From de13b81887ff04064c978d30c46707398e671e2a Mon Sep 17 00:00:00 2001
From: xuzhiwei <jsrdxzw@163.com>
Date: Sat, 8 Jun 2019 18:01:58 +0900
Subject: [PATCH] add bucket sort and binary search

---
 typescript/12_sorts/MergeSort.ts           | 58 ++++++++++++++++++++++
 typescript/12_sorts/quickSort.ts           | 18 +++----
 typescript/13_sorts/BucketSort.ts          | 52 +++++++++++++++++++
 typescript/13_sorts/CountingSort.ts        | 51 +++++++++++++++++++
 typescript/14_binarysearch/BinarySearch.ts | 28 +++++++++++
 5 files changed, 195 insertions(+), 12 deletions(-)
 create mode 100644 typescript/12_sorts/MergeSort.ts
 create mode 100644 typescript/13_sorts/BucketSort.ts
 create mode 100644 typescript/13_sorts/CountingSort.ts
 create mode 100644 typescript/14_binarysearch/BinarySearch.ts

diff --git a/typescript/12_sorts/MergeSort.ts b/typescript/12_sorts/MergeSort.ts
new file mode 100644
index 0000000..a466e19
--- /dev/null
+++ b/typescript/12_sorts/MergeSort.ts
@@ -0,0 +1,58 @@
+/**
+ * 归并排序
+ * 稳定排序，稳定的O(nlgn)时间复杂度
+ * O(n)的空间复杂度
+ * 在小规模数据排序中很常用
+ */
+class MergeSort {
+  public static mergeSort(array: number[]) {
+    if (!array || !array.length) return
+    const length = array.length
+    this.mergeSortInternally(array, 0, length - 1)
+  }
+
+  static mergeSortInternally(array: number[], p: number, r: number) {
+    if (p >= r) return
+    // 严格按照中间值作切分点
+    // js中除法需要做取整操作，不然结果有可能是小数
+    const q = Math.floor(p + (r - p) / 2)
+    this.mergeSortInternally(array, p, q)
+    this.mergeSortInternally(array, q + 1, r)
+    this.mergeArray(array, p, q, r)
+  }
+
+  private static mergeArray(a: number[], p: number, q: number, r: number) {
+    let i = p
+    let j = q + 1
+    let k = 0
+    // 定义一个临时数组来存放排序的值
+    const tmp: number[] = []
+    while (i <= q && j <= r) {
+      if (a[i] <= a[j]) {
+        tmp[k++] = a[i++]
+      } else {
+        tmp[k++] = a[j++]
+      }
+    }
+    // 判断哪个子数组中有剩余的数据
+    let start = i
+    let end = q
+    if (j <= r) {
+      start = j
+      end = r
+    }
+    // 将剩余的数据拷贝到临时数组tmp
+    while (start <= end) {
+      tmp[k++] = a[start++]
+    }
+
+    // 将tmp中的数组拷贝回a[p...r]
+    for (i = 0; i <= r - p; i++) {
+      a[p + i] = tmp[i]
+    }
+  }
+}
+
+const test4 = [1, 3, 2, 3, 10, 9, 7, 6, 0, 12]
+MergeSort.mergeSort(test4)
+console.log(test4)
diff --git a/typescript/12_sorts/quickSort.ts b/typescript/12_sorts/quickSort.ts
index ae22c62..c1963f8 100644
--- a/typescript/12_sorts/quickSort.ts
+++ b/typescript/12_sorts/quickSort.ts
@@ -3,24 +3,19 @@
  * 原地排序，空间复杂度O（1），比归并排序使用更广泛
  * 平均复杂度基本接近O(nlg(n))
  */
-interface ArraySort {
-  sort(array: number[]): void
-}
 
-class QuickSort implements ArraySort {
-  sort(array: number[]): void {
+export class QuickSort {
+  static sort(array: number[]): void {
     this.sortInternally(array, 0, array.length - 1)
   }
-
-  private sortInternally(array: number[], p: number, r: number) {
+  private static sortInternally(array: number[], p: number, r: number) {
     if (p >= r) return
     // 获取分界点
     const q: number = this.partition(array, p, r)
     this.sortInternally(array, p, q - 1)
     this.sortInternally(array, q + 1, r)
   }
-
-  private partition(array: number[], p: number, r: number): number {
+  private static partition(array: number[], p: number, r: number): number {
     /**
      * 参考值pivot，小于pivot的放在左边，大于pivot的在右边，最后再把分界点的值和它做交换
      * 这样返回的index一定是值在中间的下标
@@ -39,7 +34,7 @@ class QuickSort implements ArraySort {
     return index - 1
   }
 
