leetcode62—Unique Paths

Posted 2021-01-20 tingweichen

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

想法：采用动态规划，确立状态转移表达式f(m,n)=f(m-1,n)+f(n-1,m)表示可能性。

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