[LeetCode]Minimum Path Sum

Wally@Web3.0

于 2015-04-06 12:44:11 发布

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分类专栏： LeetCode 文章标签： leetcode

本文链接：https://blog.youkuaiyun.com/YouMengJiuZhuiBa/article/details/44901135

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本文探讨了在一个填充了非负数的mxn网格中寻找从左上角到右下角的最小路径和的问题。提供了两种解决方案，一种是使用动态规划的方法，另一种则是优化空间复杂度的策略。

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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.
思路1：这是一个简单的动态规划问题，dp[i][j] = grid[i-1][j-1] + min(dp[i-1][j],dp[i][j-1])
代码1：

public class Solution {
    public int minPathSum(int[][] grid) {
        
        int m = grid.length, n = grid[0].length;
        int[][] sums = new int[m][n];
        
        for(int i = 0; i < m; i ++){
            for(int j = 0; j < n; ++j){
                if(i == 0 && j == 0){
                    sums[i][j] = grid[i][j];
                }else if(i == 0 && j != 0){
                    sums[i][j] = grid[i][j] + sums[i][j-1];
                }else if(i !=0 && j == 0){
                    sums[i][j] = grid[i][j] + sums[i-1][j];
                }else {
                    sums[i][j] = Math.min(grid[i][j] + sums[i][j-1],grid[i][j] + sums[i-1][j]);
                }
            }
        }
        return sums[m-1][n-1];
    }
}

思路2：看到网上说可以把空间复杂度优化到O(N)