LeetCode刷题实战64:最小路径和
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2020-10-14 04:10
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今天和大家聊的问题叫做 最小路径和,我们先来看题面:
https://leetcode-cn.com/problems/minimum-path-sum/
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.
题意
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。
解题
public int minPathSum(int[][] grid) {
int m = grid.length, n = grid[0].length;
int[][] dp = new int[m][n];
dp[0][0] = grid[0][0];
//第一列只能从上面走下来
for (int i = 1; i < m; i++) {
dp[i][0] = dp[i - 1][0] + grid[i][0];
}
//第一行只能从左边走过来
for (int i = 1; i < n; i++) {
dp[0][i] = dp[0][i - 1] + grid[0][i];
}
for (int i = 1; i < m; i++) {
for (int j = 1; j < n; j++) {
//递推公式,取从上面走下来和从左边走过来的最小值+当前坐标的值
dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
}
}
return dp[m - 1][n - 1];
}
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