]*(capacity+1) for i in range(n)]
+    memo[0][0] = 0
+    if items_info[0][0] <= capacity:
+        memo[0][items_info[0][0]] = items_info[0][1]
+
+    for i in range(1, n):
+        for cur_weight in range(capacity+1):
+            if memo[i-1][cur_weight] != -1:
+                memo[i][cur_weight] = memo[i-1][cur_weight]
+                if cur_weight + items_info[i][0] <= capacity:
+                    memo[i][cur_weight + items_info[i][0]] = max(memo[i][cur_weight + items_info[i][0]],
+                                                                 memo[i-1][cur_weight] + items_info[i][1])
+    return max(memo[-1])
+
+
+if __name__ == '__main__':
+    # [weight, ...]
+    items_info = [2, 2, 4, 6, 3]
+    capacity = 9
+    print(bag(items_info, capacity))
+
+    # [(weight, value), ...]
+    items_info = [(3, 5), (2, 2), (1, 4), (1, 2), (4, 10)]
+    capacity = 8
+    print(bag_with_max_value(items_info, capacity))
diff --git a/python/40_dynamic_programming/yh_triangle.py b/python/40_dynamic_programming/yh_triangle.py
new file mode 100644
index 0000000..a652edd
--- /dev/null
+++ b/python/40_dynamic_programming/yh_triangle.py
@@ -0,0 +1,64 @@
+#!/usr/bin/python
+# -*- coding: UTF-8 -*-
+
+from typing import List
+
+Layer_nums = List[int]
+
+
+def yh_triangle(nums: List[Layer_nums]) -> int:
+    """
+    从根节点开始向下走，过程中经过的节点，只需存储经过它时最小的路径和
+    :param nums:
+    :return:
+    """
+    assert len(nums) > 0
+    n = len(nums)   # 层数
+    memo = [[0]*n for i in range(n)]
+    memo[0][0] = nums[0][0]
+
+    for i in range(1, n):
+        for j in range(i+1):
+            # 每一层首尾两个数字，只有一条路径可以到达
+            if j == 0:
+                memo[i][j] = memo[i-1][j] + nums[i][j]
+            elif j == i:
+                memo[i][j] = memo[i-1][j-1] + nums[i][j]
+            else:
+                memo[i][j] = min(memo[i-1][j-1] + nums[i][j], memo[i-1][j] + nums[i][j])
+    return min(memo[n-1])
+
+
+def yh_triangle_space_optimization(nums: List[Layer_nums]) -> int:
+    assert len(nums) > 0
+    n = len(nums)
+    memo = [0] * n
+    memo[0] = nums[0][0]
+
+    for i in range(1, n):
+        for j in range(i, -1, -1):
+            if j == i:
+                memo[j] = memo[j-1] + nums[i][j]
+            elif j == 0:
+                memo[j] = memo[j] + nums[i][j]
+            else:
+                memo[j] = min(memo[j-1] + nums[i][j], memo[j] + nums[i][j])
+    return min(memo)
+
+
+def yh_triangle_bottom_up(nums: List[Layer_nums]) -> int:
+    assert len(nums) > 0
+    n = len(nums)
+    memo = nums[-1].copy()
+
+    for i in range(n-1, 0, -1):
+        for j in range(i):
+            memo[j] = min(memo[j] + nums[i-1][j], memo[j+1] + nums[i-1][j])
+    return memo[0]
+
+
+if __name__ == '__main__':
+    nums = [[3], [2, 6], [5, 4, 2], [6, 0, 3, 2]]
+    print(yh_triangle(nums))
+    print(yh_triangle_space_optimization(nums))
+    print(yh_triangle_bottom_up(nums))

From 569cc1c0d284a4da38a1e63061b01fbee56d7306 Mon Sep 17 00:00:00 2001
From: ivan <ivan.li@practiceinsight.io>
Date: Thu, 27 Dec 2018 10:48:57 +0800
Subject: [PATCH 10/24] impl insertion Sort and selection sort and test and
 performance test

---
 scala/src/main/scala/ch11_sorts/Sorts.scala   | 41 +++++++++-------
 .../src/test/scala/ch11_sorts/SortsTest.scala | 48 +++++++++++++++++--
 2 files changed, 68 insertions(+), 21 deletions(-)

diff --git a/scala/src/main/scala/ch11_sorts/Sorts.scala b/scala/src/main/scala/ch11_sorts/Sorts.scala
index 9062989..bc918e9 100644
--- a/scala/src/main/scala/ch11_sorts/Sorts.scala
+++ b/scala/src/main/scala/ch11_sorts/Sorts.scala
@@ -30,36 +30,41 @@ object Sorts {
     items
   }
 
-  def insertSort(arr: Array[Int], n: Int): Array[Int] = {
-    for (i <- 1 until n) {
-      val tmp = arr(i)
+  def insertSort(items: Array[Int]): Array[Int] = {
+    val length = items.length
+    for (i <- Range(1, length)) {
+      val value = items(i)
+      var j = i - 1
       breakable {
-        for (j <- (i - 1) to(0, -1)) {
-          if (tmp < arr(j)) {
-            arr(j + 1) = arr(j)
+        while (j >= 0) {
+          if (items(j) > value) {
+            items(j + 1) = items(j)
           } else {
-            arr(j + 1) = tmp
             break
           }
+          j -= 1
         }
       }
+      items(j + 1) = value
     }
-    arr
+    items
   }
 
-  def selectionSort(arr: Array[Int], n: Int): Array[Int] = {
-    for (i <- 0 until n) {
-      var min = i
-      for (j <- (i + 1) until n) {
-        if (arr(j) < arr(min)) {
-          min = j
+  def selectionSort(items: Array[Int]): Array[Int] = {
+    val length = items.length
+    for (i <- Range(0, length)) {
+      var minIndex = i
+      for (j <- Range(i + 1, length)) {
+        if (items(j) < items(minIndex)) {
+          minIndex = j
         }
       }
 
-      val tmp = arr(i)
-      arr(i) = arr(min)
-      arr(min) = tmp
+      //put the min value to the front
+      val temp = items(i)
+      items(i) = items(minIndex)
+      items(minIndex) = temp
     }
-    arr
+    items
   }
 }
diff --git a/scala/src/test/scala/ch11_sorts/SortsTest.scala b/scala/src/test/scala/ch11_sorts/SortsTest.scala
index 3fc2d79..a7c507b 100644
--- a/scala/src/test/scala/ch11_sorts/SortsTest.scala
+++ b/scala/src/test/scala/ch11_sorts/SortsTest.scala
@@ -2,18 +2,60 @@ package ch11_sorts
 
 import org.scalatest.{FlatSpec, Matchers}
 
+import scala.util.Random
+
 class SortsTest extends FlatSpec with Matchers {
 
   behavior of "SortsTest"
 
   it should "bubbleSort int arrays" in {
-    var array = Array(4,5,6,3,2,1)
+    var array = Array(4, 5, 6, 3, 2, 1)
     array = Sorts.bubbleSort(array)
-    array.mkString("") should equal ("123456")
+    array.mkString("") should equal("123456")
 
     array = Array(4)
     array = Sorts.bubbleSort(array)
-    array.mkString("") should equal ("4")
+    array.mkString("") should equal("4")
   }
 
