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.
DP。
class Solution {
public:
int uniquePaths(int m, int n) {
// Start typing your C/C++ solution below
// DO NOT write int main() function
if (m == 0 || n == 0)
return 0;
vector< vector<int> > path(m, vector<int>(n));
for (int i = 0; i < m; ++i)
path[i][0] = 1;
for (int j = 0; j < n; ++j)
path[0][j] = 1;
for (int i = 1; i < m; ++i)
{
for (int j = 1; j < n; ++j)
{
path[i][j] = path[i-1][j] + path[i][j-1];
}
}
return path[m-1][n-1];
}
};