【LeetCode】 64. Minimum Path Sum 最小路径和(Medium)(JAVA)
题目地址: https://leetcode.com/problems/minimum-path-sum/
题目描述:
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.
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.
题目大意
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。
解题方法
和上一题一样的解法:【LeetCode】 63. Unique Paths II 不同路径 II(Medium)(JAVA)
1、采用动态规划,从后往前遍历
2、比较前和左的最小值
class Solution {
public int minPathSum(int[][] grid) {
if (grid.length == 0 || grid[0].length == 0) return 0;
int[][] dp = new int[grid.length][grid[0].length];
for (int i = grid.length - 1; i >= 0; i--) {
for (int j = grid[0].length - 1; j>= 0; j--) {
if (i == grid.length - 1 && j == grid[0].length - 1) {
dp[i][j] = grid[i][j];
} else if (i == grid.length - 1) {
dp[i][j] = grid[i][j] + dp[i][j + 1];
} else if (j == grid[0].length - 1) {
dp[i][j] = grid[i][j] + dp[i + 1][j];
} else {
dp[i][j] = grid[i][j] + (dp[i + 1][j] > dp[i][j + 1] ? dp[i][j + 1] : dp[i + 1][j]);
}
}
}
return dp[0][0];
}
}
执行用时 : 4 ms, 在所有 Java 提交中击败了 33.37% 的用户
内存消耗 : 42.5 MB, 在所有 Java 提交中击败了 20.81% 的用户