Minimum Path Sum

最新推荐文章于 2025-12-06 07:43:37 发布

转载最新推荐文章于 2025-12-06 07:43:37 发布 · 295 阅读

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本文介绍了一个算法问题：在一个非负数构成的网格中寻找从左上角到右下角的路径，使得路径上的数字之和最小。仅能向下或向右移动。使用动态规划求解，首先初始化边界条件，然后迭代填充中间状态。

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.

class Solution {

public:
int minPathSum(vector<vector<int> > &grid) {
int rows = grid.size();
int cols = grid[0].size();
vector<int> temp(cols, 0);
vector<vector<int> > dp(rows, temp);

dp[0][0] = grid[0][0];
for (int i=1;i<rows;i++)
dp[i][0] = grid[i][0] + dp[i-1][0];
for (int j=1;j<cols;j++)
dp[0][j] = grid[0][j] + dp[0][j-1];
for (int i=1;i<rows;i++){
for (int j=1;j<cols;j++){
dp[i][j] = min(dp[i-1][j] + grid[i][j],
dp[i][j-1] + grid[i][j]);
}
}

return dp[rows-1][cols-1];
}
};