/**
 * 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 MinimumPathSum {
	public int minPathSum(int[][] grid) {
		int[][] path = new int[grid.length][grid[0].length];
		path[0][0] = grid[0][0];
		for (int i = 1; i < grid.length; i++) {
			path[i][0] = path[i - 1][0] + grid[i][0];
		}
		for (int j = 1; j < grid[0].length; j++) {
			path[0][j] = path[0][j - 1] + grid[0][j];
		}
		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];
	}
}