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?
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: 1. Right -> Right -> Down 2. Right -> Down -> Right 3. Down -> Right -> Right
Example 2:
Input: m = 7, n = 3 Output: 28
Constraints:
1 <= m, n <= 100- It’s guaranteed that the answer will be less than or equal to
2 * 10 ^ 9.
Solution
class Solution {
public int uniquePaths(int m, int n) {
int[] temp = new int[m];
for (int i = 0; i < m; i++)
temp[i] = 1;
for (int j = 0; j < n-1; j++){
for (int c = 1; c < m; c++){
temp = temp[c-1] + temp;
}
}
return temp[m-1];
}
}