+  it should "insertSort int arrays" in {
+    var array = Array(4, 5, 6, 1, 3, 2)
+    array = Sorts.insertSort(array)
+    array.mkString("") should equal("123456")
+
+    array = Array(4)
+    array = Sorts.insertSort(array)
+    array.mkString("") should equal("4")
+  }
+
+  it should "selectionSort int arrays" in {
+    var array = Array(4, 5, 6, 1, 3, 2)
+    array = Sorts.insertSort(array)
+    array.mkString("") should equal("123456")
+
+    array = Array(4)
+    array = Sorts.insertSort(array)
+    array.mkString("") should equal("4")
+  }
+
+
+  it should "compare the sort algo" in {
+    val length = 50000
+    val array = new Array[Int](length)
+    val rnd = new Random()
+    for (i <- Range(0, length)) {
+      array(i) = rnd.nextInt()
+    }
+
+    timed("bubbleSort", Sorts.bubbleSort(array.clone()))
+    timed("insertSort", Sorts.bubbleSort(array.clone()))
+    timed("selectionSort", Sorts.bubbleSort(array.clone()))
+  }
+
+  def reportElapsed(name: String, time: Long): Unit = println(name + " takes in " + time + "ms")
+
+  def timed[T](name: String, f: => T): T = {
+    val start = System.currentTimeMillis()
+    try f finally reportElapsed(name, System.currentTimeMillis - start)
+  }
 }

From 5b3ad97fcb223a4261d0f659882ffed3d123f24f Mon Sep 17 00:00:00 2001
From: ivan <ivan.li@practiceinsight.io>
Date: Thu, 27 Dec 2018 12:27:33 +0800
Subject: [PATCH 11/24] dev merge sort

---
 .../src/main/scala/ch12_sorts/MergeSort.scala | 60 +++++++++++++++++++
 .../src/test/scala/ch11_sorts/SortsTest.scala |  2 +-
 .../test/scala/ch12_sorts/MergeSortTest.scala | 22 +++++++
 3 files changed, 83 insertions(+), 1 deletion(-)
 create mode 100644 scala/src/main/scala/ch12_sorts/MergeSort.scala
 create mode 100644 scala/src/test/scala/ch12_sorts/MergeSortTest.scala

diff --git a/scala/src/main/scala/ch12_sorts/MergeSort.scala b/scala/src/main/scala/ch12_sorts/MergeSort.scala
new file mode 100644
index 0000000..27de8b0
--- /dev/null
+++ b/scala/src/main/scala/ch12_sorts/MergeSort.scala
@@ -0,0 +1,60 @@
+package ch12_sorts
+
+object MergeSort {
+
+  def mergeSort(items: Array[Int]): Array[Int] = {
+    _mergeSort(items, 0, items.length - 1)
+    items
+  }
+
+
+  private[this] def _mergeSort(items: Array[Int], p: Int, r: Int): Unit = {
+    if (p >= r) {
+      return
+    }
+
+    val q = p + (r - p) / 2
+    _mergeSort(items, p, q)
+    _mergeSort(items, q + 1, r)
+    _merge(items, p, q, r)
+
+  }
+
+  private[this] def _merge(items: Array[Int], p: Int, q: Int, r: Int): Unit = {
+    //start of first half
+    var i = p
+    //start of second half
+    var j = q + 1
+    var k = 0
+    //temp array to hold the data
+    val tempArray = new Array[Int](r - p + 1)
+    while (i <= q && j <= r) {
+      if (items(i) <= items(j)) {
+        tempArray(k) = items(i)
+        i += 1
+      } else {
+        tempArray(k) = items(j)
+        j += 1
+      }
+      k += 1
+    }
+
+    var start = i
+    var end = q
+
+    if (j <= r) {
+      start = j
+      end = r
+    }
+
+    for (n <- start to end) {
+      tempArray(k) = items(n)
+      k += 1
+    }
+
+    //copy tempArray back to items
+    for (n <- 0 to r - p) {
+      items(p + n) = tempArray(n)
+    }
+  }
+}
diff --git a/scala/src/test/scala/ch11_sorts/SortsTest.scala b/scala/src/test/scala/ch11_sorts/SortsTest.scala
index a7c507b..2fc8d02 100644
--- a/scala/src/test/scala/ch11_sorts/SortsTest.scala
+++ b/scala/src/test/scala/ch11_sorts/SortsTest.scala
@@ -6,7 +6,7 @@ import scala.util.Random
 
 class SortsTest extends FlatSpec with Matchers {
 
-  behavior of "SortsTest"
+  behavior of "SortsTest in ch11"
 
   it should "bubbleSort int arrays" in {
     var array = Array(4, 5, 6, 3, 2, 1)
diff --git a/scala/src/test/scala/ch12_sorts/MergeSortTest.scala b/scala/src/test/scala/ch12_sorts/MergeSortTest.scala
new file mode 100644
index 0000000..6944aac
--- /dev/null
+++ b/scala/src/test/scala/ch12_sorts/MergeSortTest.scala
@@ -0,0 +1,22 @@
+package ch12_sorts
+
+
+import org.scalatest.{FlatSpec, Matchers}
+
+class MergeSortTest extends FlatSpec with Matchers {
+  behavior of "SortsTest in ch12"
+
+  it should "mergeSort int arrays" in {
+    var array = Array(4, 5, 6, 3, 2, 1)
+    array = MergeSort.mergeSort(array)
+    array.mkString("") should equal("123456")
+
+    array = Array(4)
+    array = MergeSort.mergeSort(array)
+    array.mkString("") should equal("4")
+
+    array = Array(4, 2)
+    array = MergeSort.mergeSort(array)
+    array.mkString("") should equal("24")
+  }
+}

From 0f863999d2654c3b0bd147929c125f625194f507 Mon Sep 17 00:00:00 2001
From: ivan <ivan.li@practiceinsight.io>
Date: Thu, 27 Dec 2018 13:39:38 +0800
Subject: [PATCH 12/24] fix time function

---
 scala/src/test/scala/ch11_sorts/SortsTest.scala | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/scala/src/test/scala/ch11_sorts/SortsTest.scala b/scala/src/test/scala/ch11_sorts/SortsTest.scala
index 2fc8d02..b1fad9f 100644
--- a/scala/src/test/scala/ch11_sorts/SortsTest.scala
+++ b/scala/src/test/scala/ch11_sorts/SortsTest.scala
@@ -47,15 +47,15 @@ class SortsTest extends FlatSpec with Matchers {
       array(i) = rnd.nextInt()
     }
 
-    timed("bubbleSort", Sorts.bubbleSort(array.clone()))
-    timed("insertSort", Sorts.bubbleSort(array.clone()))
-    timed("selectionSort", Sorts.bubbleSort(array.clone()))
+    timed("bubbleSort", Sorts.bubbleSort, array.clone())
+    timed("insertSort", Sorts.insertSort, array.clone())
+    timed("selectionSort", Sorts.selectionSort, array.clone())
   }
 
   def reportElapsed(name: String, time: Long): Unit = println(name + " takes in " + time + "ms")
 
-  def timed[T](name: String, f: => T): T = {
+  def timed[T](name: String, f: (Array[Int]) => T, array: Array[Int]): T = {
     val start = System.currentTimeMillis()
-    try f finally reportElapsed(name, System.currentTimeMillis - start)
+    try f(array) finally reportElapsed(name, System.currentTimeMillis - start)
   }
 }

From f5cf5c79e174e7cbe81726208f9cfe0a89a10fbc Mon Sep 17 00:00:00 2001
From: ivan <ivan.li@practiceinsight.io>
Date: Thu, 27 Dec 2018 13:40:35 +0800
Subject: [PATCH 13/24] fix timed function

---
 scala/src/test/scala/ch11_sorts/SortsTest.scala | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/scala/src/test/scala/ch11_sorts/SortsTest.scala b/scala/src/test/scala/ch11_sorts/SortsTest.scala
index b1fad9f..ee00637 100644
--- a/scala/src/test/scala/ch11_sorts/SortsTest.scala
+++ b/scala/src/test/scala/ch11_sorts/SortsTest.scala
@@ -54,7 +54,7 @@ class SortsTest extends FlatSpec with Matchers {
 
   def reportElapsed(name: String, time: Long): Unit = println(name + " takes in " + time + "ms")
 
