Merge pull request wangzheng0822#211 from KPatr1ck/dynamic_programming

dynamic programming applications in python

Author: wangzheng0822

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))

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))