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.
Example:
Input:
[
[1,3,1],
[1,5,1],
[4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.
code
import org.junit.Test;
public class MinimumPath {
//矩阵的最小路径和:从矩阵的左上角到右下角的最小路径和，每次只能向左和向下移动
public int minPathSum(int[][] grid) {
if (grid.length == 0 || grid[0].length == 0) return 0;
int m = grid.length, n = grid[0].length;
int[] dp = new int[n];
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (j == 0) dp[0] = dp[0] + grid[i][0]; // 只能从上侧走到该位置
else if (i == 0) dp[j] = dp[j - 1] + grid[0][j]; // 只能从右侧走到该位置
else dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];
}
}
return dp[n - 1];
}
@Test
public void test(){
int[][] grid={{1,3,1},{1,5,1},{4,2,1}};
System.out.println(minPathSum(grid));
}
}