-  def timed[T](name: String, f: (Array[Int]) => T, array: Array[Int]): T = {
+  def timed(name: String, f: (Array[Int]) => Unit, array: Array[Int]): Unit = {
     val start = System.currentTimeMillis()
     try f(array) finally reportElapsed(name, System.currentTimeMillis - start)
   }

From df6133619da573091c3e83bfbf49f3162134f277 Mon Sep 17 00:00:00 2001
From: ivan <ivan.li@practiceinsight.io>
Date: Thu, 27 Dec 2018 15:15:51 +0800
Subject: [PATCH 14/24] quick sort and findKthElement in array

---
 .../src/main/scala/ch12_sorts/QuickSort.scala | 54 +++++++++++++++++++
 .../src/test/scala/ch11_sorts/SortsTest.scala |  3 ++
 .../test/scala/ch12_sorts/QuickSortTest.scala | 31 +++++++++++
 3 files changed, 88 insertions(+)
 create mode 100644 scala/src/main/scala/ch12_sorts/QuickSort.scala
 create mode 100644 scala/src/test/scala/ch12_sorts/QuickSortTest.scala

diff --git a/scala/src/main/scala/ch12_sorts/QuickSort.scala b/scala/src/main/scala/ch12_sorts/QuickSort.scala
new file mode 100644
index 0000000..afcea21
--- /dev/null
+++ b/scala/src/main/scala/ch12_sorts/QuickSort.scala
@@ -0,0 +1,54 @@
+package ch12_sorts
+
+object QuickSort {
+
+  //find the K th smallest element int the array
+  def findKthElement(items: Array[Int], k: Int): Int = {
+    _findKthElement(items, k, 0, items.length - 1)
+  }
+
+  private[this] def _findKthElement(items: Array[Int], k: Int, p: Int, r: Int): Int = {
+    val q = _partition(items, p, r)
+
+    if (k == q + 1) {
+      items(q)
+    } else if (k < q + 1) {
+      _findKthElement(items, k, p, q - 1)
+    } else {
+      _findKthElement(items, k, q + 1, r)
+    }
+  }
+
+  def quickSort(items: Array[Int]): Array[Int] = {
+    _quickSort(items, 0, items.length - 1)
+    items
+  }
+
+  private[this] def _quickSort(items: Array[Int], p: Int, r: Int): Unit = {
+    if (p >= r) {
+      return
+    }
+    val q = _partition(items, p, r)
+    _quickSort(items, p, q - 1)
+    _quickSort(items, q + 1, r)
+  }
+
+  private[this] def _partition(items: Array[Int], p: Int, r: Int): Int = {
+    val pivot = items(r)
+    var i = p
+    for (j <- Range(p, r)) {
+      if (items(j) < pivot) {
+        val temp = items(i)
+        items(i) = items(j)
+        items(j) = temp
+        i += 1
+      }
+    }
+
+    val temp = items(i)
+    items(i) = items(r)
+    items(r) = temp
+
+    i
+  }
+}
diff --git a/scala/src/test/scala/ch11_sorts/SortsTest.scala b/scala/src/test/scala/ch11_sorts/SortsTest.scala
index ee00637..d18854a 100644
--- a/scala/src/test/scala/ch11_sorts/SortsTest.scala
+++ b/scala/src/test/scala/ch11_sorts/SortsTest.scala
@@ -1,5 +1,6 @@
 package ch11_sorts
 
+import ch12_sorts.{MergeSort, QuickSort}
 import org.scalatest.{FlatSpec, Matchers}
 
 import scala.util.Random
@@ -50,6 +51,8 @@ class SortsTest extends FlatSpec with Matchers {
     timed("bubbleSort", Sorts.bubbleSort, array.clone())
     timed("insertSort", Sorts.insertSort, array.clone())
     timed("selectionSort", Sorts.selectionSort, array.clone())
+    timed("mergeSort", MergeSort.mergeSort, array.clone())
+    timed("quickSort", QuickSort.quickSort, array.clone())
   }
 
   def reportElapsed(name: String, time: Long): Unit = println(name + " takes in " + time + "ms")
diff --git a/scala/src/test/scala/ch12_sorts/QuickSortTest.scala b/scala/src/test/scala/ch12_sorts/QuickSortTest.scala
new file mode 100644
index 0000000..cafeedb
--- /dev/null
+++ b/scala/src/test/scala/ch12_sorts/QuickSortTest.scala
@@ -0,0 +1,31 @@
+package ch12_sorts
+
+import org.scalatest.{FlatSpec, Matchers}
+
+class QuickSortTest extends FlatSpec with Matchers {
+
+  behavior of "QuickSortTest"
+
+  it should "quickSort" in {
+    var array = Array(4, 5, 6, 3, 2, 1)
+    array = QuickSort.quickSort(array)
+    array.mkString("") should equal("123456")
+
+    array = Array(4)
+    array = QuickSort.quickSort(array)
+    array.mkString("") should equal("4")
+
+    array = Array(4, 2)
+    array = QuickSort.quickSort(array)
+    array.mkString("") should equal("24")
+  }
+
+  it should "find the Kth element in the array" in {
+    val array = Array(4, 2, 5, 12, 3)
+
+    QuickSort.findKthElement(array, 3) should equal(4)
+    QuickSort.findKthElement(array, 5) should equal(12)
+    QuickSort.findKthElement(array, 1) should equal(2)
+  }
+
+}

From 8aced9e71f9facebbb99455513b454ae545be751 Mon Sep 17 00:00:00 2001
From: ivan <ivan.li@practiceinsight.io>
Date: Fri, 28 Dec 2018 11:25:45 +0800
Subject: [PATCH 15/24] impl sqrt and b search

---
 .../src/main/scala/ch15_bsearch/BSearch.scala | 60 ++++++++++++++-----
 .../scala/ch15_bsearch/BSearchRecursive.scala | 31 +++++-----
 .../ch15_bsearch/BSearchRecursiveTest.scala   | 25 ++++++++
 .../test/scala/ch15_bsearch/BSearchTest.scala | 37 ++++++++++++
 4 files changed, 123 insertions(+), 30 deletions(-)
 create mode 100644 scala/src/test/scala/ch15_bsearch/BSearchRecursiveTest.scala
 create mode 100644 scala/src/test/scala/ch15_bsearch/BSearchTest.scala

diff --git a/scala/src/main/scala/ch15_bsearch/BSearch.scala b/scala/src/main/scala/ch15_bsearch/BSearch.scala
index 2165938..9a9ef02 100644
--- a/scala/src/main/scala/ch15_bsearch/BSearch.scala
+++ b/scala/src/main/scala/ch15_bsearch/BSearch.scala
@@ -1,20 +1,50 @@
 package ch15_bsearch
 
-object BSearch {
-    def search(nums: Array[Int], target: Int): Int = {
-        var low = 0
-        var high = nums.length - 1
-        while(low <= high){
-            val mid = low + ((high - low) >> 2)
-            if(nums(mid) > target){
-                high = mid - 1
-            } else if (nums(mid) < target){
-                low = mid + 1
-            } else {
-                return mid
-            }
-        }
+import scala.math.abs
 
