62.unique-paths 不同路径

问题描述

62.不同路径

解题思路

还是找递推关系：
\(dp_{mn} = dp_{(m-1)n} + dp_{m(n-1)}\)

代码

#include <vector>
using std::vector;
class Solution {
  public:
    int uniquePaths(int m, int n) {
        vector<vector<int>> dp(m + 1, vector<int>(n + 1, 0));
        dp[1][1] = 1;
        // dp[1][2] = 1;
        // dp[2][1] = 1;
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                if (i == 1 && j == 1)
                    dp[i][j] = 1;
                else
                    dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
            }
        }
        return dp[m][n];
    }
};