/**
* 给定一个由非负整数填充的m x n的二维数组，
* 现在要从二维数组的左上角走到右下角，
* 请找出路径上的所有数字之和最小的路径。
* 注意：你每次只能向下或向右移动。
*
* 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.
*/
/**
* 给定一个由非负整数填充的m x n的二维数组，
* 现在要从二维数组的左上角走到右下角，
* 请找出路径上的所有数字之和最小的路径。
* 注意：你每次只能向下或向右移动。
*
* 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 Main52 {
public static void main(String[] args) {
int[][] grid = new int[3][7];
System.out.println(Main52.minPathSum(grid));
}
public static int minPathSum(int[][] grid) {
int m = grid.length;
int n = grid[0].length;
int[][] dp = new int[m][n];
dp[0][0] = grid[0][0];
//第一行
for (int i = 1; i < n; i++) {
dp[0][i] = dp[0][i-1] + grid[0][i];
}
//第一列
for (int i = 1; i < m; i++) {
dp[i][0] = dp[i-1][0] + grid[i][0];
}
for (int i = 1; i < m; i++) {
for (int j = 1; j < n; j++) {
dp[i][j] = Math.min(dp[i-1][j], dp[i][j-1]) + grid[i][j];
}
}
return dp[m-1][n-1];
}
}