LeetCode #: 62
Difficulty: Medium
Topics: Array, Dynamic Programming.
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.
Time complexity: O(m * n). We loop through every cell in the m * n grid.
Space complexiy: O(n). We use a dp array to store n numbers.