Description
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?
The original problem is here.
The original code is here.
My Solution
I solve this problem in C++, as below:
/*
*Unique Paths
*Author: shuaijiang
*Email: zhaoshuaijiang8@gmail.com
*/
#include<iostream>
#include<stdlib.h>
using namespace std;
class Solution {
public:
int uniquePaths(int m, int n) {
int matrix[100][100];
matrix[0][0] = 1;
for(int i=1;i<n;i++)
matrix[0][i]=1;
for(int j=1;j<m;j++)
matrix[j][0] = 1;
for(int i=1;i<m;i++){
for(int j=1;j<n;j++){
matrix[i][j] = matrix[i-1][j] + matrix[i][j-1];
}
}
return matrix[m-1][n-1];
}
};
Note
Dynamic programming is used. The number of paths to get (i,j) in grid is equal to the sum of the result of (i,j-1) and (i-1,j).