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 7 x 3 grid. How many possible unique paths are there?
Note: m and n will be at most 100.
Example 1:
Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
- Right -> Right -> Down
- Right -> Down -> Right
- Down -> Right -> Right
Example 2:
Input: m = 7, n = 3
Output: 28
public int uniquePaths(int m, int n) {
int[][] res = new int[m+1][n+1];
for(int i = 1; i <= m; i++){
res[i][1] = 1;
}
for(int i = 1; i <= n; i++){
res[1][i] = 1;
}
for(int i = 2; i <= m; i++){
for(int j = 2; j <= n; j++){
res[i][j] = res[i-1][j] + res[i][j-1];
}
}
return res[m][n];
}