[LeetCode]Unique Paths

题目描述:

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

解题思路:

组合数学中的例子，向下m - 1步，向右n - 1步，也就是m + n - 2个数中选择m - 1个数的组合数。

class Solution {
public:
    int uniquePaths(int m, int n) {
        // 递归超时
        // if (n == 1 || m == 1) {
        //     return 1;
        // } else {
        //     return uniquePaths(m - 1, n) + uniquePaths(m, n - 1);
        // }
        
        // DP
        vector<vector<int>> matrix(m, vector<int>(n, 1));
        for (int i = 1; i< m; ++i) {
            for (int j = 1; j < n; ++j) {
                matrix[i][j] = matrix[i - 1][j] + matrix[i][j - 1];
            }
        }
        
        return matrix[m - 1][n - 1];
    }
};