-        return -1
+object BSearch {
+
+  def search(items: Array[Int], target: Int): Int = {
+    var low = 0
+    var high = items.length - 1
+    while (low <= high) {
+      val mid = low + (high - low) / 2
+      if (items(mid) == target) {
+        return mid
+      } else if (items(mid) > target) {
+        high = mid - 1
+      } else {
+        low = mid + 1
+      }
     }
+
+    -1
+  }
+
+  def sqrt(x: Double, precision: Double): Double = {
+
+    require(precision > 0, "precision must > 0")
+    require(x > 0, "input value for sqrt must > 0")
+    var low = 0.0
+    var high = x
+    val actualPrecision = precision / 10
+
+    if (x > 0 && x < 1) {
+      low = x
+      high = 1
+    }
+    while (high - low > actualPrecision) {
+      val mid = low + (high - low) / 2
+      if (abs(mid * mid - x) < actualPrecision) {
+        //find it
+        return mid
+      } else if (mid * mid > x) {
+        high = mid
+      } else {
+        low = mid
+      }
+    }
+    throw new IllegalStateException("could not determine the sqrt value for " + x)
+
+  }
 }
diff --git a/scala/src/main/scala/ch15_bsearch/BSearchRecursive.scala b/scala/src/main/scala/ch15_bsearch/BSearchRecursive.scala
index ca7befc..8ea4010 100644
--- a/scala/src/main/scala/ch15_bsearch/BSearchRecursive.scala
+++ b/scala/src/main/scala/ch15_bsearch/BSearchRecursive.scala
@@ -1,22 +1,23 @@
 package ch15_bsearch
 
 object BSearchRecursive {
-    def search(nums: Array[Int], target: Int): Int = {
-        return searchInternal(nums, target, 0, nums.length - 1)
+
+  def search(items: Array[Int], target: Int): Int = {
+    _search(items, target, 0, items.length - 1)
+  }
+
+  private[this] def _search(items: Array[Int], target: Int, low: Int, high: Int): Int = {
+    if (low > high) {
+      return -1
     }
 
-    def searchInternal(nums:Array[Int], target: Int, low: Int, high: Int): Int = {
-        if(low <= high){
-            val mid = low + ((high - low) >> 2)
-            if(nums(mid) > target){
-                searchInternal(nums, target, low, mid - 1)
-            } else if (nums(mid) < target){
-                searchInternal(nums, target, mid + 1, high)
-            } else {
-                return mid
-            }
-        }else{
-            return -1
-        }
+    val mid = low + (high - low) / 2
+    if (items(mid) == target) {
+      mid
+    } else if (items(mid) > target) {
+      _search(items, target, low, mid - 1)
+    } else {
+      _search(items, target, mid + 1, high)
     }
+  }
 }
diff --git a/scala/src/test/scala/ch15_bsearch/BSearchRecursiveTest.scala b/scala/src/test/scala/ch15_bsearch/BSearchRecursiveTest.scala
new file mode 100644
index 0000000..0aa1702
--- /dev/null
+++ b/scala/src/test/scala/ch15_bsearch/BSearchRecursiveTest.scala
@@ -0,0 +1,25 @@
+package ch15_bsearch
+
+import ch12_sorts.QuickSort
+import org.scalatest.{FlatSpec, Matchers}
+
+import scala.util.Random
+
+class BSearchRecursiveTest extends FlatSpec with Matchers {
+
+  behavior of "BSearchRecursiveTest"
+
+  it should "search with exist value" in {
+    val length = 50000
+    val array = new Array[Int](length)
+    val rnd = new Random()
+    for (i <- Range(0, length)) {
+      array(i) = rnd.nextInt()
+    }
+
+    val target = array(2698)
+
+    BSearchRecursive.search(QuickSort.quickSort(array), target) should be > -1
+  }
+
+}
diff --git a/scala/src/test/scala/ch15_bsearch/BSearchTest.scala b/scala/src/test/scala/ch15_bsearch/BSearchTest.scala
new file mode 100644
index 0000000..437e96a
--- /dev/null
+++ b/scala/src/test/scala/ch15_bsearch/BSearchTest.scala
@@ -0,0 +1,37 @@
+package ch15_bsearch
+
+import ch12_sorts.QuickSort
+import org.scalatest.{FlatSpec, Matchers}
+
+import scala.util.Random
+
+class BSearchTest extends FlatSpec with Matchers {
+
+  behavior of "BSearchTest"
+
+  it should "search with exist value" in {
+    val length = 50000
+    val array = new Array[Int](length)
+    val rnd = new Random()
+    for (i <- Range(0, length)) {
+      array(i) = rnd.nextInt()
+    }
+
+    val target = array(2698)
+
+    BSearch.search(QuickSort.quickSort(array), target) should be > -1
+  }
+
+  it should "calculate sqrt value -1 " in {
+    val x = 4
+    val precision = 0.000001
+    BSearch.sqrt(x, precision) should equal(2.0)
+  }
+
+  it should "calculate sqrt value -2 " in {
+    val x = 0.04
+    val precision = 0.000001
+    BSearch.sqrt(x, precision) should equal(0.2 +- precision)
+  }
+
+}

From 93927772601b5681953e5e2d5e3ed70d7cc4d667 Mon Sep 17 00:00:00 2001
From: ivan <ivan.li@practiceinsight.io>
Date: Fri, 28 Dec 2018 14:29:42 +0800
Subject: [PATCH 16/24] transformed binary search

---
 .../src/main/scala/ch16_bsearch/BSearch.scala | 87 +++++++++++++++++++
 .../test/scala/ch16_bsearch/BSearchTest.scala | 31 +++++++
 2 files changed, 118 insertions(+)
 create mode 100644 scala/src/main/scala/ch16_bsearch/BSearch.scala
 create mode 100644 scala/src/test/scala/ch16_bsearch/BSearchTest.scala

diff --git a/scala/src/main/scala/ch16_bsearch/BSearch.scala b/scala/src/main/scala/ch16_bsearch/BSearch.scala
new file mode 100644
index 0000000..74e2fbe
--- /dev/null
+++ b/scala/src/main/scala/ch16_bsearch/BSearch.scala
@@ -0,0 +1,87 @@
+package ch16_bsearch
+
+object BSearch {
+
+  //find the first index of given value
+  //-1 if not found
+  def findFirstValue(items: Array[Int], target: Int): Int = {
+    require(items.length > 0, "given array is empty")
+    var low = 0
+    var high = items.length - 1
+    while (low <= high) {
+      val mid = low + (high - low) / 2
+      if (items(mid) > target) {
+        high = mid - 1
+      } else if (items(mid) < target) {
+        low = mid + 1
+      } else {
+        //find the value in the array
+        if (mid == 0 || items(mid - 1) != target) {
+          return mid
+        } else {
+          high = mid - 1
+        }
+      }
+    }
+    -1
+  }
+
+  def findLastValue(items: Array[Int], target: Int): Int = {
+    var low = 0
+    var high = items.length - 1
+    while (low <= high) {
+      val mid = low + (high - low) / 2
+      if (items(mid) > target) {
+        high = mid - 1
+      } else if (items(mid) < target) {
+        low = mid + 1
+      } else {
+        //find the target value
+        if (mid == items.length - 1 || items(mid + 1) != target) {
+          return mid
+        } else {
+          low = mid + 1
+        }
+      }
+    }
+    -1
+  }
+
+  def findFirstGreaterThan(items: Array[Int], target: Int): Int = {
+    var low = 0
+    var high = items.length
+    while (low <= high) {
+      val mid = low + (high - low) / 2
+      if (items(mid) >= target) {
+        //find the range
+        if (mid == 0 || items(mid - 1) < target) {
+          return mid
+        } else {
+          high = mid - 1
+        }
+      } else {
+        low = mid + 1
+      }
+    }
+    -1
+  }
+
+  def findLastSmallerThan(items: Array[Int], target: Int): Int = {
+    var low = 0
+    var high = items.length - 1
+    while (low <= high) {
+      var mid = low + (high - low) / 2
+      if (items(mid) <= target) {
+        //find the range
+        if (mid == items.length - 1 || items(mid + 1) > target) {
+          return mid
+        } else {
+          low = mid + 1
+        }
+      } else {
+        high = mid - 1
+      }
+    }
+    -1
+  }
+}
diff --git a/scala/src/test/scala/ch16_bsearch/BSearchTest.scala b/scala/src/test/scala/ch16_bsearch/BSearchTest.scala
new file mode 100644
index 0000000..89da6fa
--- /dev/null
+++ b/scala/src/test/scala/ch16_bsearch/BSearchTest.scala
@@ -0,0 +1,31 @@
+package ch16_bsearch
+
+import org.scalatest.{FlatSpec, Matchers}
+
+class BSearchTest extends FlatSpec with Matchers {
+
+  behavior of "BSearchTest"
+
+  it should "findFirstValue" in {
+    val items = Array(1, 3, 4, 5, 6, 8, 8, 8, 11, 18)
+    BSearch.findFirstValue(items, 8) should equal(5)
+  }
+
+  it should "findLastValue" in {
+    val items = Array(1, 3, 4, 5, 6, 8, 8, 8, 11, 18)
+    BSearch.findLastValue(items, 8) should equal(7)
+  }
+
+  it should "findFirstGreaterThan" in {
+    val items = Array(1, 3, 4, 5, 6, 8, 8, 8, 11, 18)
+    BSearch.findFirstGreaterThan(items, 2) should equal(1)
+    BSearch.findFirstGreaterThan(items, 8) should equal(5)
+  }
+
+  it should "findLastSmallerThan" in {
+    val items = Array(1, 3, 4, 5, 6, 8, 8, 8, 11, 18)
+    BSearch.findLastSmallerThan(items, 2) should equal(0)
+    BSearch.findLastSmallerThan(items, 8) should equal(7)
+  }
+
+}

