Minimum Path Sum，最短路径问题，动态规划

问题描述：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.

问题分析：参考路径问题，其实就是加权的路径问题，求最小的权值和。动态规划问题，核心递推公式，d[i][j] = min(d[i-1][j],d[i][j-1])+a[i][j].

public class MinPathSum
{
	public int minPathSum(int[][] grid)
	{
		for(int i = 1; i < grid.length; i ++)//初始化第一行第一列
		{
			grid[i][0] += grid[i-1][0];
		}
		for(int i = 1; i < grid[0].length; i ++)
		{
			grid[0][i] += grid[0][i-1];
		}
        for(int i = 1; i < grid.length; i ++)
        {
        	for(int j = 1; j < grid[0].length; j ++)
        	{
        		grid[i][j] = Math.min(grid[i-1][j], grid[i][j-1])+grid[i][j];//核心递推公式
        	}
        }
        return grid[grid.length-1][grid[0].length];
    }
}