Leetcode Minimum Path Sum

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.

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解题思路：

Dynamic Programming

dp[i][j] = grid[i][j] + Math.min(dp[i-1][j], dp[i][j-1])

但不要忘记初始化第一行与第一列。算法复杂度：O(mn)

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Java code:

public class Solution {
    public int minPathSum(int[][] grid) {
        if(grid == null || grid.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];
        //initialize top row
        for(int i = 1; i < n; i++) {
            dp[0][i] = dp[0][i-1] + grid[0][i];
        }
        //initialize left column
        for(int i = 1; i < m; i++) {
            dp[i][0] = dp[i-1][0] + grid[i][0];
        }
        for(int i = 1; i < m; i++) {
            for(int j = 1; j < n; j++) {
                dp[i][j] = grid[i][j] + Math.min(dp[i-1][j], dp[i][j-1]);
            }
        }
        return dp[m-1][n-1];
    }
}

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Reference:

1. http://www.programcreek.com/2014/05/leetcode-minimum-path-sum-java/