[LintCode/LeetCode] Minimum Path Sum

CntChen 发布于2019-08-14 15:28 / 2337人阅读

摘要：遍历整个矩阵，对于，取上方和左边较小值，与相加可得该点最小值。

Problem

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.

You can only move either down or right at any point in time.

Note

遍历整个矩阵，对于dp[i][j]，取上方dp[i-1][j]和左边dp[i][j-1]较小值，与grid[i][j]相加可得该点最小值。

Solution

public class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length, n = grid[0].length;
        int[][] dp = new int[m][n];
        dp[0][0] = grid[0][0];
        for (int i = 1; i < m; i++) {
            dp[i][0] = dp[i-1][0] + grid[i][0];
        }
        for (int i = 1; i < n; i++) {
            dp[0][i] = dp[0][i-1] + grid[0][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];
            }
        }
        return dp[m-1][n-1];
    }
}

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