From c05dfce66756d0d20258e57d6fa138b134291c18 Mon Sep 17 00:00:00 2001
From: Wenru Dong <dongwenru.aaron.shenyang@gmail.com>
Date: Sun, 30 Dec 2018 22:07:06 +0000
Subject: [PATCH 17/24] minimum distance dynamic programming in python

---
 python/41_dynamic_programming/min_dist.py | 39 +++++++++++++++++++++++
 1 file changed, 39 insertions(+)
 create mode 100644 python/41_dynamic_programming/min_dist.py

diff --git a/python/41_dynamic_programming/min_dist.py b/python/41_dynamic_programming/min_dist.py
new file mode 100644
index 0000000..2b8e60a
--- /dev/null
+++ b/python/41_dynamic_programming/min_dist.py
@@ -0,0 +1,39 @@
+"""
+    Author: Wenru Dong
+"""
+
+from typing import List
+from itertools import accumulate
+
+def min_dist(weights: List[List[int]]) -> int:
+    """Find the minimum weight path from the weights matrix."""
+    m, n = len(weights), len(weights[0])
+    table = [[0] * n for _ in range(m)]
+    # table[i][j] is the minimum distance (weight) when
+    # there are i vertical moves and j horizontal moves
+    # left.
+    table[0] = list(accumulate(reversed(weights[-1])))
+    for i, v in enumerate(accumulate(row[-1] for row in reversed(weights))):
+        table[i][0] = v
+    for i in range(1, m):
+        for j in range(1, n):
+            table[i][j] = weights[~i][~j] + min(table[i - 1][j], table[i][j - 1])
+    return table[-1][-1]
+
+
+def min_dist_recur(weights: List[List[int]]) -> int:
+    m, n = len(weights), len(weights[0])
+    table = [[0] * n for _ in range(m)]
+    def min_dist_to(i: int, j: int) -> int:
+        if i == j == 0: return weights[0][0]
+        if table[i][j]: return table[i][j]
+        min_left = float("inf") if j - 1 < 0 else min_dist_to(i, j - 1)
+        min_up = float("inf") if i - 1 < 0 else min_dist_to(i - 1, j)
+        return weights[i][j] + min(min_left, min_up)
+    return min_dist_to(m - 1, n - 1)
+
+
+if __name__ == "__main__":
+    weights = [[1, 3, 5, 9], [2, 1, 3, 4], [5, 2, 6, 7], [6, 8, 4, 3]]
+    print(min_dist(weights))
+    print(min_dist_recur(weights))

From 66f31db7999d09ccabb169ce3b24f4286a6ecbdd Mon Sep 17 00:00:00 2001
From: KP <109694228@qq.com>
Date: Tue, 1 Jan 2019 17:12:50 +0800
Subject: [PATCH 18/24] coins problem DP & BackTracking solution

---
 .../41_dynamic_programming/coins_problem.py   | 45 +++++++++++++++++++
 1 file changed, 45 insertions(+)
 create mode 100644 python/41_dynamic_programming/coins_problem.py

diff --git a/python/41_dynamic_programming/coins_problem.py b/python/41_dynamic_programming/coins_problem.py
new file mode 100644
index 0000000..3254347
--- /dev/null
+++ b/python/41_dynamic_programming/coins_problem.py
@@ -0,0 +1,45 @@
+#!/usr/bin/python
+# -*- coding: UTF-8 -*-
+
+from typing import List
+
+
+def coins_dp(values: List[int], target: int) -> int:
+    # memo[i]表示target为i的时候，所需的最少硬币数
+    memo = [0] * (target+1)
+    # 0元的时候为0个
+    memo[0] = 0
+
+    for i in range(1, target+1):
+        min_num = 999999
+        # 对于values中的所有n
+        # memo[i]为 min(memo[i-n1], memo[i-n2], ...) + 1
+        for n in values:
+            if i >= n:
+                min_num = min(min_num, 1 + memo[i-n])
+            else:   # values中的数值要从小到大排序
+                break
+        memo[i] = min_num
+
+    # print(memo)
+    return memo[-1]
+
+
+min_num = 999999
+def coins_backtracking(values: List[int], target: int, cur_value: int, coins_count: int):
+    if cur_value == target:
+        global min_num
+        min_num = min(coins_count, min_num)
+    else:
+        for n in values:
+            if cur_value + n <= target:
+                coins_backtracking(values, target, cur_value+n, coins_count+1)
+
+
+if __name__ == '__main__':
+    values = [1, 3, 5]
+    target = 23
+    print(coins_dp(values, target))
+    coins_backtracking(values, target, 0, 0)
+    print(min_num)
+

From 157edb426bcfe24966f7bb5ccee63bf5a72f3dbf Mon Sep 17 00:00:00 2001
From: Wenru Dong <dongwenru.aaron.shenyang@gmail.com>
Date: Tue, 1 Jan 2019 20:38:06 +0000
Subject: [PATCH 19/24] minimum edit distance in python

