Minimum Path Sum

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.

Solution & Complexity

Dynamic Programming. Space O(N).

Code

public class Solution {
    public int minPathSum(int[][] grid) {
        if (grid.length == 0) return Integer.MIN_VALUE;
        int M = grid.length, N = grid[0].length;
        int[] dp = new int[N];
        dp[0] = grid[0][0];
        for (int i = 1; i < N; ++i)
            dp[i] = grid[0][i] + dp[i-1];
        
        for (int i = 1; i < M; ++i)
        {
            dp[0] += grid[i][0];
            for (int j = 1; j < N; ++j)
                dp[j] = Math.min(dp[j-1], dp[j]) + grid[i][j];
        }
        
        return dp[N-1];  
    }
}