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?
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class Solution {
public:
int uniquePaths(int m, int n) {
int temp[m][n];
for (size_t i = 0; i != m; i++)
for(size_t j = 0; j != n; j++)
temp[i][j] = -1;
temp[0][0] = 1;
for (size_t i = 0; i != m; i++) {
for(size_t j = 0; j != n; j++) {
if(j != n-1) {
if(temp[i][j+1] != -1)
temp[i][j+1] += temp[i][j];
else
temp[i][j+1] = temp[i][j];
}
if(i != m-1) {
if(temp[i+1][j] != -1)
temp[i+1][j] += temp[i][j];
else
temp[i+1][j] = temp[i][j] ;
}
}
}
return temp[m-1][n-1];
}
};
Note: m and n will be at most 100.
