64. 最小路径和(Medium)

题目描述

给定一个包含非负整数的 m x n 网格 grid ，请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。

**说明：**每次只能向下或者向右移动一步。

样例

Input：grid = [[1,3,1],[1,5,1],[4,2,1]]
Output：7
解释：因为路径 1→3→1→1→1 的总和最小。

Input：grid = [[1,2,3],[4,5,6]]
Output：12

题解

动态规划

Python示例

class Solution:
    def minPathSum(self, grid: List[List[int]]) -> int:
        if not grid: return 0
        n, m = len(grid), len(grid[0])
        dp = [[0] * m for _ in range(n)]
        dp[0][0] = grid[0][0]
        for i in range(1, m):
            dp[0][i] = dp[0][i - 1] + grid[0][i]
        for i in range(1, n):
            dp[i][0] = dp[i - 1][0] + grid[i][0]

        for i in range(1, n):
            for j in range(1, m):
                dp[i][j] = grid[i][j] + min(dp[i - 1][j], dp[i][j - 1])
        return dp[n - 1][m - 1]

Go 示例

func min (a, b int) int {
    if a > b {
        return b
    }
    return a
}

func minPathSum(grid [][]int) int {
    if len(grid) == 0 || len(grid[0]) == 0 {
        return 0
    }
    n, m := len(grid), len(grid[0])
    dp := make([][]int, n)
    for i := 0; i < n; i++ {
        dp[i] = make([]int, m)
    }
    dp[0][0] = grid[0][0]
    for i := 1; i < m; i ++ {
        dp[0][i] = dp[0][i - 1] + grid[0][i]
    }
    for i := 1; i < n; i ++ {
        dp[i][0] = dp[i - 1][0] + grid[i][0]
    }
    
    for i := 1; i < n; i++ {
        for j:= 1; j < m; j++ {
            dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j]
        }
    }
    fmt.Println(dp)
    return dp[n - 1][m - 1]
}