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package dynamicprogramming;
/**
* @ProjectName: leetcode
* @Package: dynamicprogramming
* @ClassName: Dp64
* @Author: markey
* @Description:
* 给定一个包含非负整数的 m x n 网格，请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。
*
* 说明：每次只能向下或者向右移动一步。
*
* 示例:
*
* 输入:
* [
* [1,3,1],
* [1,5,1],
* [4,2,1]
* ]
* 输出: 7
* 解释: 因为路径 1→3→1→1→1 的总和最小。
*
* 来源：力扣（LeetCode）
* 链接：https://leetcode-cn.com/problems/minimum-path-sum
* 著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。
* @Date: 2020/1/5 10:41
* @Version: 1.0
*/
public class Dp64 {
/**
* Runtime: 2 ms, faster than 90.95% of Java online submissions for Minimum Path Sum.
* Memory Usage: 42.4 MB, less than 79.73% of Java online submissions for Minimum Path Sum.
* @param grid
* @return
*/
public int minPathSum(int[][] grid) {
int m = grid.length;
int n = grid[0].length;
int[][] res = new int[m][n];
res[0][0] = grid[0][0];
for (int i = 1; i < n; i++) {
res[0][i] = res[0][i - 1] + grid[0][i];
}
for (int i = 1; i < m; i++) {
res[i][0] = res[i - 1][0] + grid[i][0];
}
for (int i = 1; i < m; i++) {
for (int j = 1; j < n; j++) {
res[i][j] = Math.min(res[i - 1][j], res[i][j - 1]) + grid[i][j];
}
}
return res[m-1][n-1];
}
}