Merge pull request #211 from KPatr1ck/dynamic_programming

dynamic programming applications in python

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))