路径求和(dp经典, 暂时用二维数组存储中间状态, 可考虑滚动数组降维)

Author: cls1991

DynamicProgramming/122_BestTimeToBuyAndSellStockII.py

@@ -29,14 +29,8 @@ def maxProfit(self, prices):
     # 搜索所有的上升子序列, 求和
     def dynamic_max_profit(self, prices):
         ans = 0
-        start = 0
         for i in range(1, len(prices)):
-            delta = prices[i] - prices[i - 1]
-            if delta < 0:
-                ans += prices[i - 1] - prices[start]
-                start = i
-
-        if prices[-1] > prices[start]:
-            ans += prices[-1] - prices[start]
+            if prices[i] > prices[i - 1]:
+                ans += prices[i] - prices[i - 1]
 
         return ans

DynamicProgramming/62_UniquePaths.py

@@ -0,0 +1,46 @@
+# coding: utf8
+
+
+"""
+    题目链接: https://leetcode.com/problems/unique-paths/description.
+    题目描述:
+
+    A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).
+
+    The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right
+    corner of the grid (marked 'Finish' in the diagram below).
+
+    How many possible unique paths are there?
+
+
+    Above is a 3 x 7 grid. How many possible unique paths are there?
+
+    Note: m and n will be at most 100.
+
+"""
+
+
+class Solution(object):
+    def uniquePaths(self, m, n):
+        """
+        :type m: int
+        :type n: int
+        :rtype: int
+        """
+        if m <= 1 or n <= 1:
+            return 1
+
+        return self.dynamic_unique_paths(m, n)
+
+    # 常规dp
+    def dynamic_unique_paths(self, m, n):
+        dp = [[0 for _ in range(n)] for _ in range(m)]
+        for i in range(m):
+            dp[i][0] = 1
+        for j in range(n):
+            dp[0][j] = 1
+        for i in range(1, m):
+            for j in range(1, n):
+                dp[i][j] = dp[i][j - 1] + dp[i - 1][j]
+
+        return dp[m - 1][n - 1]

DynamicProgramming/64_MinimumPathSum.py

@@ -0,0 +1,49 @@
+# coding: utf8
+
+
+"""
+    题目链接: https://leetcode.com/problems/minimum-path-sum/description.
+    题目描述:
+
+    Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the
+    sum of all numbers along its path.
+
+    Note: You can only move either down or right at any point in time.
+
+    Example 1:
+    [[1,3,1],
+     [1,5,1],
+     [4,2,1]]
+    Given the above grid map, return 7. Because the path 1→3→1→1→1 minimizes the sum.
+
+"""
+
+
+class Solution(object):
+    def minPathSum(self, grid):
+        """
+        :type grid: List[List[int]]
+        :rtype: int
+        """
+        if not any(grid):
+            return 0
+
+        return self.dynamic_min_path_sum(grid)
+
+    # 动态规划:
+    # 递推公式: dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + grid[i][j], i>=1, j>=1
+    def dynamic_min_path_sum(self, grid):
+        rows = len(grid)
+        columns = len(grid[0])
+        dp = [[0 for _ in range(columns)] for _ in range(rows)]
+        dp[0][0] = grid[0][0]
+        for i in range(1, rows):
+            dp[i][0] = dp[i - 1][0] + grid[i][0]
+        for j in range(1, columns):
+            dp[0][j] = dp[0][j - 1] + grid[0][j]
+
+        for i in range(1, rows):
+            for j in range(1, columns):
+                dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j]
+
+        return dp[rows - 1][columns - 1]