-  private swap(array: number[], p: number, q: number) {
+  private static swap(array: number[], p: number, q: number) {
     const temp = array[p]
     array[p] = array[q]
     array[q] = temp
@@ -47,6 +42,5 @@ class QuickSort implements ArraySort {
 }
 
 const testSort = [1, 3, 2, 3, 10, 9, 7, 6, 0, -12]
-const quickSort: ArraySort = new QuickSort()
-quickSort.sort(testSort)
+QuickSort.sort(testSort)
 console.log(testSort)
diff --git a/typescript/13_sorts/BucketSort.ts b/typescript/13_sorts/BucketSort.ts
new file mode 100644
index 0000000..c7004a2
--- /dev/null
+++ b/typescript/13_sorts/BucketSort.ts
@@ -0,0 +1,52 @@
+/**
+ * 桶排序对数据的要求比较高
+ * 首先要知道数据的范围
+ * 然后根据范围将数据分到小范围的桶中
+ * 每个桶采用快速排序
+ * 当桶的数量接近数据量大小的时候，时间复杂度为O(n)
+ */
+import { QuickSort } from '../12_sorts/quickSort'
+
+class BucketSort {
+  static sort(array: number[], bucketSize: number = 5) {
+    const length = array.length
+    if (length === 0) return array
+    // 首先要确定数据的范围
+    let min = array[0]
+    let max = array[0]
+    for (let i = 0; i < length; i++) {
+      if (array[i] < min) {
+        min = array[i]
+      } else if (array[i] > max) {
+        max = array[i]
+      }
+    }
+
+    // 初始化桶,确定桶的数量
+    // 因为不能保证正好被整除，需要+1 存放剩余的元素
+    const bucketCount = Math.floor((max - min) / bucketSize) + 1
+    // 桶是个二维数组
+    const buckets = new Array(bucketCount)
+    for (let i = 0; i < bucketCount; i++) {
+      buckets[i] = []
+    }
+
+    // 利用映射函数将数据分配到各个桶中
+    // 这个时间复杂度为O(n)
+    for (let i = 0; i < length; i++) {
+      buckets[Math.floor((array[i]-min) / bucketSize)].push(array[i])
+    }
+    array.length = 0 // 返回数组
+    for (let i = 0; i < bucketCount; i++) {
+      // 每个桶里根据具体情况排序，使用插入排序或者快速排序等等
+      QuickSort.sort(buckets[i])
+      for (let j = 0; j < buckets[i].length; j++) {
+        array.push(buckets[i][j]);
+      }
+    }
+  }
+}
+
+const bucketTest = [1, 3, 2, 3, 10, 9, 7, 6, 0, -12]
+BucketSort.sort(bucketTest)
+console.log(bucketTest)
diff --git a/typescript/13_sorts/CountingSort.ts b/typescript/13_sorts/CountingSort.ts
new file mode 100644
index 0000000..ba8ea3e
--- /dev/null
+++ b/typescript/13_sorts/CountingSort.ts
@@ -0,0 +1,51 @@
+/**
+ * 计数排序
+ * 也是线性时间复杂度，和桶排序非常类似
+ * 适用于值范围较小的大数据排序
+ * 注意值范围需要不小于0，不然需要将数据预处理
+ * 并非原地排序
+ */
+class CountingSort {
+  static sort(array: number[]) {
+    const length = array.length
+
+    // 找到这个数组的最大值
+    let max = array[0]
+    array.forEach((item) => {
+      if (item > max) {
+        max = item
+      }
+    })
+
+    // 初始化值范围数组
+    const countArray = new Array(max + 1).fill(0, 0, max + 1)
+    // 先计算每个元素的出现个数
+    for (let i = 0; i < length; i++) {
+      countArray[array[i]] = countArray[array[i]] + 1
+    }
+    // 计算元素的累计出现个数
+    for (let i = 1; i <= max; i++) {
+      countArray[i] = countArray[i - 1] + countArray[i]
+    }
+
+    // 接下来开始计数排序了
+    // 空间还是要申请
+    const sortedArray = []
+    // 倒序遍历能够达到稳定排序的作用
+    for (let i = length - 1; i >= 0; i--) {
+      // -1是为了填补sortedArray在0的位置,因为countArray在0的位置中一定么有值
+      const index = countArray[array[i]] - 1
+      sortedArray[index] = array[i]
+      countArray[array[i]]--
+    }
+    for (let i = 0; i < length; i++) {
+      array[i] = sortedArray[i]
+    }
+  }
+}
+
+
+const testSort2 = [1, 3, 2, 3, 10, 9, 7, 6, 0]
+CountingSort.sort(testSort2)
+console.log(testSort2)
+
diff --git a/typescript/14_binarysearch/BinarySearch.ts b/typescript/14_binarysearch/BinarySearch.ts
new file mode 100644
index 0000000..cda4877
--- /dev/null
+++ b/typescript/14_binarysearch/BinarySearch.ts
@@ -0,0 +1,28 @@
+/**
+ * 二分查找适合于连续内存的数组查找
+ * 并且是已经排好序的数组
+ * 时间复杂度只有log(n)
+ */
+class BinarySearch {
+  static bSearch(array: number[], target: number) {
+    if (!array || array.length === 0) return -1
+    const length = array.length
+    let low = 0
+    let high = length - 1
+    while (low <= high) {
+      // 一定是整数,这边的移位运算优先级低于+，-运算符，需要加括号
+      const mid = low + ((high - low) >> 1)
+      if (array[mid] === target) {
+        return mid
+      } else if (array[mid] > target) {
+        high = mid - 1
+      } else {
+        low = mid + 1
+      }
+    }
+    return -1
+  }
+}
+
+const testBinarySearch = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+console.log(BinarySearch.bSearch(testBinarySearch, 10))