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];
}
}
原文：http://www.cnblogs.com/masterlibin/p/5775955.html