Unique Paths

A robot is located at the top-left corner of a m x n grid. The robot can only move either down or right at any point in time. Find the number of unique paths to the bottom-right corner.

10 min read

Solve on LeetCode

Problem Understanding

We need to count how many ways to reach (m-1, n-1) from (0, 0) moving only Right or Down.

Example: m = 3, n = 2

Right -> Down -> Down
Down -> Down -> Right
Down -> Right -> Down
Output: 3

Algorithm Strategy

This is a classic DP problem on a grid.

Key Insight:
To reach cell (i, j), you must have come from either:

Top: (i-1, j)
Left: (i, j-1)

Recurrence: dp[i][j] = dp[i-1][j] + dp[i][j-1]
Base Cases: dp[i][0] = 1 and dp[0][j] = 1 (only 1 way to reach cells in first row/col - go straight).

Interactive Visualization

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Initializing...

Custom Input

Watch how the number of paths sums up. Each cell is the sum of the cell directly above and to the left.

Click 'Randomize' to test different grid sizes.

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