[LeetCode]Unique Paths

Posted 2020-06-25 skycore

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

 1 class Solution {
 2 public:
 3     int uniquePaths(int m, int n) {
 4         // 递归超时
 5         // if (n == 1 || m == 1) {
 6         //     return 1;
 7         // } else {
 8         //     return uniquePaths(m - 1, n) + uniquePaths(m, n - 1);
 9         // }
10         
11         // DP
12         vector<vector<int>> matrix(m, vector<int>(n, 1));
13         for (int i = 1; i< m; ++i) {
14             for (int j = 1; j < n; ++j) {
15                 matrix[i][j] = matrix[i - 1][j] + matrix[i][j - 1];
16             }
17         }
18         
19         return matrix[m - 1][n - 1];
20     }
21 };