leetcode 62、Unique Paths

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

Note: m and n will be at most 100.

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right

Example 2:

Input: m = 7, n = 3
Output: 28

题目大意：

从m乘n矩阵左上角走到右下角，每一步只能向右或向下，求共有多少条不同路径。

递归解决：

 class Solution {
 public:
     vector<vector<int>> v;

     int solve(int m, int n) {//从(m, n)到(1, 1)有多少条路径
         if (m ==  || n == )
             return ;
         if (v[m][n] >= )
             return v[m][n];
         v[m][n] = solve(m - , n) + solve(m, n - );
         return v[m][n];
     }

     int uniquePaths(int m, int n) {
         if (m ==  || n == )
             return ;
         if (m ==  || n == )
             return ;
         v.resize(m + , vector<int>(n + , -));
         return solve(m - , n) + solve(m, n - );
     }
 };

迭代：

 class Solution {
 public:

     int uniquePaths(int m, int n) {
         if (m ==  || n == )
             return ;
         vector<vector<int>> v(m, vector<int>(n));
         int i, j;
         for (i = ; i < m; i++) {
             for (j = ; j < n; j++) {
                 if (i ==  || j == )
                     v[i][j] = ;
                 else
                     v[i][j] = v[i - ][j] + v[i][j - ];
             }
         }
         return v[m - ][n - ];
     }
 };