backtrack applications

python/39_back_track/01_bag.py

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+#!/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))

python/39_back_track/eight_queens.py

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+#!/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)

python/39_back_track/permutations.py

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+#!/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)
+

python/39_back_track/regex.py

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+#!/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)