---
 .../42_dynamic_programming/min_edit_dist.py   | 31 +++++++++++++++++++
 1 file changed, 31 insertions(+)
 create mode 100644 python/42_dynamic_programming/min_edit_dist.py

diff --git a/python/42_dynamic_programming/min_edit_dist.py b/python/42_dynamic_programming/min_edit_dist.py
new file mode 100644
index 0000000..5bab109
--- /dev/null
+++ b/python/42_dynamic_programming/min_edit_dist.py
@@ -0,0 +1,31 @@
+"""
+    Author: Wenru Dong
+"""
+
+def levenshtein_dp(s: str, t: str) -> int:
+    m, n = len(s), len(t)
+    table = [[0] * (n + 1) for _ in range(m + 1)]
+    table[0] = [j for j in range(m + 1)]
+    for i in range(m + 1):
+        table[i][0] = i
+    for i in range(1, m + 1):
+        for j in range(1, n + 1):
+            table[i][j] = min(1 + table[i - 1][j], 1 + table[i][j - 1], int(s[i - 1] != t[j - 1]) + table[i - 1][j - 1])
+    return table[-1][-1]
+
+
+def common_substring_dp(s: str, t: str) -> int:
+    m, n = len(s), len(t)
+    table = [[0] * (n + 1) for _ in range(m + 1)]
+    for i in range(1, m + 1):
+        for j in range(1, n + 1):
+            table[i][j] = max(table[i - 1][j], table[i][j - 1], int(s[i - 1] == t[j - 1]) + table[i - 1][j - 1])
+    return table[-1][-1]
+
+
+if __name__ == "__main__":
+    s = "mitcmu"
+    t = "mtacnu"
+
+    print(levenshtein_dp(s, t))
+    print(common_substring_dp(s, t))
\ No newline at end of file

From 3c81d9de91a332fc958769fa5a11633001050388 Mon Sep 17 00:00:00 2001
From: KP <109694228@qq.com>
Date: Wed, 2 Jan 2019 16:41:11 +0800
Subject: [PATCH 20/24] Longest Increasing Subsequence DP solution

---
 .../longest_increasing_subsequence.py         | 58 +++++++++++++++++++
 1 file changed, 58 insertions(+)
 create mode 100644 python/42_dynamic_programming/longest_increasing_subsequence.py

diff --git a/python/42_dynamic_programming/longest_increasing_subsequence.py b/python/42_dynamic_programming/longest_increasing_subsequence.py
new file mode 100644
index 0000000..634dc9b
--- /dev/null
+++ b/python/42_dynamic_programming/longest_increasing_subsequence.py
@@ -0,0 +1,58 @@
+#!/usr/bin/python
+# -*- coding: UTF-8 -*-
+
+from typing import List
+
+
+def longest_increasing_subsequence(nums: List[int]) -> int:
+    """
+    最长子上升序列的一种DP解法，从回溯解法转化，思路类似于有限物品的背包问题
+    每一次决策都算出当前可能的lis的长度，重复子问题合并，合并策略是lis的末尾元素最小
+    时间复杂度：O(n^2)
+    空间复杂度：O(n^2)，可优化至O(n)
+
+    没leetcode上的参考答案高效，提供另一种思路作为参考
+    https://leetcode.com/problems/longest-increasing-subsequence/solution/
+    :param nums:
+    :return:
+    """
+    if not nums:
+        return 0
+
+    n = len(nums)
+    # memo[i][j] 表示第i次决策，长度为j的lis的 最小的 末尾元素数值
+    # 每次决策都根据上次决策的所有可能转化，空间上可以类似背包优化为O(n)
+    memo = [[-1] * (n+1) for _ in range(n)]
+
+    # 第一列全赋值为0，表示每次决策都不选任何数
+    for i in range(n):
+        memo[i][0] = 0
+    # 第一次决策选数组中的第一个数
+    memo[0][1] = nums[0]
+
+    for i in range(1, n):
+        for j in range(1, n+1):
+            # case 1: 长度为j的lis在上次决策后存在，nums[i]比长度为j-1的lis末尾元素大
+            if memo[i-1][j] != -1 and nums[i] > memo[i-1][j-1]:
+                memo[i][j] = min(nums[i], memo[i-1][j])
+
+            # case 2: 长度为j的lis在上次决策后存在，nums[i]比长度为j-1的lis末尾元素小/等
+            if memo[i-1][j] != -1 and nums[i] <= memo[i-1][j-1]:
+                memo[i][j] = memo[i-1][j]
+
+            if memo[i-1][j] == -1:
+                # case 3: 长度为j的lis不存在，nums[i]比长度为j-1的lis末尾元素大
+                if nums[i] > memo[i-1][j-1]:
+                    memo[i][j] = nums[i]
+                # case 4: 长度为j的lis不存在，nums[i]比长度为j-1的lis末尾元素小/等
+                break
+
+    for i in range(n, -1, -1):
+        if memo[-1][i] != -1:
+            return i
+
+
+if __name__ == '__main__':
+    # 要求输入的都是大于0的正整数(可优化至支持任意整数)
+    nums = [2, 9, 3, 6, 5, 1, 7]
+    print(longest_increasing_subsequence(nums))

From bd41e13780b1b3ef040216b7646404e0466e5958 Mon Sep 17 00:00:00 2001
From: Ivan Li <email2liyang@gmail.com>
Date: Thu, 3 Jan 2019 15:50:49 +0800
Subject: [PATCH 21/24] impl skip list

---
 .../main/scala/ch17_skip_list/SkipList.scala  | 99 +++++++++++++++++++
 .../scala/ch17_skip_list/SkipListTest.scala   | 44 +++++++++
 2 files changed, 143 insertions(+)
 create mode 100644 scala/src/main/scala/ch17_skip_list/SkipList.scala
 create mode 100644 scala/src/test/scala/ch17_skip_list/SkipListTest.scala

diff --git a/scala/src/main/scala/ch17_skip_list/SkipList.scala b/scala/src/main/scala/ch17_skip_list/SkipList.scala
new file mode 100644
index 0000000..2379115
--- /dev/null
+++ b/scala/src/main/scala/ch17_skip_list/SkipList.scala
@@ -0,0 +1,99 @@
+package ch17_skip_list
+
+import scala.util.Random
+
+class Node(var data: Int, var forwards: Array[Node], var maxLevel: Int)
+
+class SkipList(var head: Node, var skipListLevel: Int) {
+
+  def this() = this(new Node(-1, new Array[Node](16), 0), 1)
+
+  val MAX_LEVEL = 16
+  val random = new Random()
+
+  def find(value: Int): Option[Node] = {
+    var p = head
+    for (i <- skipListLevel - 1 to 0 by -1) {
+      while (p.forwards(i) != null && p.forwards(i).data < value) {
+        p = p.forwards(i)
+      }
+    }
+    if (p.forwards(0) != null && p.forwards(0).data == value) {
+      Some(p.forwards(0))
+    } else {
+      None
+    }
+  }
+
+  def insert(value: Int): Unit = {
+    //init the new node
+    val level = randomLevel()
+    val newNode = new Node(value, new Array[Node](level), level)
+
+    //use updtes array to record all nodes in all level before the inserted node
+    val updates: Array[Node] = new Array[Node](level)
+    var p = head
+    for (i <- level - 1 to 0 by -1) {
+      while (p.forwards(i) != null && p.forwards(i).data < value) {
+        p = p.forwards(i)
+      }
+      updates(i) = p
+    }
+
+    for (i <- Range(0, level)) {
+      newNode.forwards(i) = updates(i).forwards(i)
+      updates(i).forwards(i) = newNode
+    }
+
+    if (level > skipListLevel) {
+      skipListLevel = level
+    }
+  }
+
+  def delete(value: Int): Unit = {
+    var p = head
+    val updates: Array[Node] = new Array[Node](skipListLevel)
+
+    //try to locate the given node with the value
+    for (i <- skipListLevel - 1 to 0 by -1) {
+      while (p.forwards(i) != null && p.forwards(i).data < value) {
+        p = p.forwards(i)
+      }
+      updates(i) = p
+    }
+
+    if (p.forwards(0) != null && p.forwards(0).data == value) {
+      //find the value node, start to delete the node from the skip list
+      for (i <- skipListLevel - 1 to 0 by -1) {
+        if (updates(i).forwards(i) != null && updates(i).forwards(i).data == value) {
+          updates(i).forwards(i) = updates(i).forwards(i).forwards(i)
+        }
+      }
+    }
+
+  }
+
+  def randomLevel(): Int = {
+    var level = 1
+    for (i <- Range(1, MAX_LEVEL)) {
+      if (random.nextInt() % 2 == 1) {
+        level += 1
+      }
+    }
+
+    level
+  }
+
+  def mkString(): String = {
+    val builder = new StringBuilder
+    var p = head
+    while (p.forwards(0) != null) {
+      p = p.forwards(0)
+      builder.append(p.data)
+    }
+
+    builder.mkString
+  }
+}
+
+
diff --git a/scala/src/test/scala/ch17_skip_list/SkipListTest.scala b/scala/src/test/scala/ch17_skip_list/SkipListTest.scala
new file mode 100644
index 0000000..0b183e6
--- /dev/null
+++ b/scala/src/test/scala/ch17_skip_list/SkipListTest.scala
@@ -0,0 +1,44 @@
+package ch17_skip_list
+
+import org.scalatest.{FlatSpec, Matchers}
+
+import scala.util.Random
+
+class SkipListTest extends FlatSpec with Matchers {
+
+  behavior of "SkipListTest"
+
+  it should "insert skip list" in {
+    val list = new SkipList()
+    for (i <- Range(0, 10)) {
+      list.insert(i)
+    }
+
+    list.mkString() should equal("0123456789")
+  }
+
+  it should "delete skip list" in {
+    val list = new SkipList()
+    for (i <- Range(0, 10)) {
+      list.insert(i)
+    }
+
+    list.delete(5)
+    list.mkString() should equal("012346789")
+  }
+
+  it should "find value in skip list" in {
+    val list = new SkipList()
+    val length = 5000
+    val array = new Array[Int](length)
+    val rnd = new Random()
+    for (i <- Range(0, length)) {
+      array(i) = rnd.nextInt(length)
+      list.insert(array(i))
+    }
+
+    assert(list.find(array(rnd.nextInt(length - 1))).isDefined)
+    assert(list.find(array(rnd.nextInt(length - 1)) + length + 1).isEmpty)
+
+  }
+}

