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 == 1 || n == 1)
            return 1;
        if (v[m][n] >= 0)
            return v[m][n];
        v[m][n] = solve(m - 1, n) + solve(m, n - 1);
        return v[m][n];
    }
    
    int uniquePaths(int m, int n) {
        if (m == 0 || n == 0)
            return 0;
        if (m == 1 || n == 1)
            return 1;
        v.resize(m + 1, vector<int>(n + 1, -1));
        return solve(m - 1, n) + solve(m, n - 1);
    }
};

 迭代：

class Solution {
public:
    
    int uniquePaths(int m, int n) {
        if (m == 0 || n == 0)
            return 0;
        vector<vector<int>> v(m, vector<int>(n));
        int i, j;
        for (i = 0; i < m; i++) {
            for (j = 0; j < n; j++) {
                if (i == 0 || j == 0)
                    v[i][j] = 1;
                else
                    v[i][j] = v[i - 1][j] + v[i][j - 1];
            }
        }
        return v[m - 1][n - 1];
    }
};