leetcode 062 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?

Note: m and n will be at most 100.

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// class Solution {
// public:
// int uniquePaths(int m, int n) {
// vector<vector<int> > matrix(100, vector<int>(100, 1));

// //matrix[i][j] = matrix[i][j-1]+matrix[i-1][j]
// for(int i = 1; i < n; i++) {
// for(int j = 1; j < m; j++) {
// matrix[i][j] = matrix[i][j-1]+matrix[i-1][j];
// }
// }

// return matrix[n-1][m-1];
// }
// }

class Solution {
public:
int uniquePaths(int m, int n) {
if(m > n) return uniquePaths(n, m);
vector<int> cur(m,1);

//matrix[i][j] = matrix[i][j-1]+matrix[i-1][j]

for(int j=1; j < n; j++) {
for(int i=1; i < m; i++) {
cur[i] += cur[i-1];
}
}

return cur[m-1];
}
}