{"id":818,"date":"2025-08-02T17:33:20","date_gmt":"2025-08-02T12:03:20","guid":{"rendered":"https:\/\/codeanddebug.in\/blog\/?p=818"},"modified":"2025-08-02T17:33:22","modified_gmt":"2025-08-02T12:03:22","slug":"unique-paths","status":"publish","type":"post","link":"https:\/\/codeanddebug.in\/blog\/unique-paths\/","title":{"rendered":"Unique Paths | Leetcode 62 | All 4 DP Solutions"},"content":{"rendered":"\n

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

Given the two integers m<\/code> and n<\/code>, return the number of possible unique paths that the robot can take to reach the bottom-right corner<\/em>.<\/p>\n\n\n\n

Here’s the [Problem Link<\/span><\/mark><\/a><\/strong>] to begin with.<\/p>\n\n\n\n

The test cases are generated so that the answer will be less than or equal to 2 * 109<\/sup><\/code>.<\/p>\n\n\n\n

Example 1:<\/strong><\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n
Input:<\/strong> m = 3, n = 7
Output:<\/strong> 28<\/pre>\n\n\n\n
Example 2:<\/strong><\/p>\n\n\n\n
Input:<\/strong> m = 3, n = 2
Output:<\/strong> 3
Explanation:<\/strong> 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<\/pre>\n\n\n\n
Constraints:<\/strong><\/p>\n\n\n\n