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Distinct Paths

Medium Acceptance 50.00% Points 30.00

There is a scholar on an m x n grid. The scholar is initially located at the top-left corner (i.e., grid[0][0]). The scholar tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The scholar can only move either down or right at any point in time.

Given the two integers m and n, return the number of possible distinct paths that the scholar can take to reach the bottom-right corner.

Examples
Example 1

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 -> Down -> Down 2. Down -> Down -> Right 3. Down -> Right -> Down

Hints
Hint 1
Expected Time Complexity: O(n^2)
Hint 2
Expected Auxiliary Space: O(n^2)
Constraints
  • 1 <= m, n <= 100
Companies
Amazon Microsoft Google
Topics
Array Recursion Dynamic Programming + 1 more
Solution.cs C#JavaPythonC++Javascript

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