From d584fe66601bb3f21b6cac695e484018281727a6 Mon Sep 17 00:00:00 2001
From: Wenru Dong <dongwenru.aaron.shenyang@gmail.com>
Date: Thu, 3 Jan 2019 21:54:32 +0000
Subject: [PATCH 22/24] topological sorting in python

---
 .../topological_sorting.py                    | 63 +++++++++++++++++++
 1 file changed, 63 insertions(+)
 create mode 100644 python/43_topological_sorting/topological_sorting.py

diff --git a/python/43_topological_sorting/topological_sorting.py b/python/43_topological_sorting/topological_sorting.py
new file mode 100644
index 0000000..8971740
--- /dev/null
+++ b/python/43_topological_sorting/topological_sorting.py
@@ -0,0 +1,63 @@
+"""
+    Author: Wenru Dong
+"""
+
+from collections import deque
+from itertools import filterfalse
+
+class Graph:
+    def __init__(self, num_vertices: int):
+        self._num_vertices = num_vertices
+        self._adjacency = [[] for _ in range(num_vertices)]
+    
+    def add_edge(self, s: int, t: int) -> None:
+        self._adjacency[s].append(t)
+
+    def tsort_by_kahn(self) -> None:
+        in_degree = [0] * self._num_vertices
+        for v in range(self._num_vertices):
+            if len(self._adjacency[v]):
+                for neighbour in self._adjacency[v]:
+                    in_degree[neighbour] += 1
+        q = deque(filterfalse(lambda x: in_degree[x], range(self._num_vertices)))
+        while q:
+            v = q.popleft()
+            print(f"{v} -> ", end="")
+            for neighbour in self._adjacency[v]:
+                in_degree[neighbour] -= 1
+                if not in_degree[neighbour]:
+                    q.append(neighbour)
+        print("\b\b\b   ")
+
+    def tsort_by_dfs(self) -> None:
+        inverse_adjacency = [[] for _ in range(self._num_vertices)]
+        for v in range(self._num_vertices):
+            if len(self._adjacency[v]):
+                for neighbour in self._adjacency[v]:
+                    inverse_adjacency[neighbour].append(v)
+        visited = [False] * self._num_vertices
+
+        def dfs(vertex: int) -> None:
+            if len(inverse_adjacency[vertex]):
+                for v in inverse_adjacency[vertex]:
+                    if not visited[v]:
+                        visited[v] = True
+                        dfs(v)
+            print(f"{vertex} -> ", end="")
+        
+        for v in range(self._num_vertices):
+            if not visited[v]:
+                visited[v] = True
+                dfs(v)
+        
+        print("\b\b\b   ")
+
+
+if __name__ == "__main__":
+
+    dag = Graph(4)
+    dag.add_edge(1, 0)
+    dag.add_edge(2, 1)
+    dag.add_edge(1, 3)
+    dag.tsort_by_kahn()
+    dag.tsort_by_dfs()

From b639322dc565866c9769b2317cfc32a99e95b25e Mon Sep 17 00:00:00 2001
From: Ivan Li <email2liyang@gmail.com>
Date: Fri, 4 Jan 2019 19:01:17 +0800
Subject: [PATCH 23/24] impl LRU cache based on hashmap and linked list

---
 .../scala/ch20_linked_hash_map/LRUCache.scala | 149 ++++++++++++++++++
 .../ch20_linked_hash_map/LRUCacheTest.scala   |  22 +++
 2 files changed, 171 insertions(+)
 create mode 100644 scala/src/main/scala/ch20_linked_hash_map/LRUCache.scala
 create mode 100644 scala/src/test/scala/ch20_linked_hash_map/LRUCacheTest.scala

