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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.
 */
public class Solution {
    public int minPathSum(int[][] grid) {
        int[][] path = new int[grid.length][grid[0].length];
        path[0][0] = grid[0][0];
        // Initialize the border: Up and left
        for(int i = 1; i < grid.length; i++){
           path[i][0] = path[i - 1][0] + grid[i][0]; 
        }
        for(int i = 1; i < grid[0].length; i++){
            path[0][i] = path[0][i - 1] + grid[0][i];
        }
        // walk the grid
        for(int i = 1; i < grid.length; i++){
            for(int j = 1; j < grid[0].length; j++){
                path[i][j] = Math.min(path[i - 1][j], path[i][j - 1]) + grid[i][j];
            }
        }
        return path[grid.length - 1][grid[0].length - 1];
    }
}