64.最小路径和.md

64. 最小路径和

url

题目

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。

输入：grid = [[1,3,1],[1,5,1],[4,2,1]]
输出：7
解释：因为路径 1→3→1→1→1 的总和最小。
输入：grid = [[1,2,3],[4,5,6]]
输出：12

方法

code

js

let minPathSum = grid => {
    if (grid === null || grid.length === 0 || grid[0].length === 0) return 0;
    let m = grid.length, n = grid[0].length;
    let dp = Array(m).fill(0).map(() => Array(n).fill(0));
    dp[0][0] = grid[0][0];
    // 第一列
    for (let i = 1; i < m; i++) {
        dp[i][0] = dp[i - 1][0] + grid[i][0];
    }
    for (let j = 1; j < n; j++) {
        dp[0][j] = dp[0][j - 1] + grid[0][j];
    }
    for (let i = 1; i < m; i++) {
        for (let j = 1; j < n; j++) {
            dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
        }
    }
    return dp[m - 1][n - 1];
}

go

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

java

class Solution {
    public int minPathSum(int[][] grid) {
        if (grid == null || grid.length == 0 || grid[0].length == 0)
            return 0;
        int m = grid.length;
        int n = grid[0].length;
        int[][] dp = new int[m][n];
        dp[0][0] = grid[0][0];
        // 第一列
        for (int i = 1; i < m; i++){
            dp[i][0] = dp[i - 1][0] + grid[i][0];
        }
        // 第一行
        for (int j = 1; j < n; j++){
            dp[0][j] = dp[0][j - 1] + grid[0][j];
        }
        for (int i = 0; i < dp.length; i++) {
            System.out.println(Arrays.toString(dp[i]));
        }
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++){
                dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
            }
        }
        for (int i = 0; i < dp.length; i++) {
            System.out.println(Arrays.toString(dp[i]));
        }
        return dp[m - 1][n - 1];
    }
}