diff --git a/scala/src/main/scala/ch20_linked_hash_map/LRUCache.scala b/scala/src/main/scala/ch20_linked_hash_map/LRUCache.scala
new file mode 100644
index 0000000..ec64fdf
--- /dev/null
+++ b/scala/src/main/scala/ch20_linked_hash_map/LRUCache.scala
@@ -0,0 +1,149 @@
+package ch20_linked_hash_map
+
+class Node[K, V](var key: Option[K], var data: Option[V], var prev: Option[Node[K, V]], var next: Option[Node[K, V]],
+                 var hNext: Option[Node[K, V]]) {
+
+  def this(key: Option[K], data: Option[V]) = this(key, data, None, None, None)
+}
+
+/**
+  * LRU cache - https://leetcode.com/problems/lru-cache/ see unit test from LRUCacheTest
+  *
+  * @author email2liyang@gmail.com
+  */
+class LRUCache[K, V](var head: Node[K, V], var tail: Node[K, V], var table: Array[Node[K, V]],
+                     capacity: Int = 1000, var elementCount: Int = 0) {
+
+  head.next = Some(tail)
+  tail.prev = Some(head)
+
+  def this(capacity: Int) = this(new Node(None, None), new Node(None, None), new Array[Node[K, V]](capacity), capacity)
+
+  def get(key: K): Option[V] = {
+    val index = indexFor(key.hashCode())
+    var hNode = table(index)
+    if (hNode == null) {
+      None
+    } else {
+      while (!hNode.key.get.equals(key) && hNode.hNext.isDefined) {
+        hNode = hNode.hNext.get
+      }
+      if (hNode.key.get.equals(key)) {
+        //move this to the end of the linked list
+        moveHNodeToTail(hNode)
+        hNode.data
+      } else {
+        None
+      }
+    }
+  }
+
+
+  //put data into the linked hash map
+  //1: check if the data exist in the linked list
+  //2: if it's not exist , append it in the linked list
+  //3: if it's exist in the list, move it to the tail of the linked list
+  //4: return old value if it's exist
+  def put(key: K, value: V): Option[V] = {
+
+    if (elementCount == capacity) {
+      deleteLRUElement()
+    }
+
+    val node = new Node(Some(key), Some(value))
+    val index = indexFor(key.hashCode())
+    var hNode = table(index)
+    var result: Option[V] = None
+    if (hNode == null) {
+      //if it's not exist , append it in the linked list
+      node.prev = tail.prev
+      node.next = Some(tail)
+      tail.prev.get.next = Some(node)
+      tail.prev = Some(node)
+      table(index) = node
+      elementCount += 1
+    } else {
+      //we find a key conflict in the hash table
+      //start to loop the hNode to match the key
+      while (!hNode.key.get.equals(key) && hNode.hNext.isDefined) {
+        hNode = hNode.hNext.get
+      }
+
+      if (hNode.key.get.equals(key)) {
+        //find the old data from the hash table
+        result = hNode.data
+        hNode.data = Some(value)
+        //move the node to the tail of the linked list
+        moveHNodeToTail(hNode)
+        //hNext pointer stay untouched
+      } else {
+        //could not find the old data
+        //put the new node into the tail of the linked list
+        node.prev = tail.prev
+        node.next = Some(tail)
+        tail.prev.get.next = Some(node)
+        tail.prev = Some(node)
+
+        //put it the tail of the hash table's list
+        //iterator to the end of hNode
+        while (hNode.hNext.isDefined) {
+          hNode = hNode.hNext.get
+        }
+        hNode.hNext = Some(node)
+        elementCount += 1
+      }
+    }
+    result
+  }
+
+  private[this] def moveHNodeToTail(hNode: Node[K, V]) = {
+    hNode.prev.get.next = hNode.next
+    hNode.next.get.prev = hNode.prev
+    hNode.prev = tail.prev
+    hNode.next = Some(tail)
+    tail.prev.get.next = Some(hNode)
+    tail.prev = Some(hNode)
+  }
+
+  private[this] def deleteLRUElement(): Unit = {
+    //cache is full, start to delete element from the head
+    val node = head.next.get
+
+    //delete it from head
+    node.next.get.prev = Some(head)
+    head.next = node.next
+
+    //deal with hNext in the table
+    val index = indexFor(node.key.get.hashCode())
+    var hNode = table(index)
+    //deal with first element in the hash table
+    if (hNode.key.get.equals(node.key.get)) {
+      hNode.hNext match {
+        case Some(n) => table(index) = n
+        case None => table(index) = null
+      }
+    } else {
+      //deal with not first element in the hash table
+      var hNodePrev = hNode
+      hNode = hNode.next.get
+      while (!hNode.key.get.equals(node.key.get)) {
+        hNode = hNode.next.get
+        hNodePrev = hNodePrev.next.get
+      }
+      //now hNodePrev is the previous hNode in the hashtable
+      //remove the hNode
+      hNodePrev.next = hNode.next
+
+      hNode.next match {
+        case Some(n) => n.prev = Some(hNodePrev)
+        case None =>
+      }
+    }
+
+    elementCount -= 1
+  }
+
+  private[this] def indexFor(hash: Int): Int = {
+    hash % table.length
+  }
+}
diff --git a/scala/src/test/scala/ch20_linked_hash_map/LRUCacheTest.scala b/scala/src/test/scala/ch20_linked_hash_map/LRUCacheTest.scala
new file mode 100644
index 0000000..26591ad
--- /dev/null
+++ b/scala/src/test/scala/ch20_linked_hash_map/LRUCacheTest.scala
@@ -0,0 +1,22 @@
+package ch20_linked_hash_map
+
+import org.scalatest.{FlatSpec, Matchers}
+
+class LRUCacheTest extends FlatSpec with Matchers {
+
+  behavior of "LRUCacheTest"
+
+  it should "put data and get back" in {
+    val cache = new LRUCache[Int, Int](2)
+    cache.put(1, 1)
+    cache.put(2, 2)
+    cache.get(1) should equal(Some(1)) // returns 1
+    cache.put(3, 3) // evicts key 2
+    cache.get(2) should equal(None) //should not find
+    cache.put(4, 4) // evicts key 1
+    cache.get(1) should equal(None) //should not find
+    cache.get(3) should equal(Some(3)) // returns 3
+    cache.get(4) should equal(Some(4)) // returns 4
+  }
+
+}

From 5a6f54fdce7d0d037fccfe01c56d0703fff4605c Mon Sep 17 00:00:00 2001
From: Wenru Dong <dongwenru.aaron.shenyang@gmail.com>
Date: Sun, 6 Jan 2019 21:03:03 +0000
Subject: [PATCH 24/24] shortest path algorithm in python

---
 python/44_shortest_path/shortest_path.py | 64 ++++++++++++++++++++++++
 1 file changed, 64 insertions(+)
 create mode 100644 python/44_shortest_path/shortest_path.py

diff --git a/python/44_shortest_path/shortest_path.py b/python/44_shortest_path/shortest_path.py
new file mode 100644
index 0000000..57387bd
--- /dev/null
+++ b/python/44_shortest_path/shortest_path.py
@@ -0,0 +1,64 @@
+"""
+    Dijkstra algorithm
+
+    Author: Wenru Dong
+"""
+
+from dataclasses import dataclass
+from queue import PriorityQueue
+
+@dataclass
+class Edge:
+    start_id: int
+    end_id: int
+    weight: int
+
+@dataclass(order=True)
+class Vertex:
+    distance_to_start = float("inf")
+    vertex_id: int
+
+class Graph:
+    def __init__(self, num_vertices: int):
+        self._num_vertices = num_vertices
+        self._adjacency = [[] for _ in range(num_vertices)]
+    
+    def add_edge(self, from_vertex: int, to_vertex: int, weight: int) -> None:
+        self._adjacency[from_vertex].append(Edge(from_vertex, to_vertex, weight))
+
+    def dijkstra(self, from_vertex: int, to_vertex: int) -> None:
+        vertices = [Vertex(i) for i in range(self._num_vertices)]
+        vertices[from_vertex].distance_to_start = 0
+        visited = [False] * self._num_vertices
+        predecessor = [-1] * self._num_vertices
+        q = PriorityQueue()
+        q.put(vertices[from_vertex])
+        visited[from_vertex] = True
+        while not q.empty():
+            min_vertex = q.get()
+            if min_vertex.vertex_id == to_vertex:
+                break
+            for edge in self._adjacency[min_vertex.vertex_id]:
+                next_vertex = vertices[edge.end_id]
+                if min_vertex.distance_to_start + edge.weight < next_vertex.distance_to_start:
+                    next_vertex.distance_to_start = min_vertex.distance_to_start + edge.weight
+                    predecessor[next_vertex.vertex_id] = min_vertex.vertex_id
+                    if not visited[next_vertex.vertex_id]:
+                        q.put(next_vertex)
+                        visited[next_vertex.vertex_id] = True
+            
+        path = lambda x: path(predecessor[x]) + [str(x)] if from_vertex != x else [str(from_vertex)]
+        print("->".join(path(to_vertex)))
+
+
+if __name__ == "__main__":
+    graph = Graph(6)
+    graph.add_edge(0, 1, 10)
+    graph.add_edge(0, 4, 15)
+    graph.add_edge(1, 2, 15)
+    graph.add_edge(1, 3, 2)
+    graph.add_edge(2, 5, 5)
+    graph.add_edge(3, 2, 1)
+    graph.add_edge(3, 5, 12)
+    graph.add_edge(4, 5, 10)
+    graph.dijkstra(0, 5)