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

简单的dynamic programming。paths[i][j]=paths[i-1][j]+paths[i][j-1]

 

class Solution {

public:

    int uniquePaths(int m, int n) {

        // Start typing your C/C++ solution below

        // DO NOT write int main() function

        vector<vector<int>> paths(m,vector<int>(n,0));

        for(int i=0;i<m;i++)

            paths.at(i).at(0)=1;

        for(int i=0;i<n;i++)

            paths.at(0).at(i)=1;

            

        for(int i=1;i<m;i++)

        {

            for(int j=1;j<n;j++)

            {

                paths.at(i).at(j)=paths.at(i).at(j-1)+paths.at(i-1).at(j);

            }

        }

        

        return paths.at(m-1).at(n-1);

    }

};