#111 Medium Time O(m·n) Space O(m·n) Animated

Unique Paths

Count unique paths from top-left to bottom-right in m×n grid.

LeetCode ↗

Tutor Mode Build the mental model before you memorize the code.

1 Predict
2 Trace
3 Explain
4 Implement

Pattern Two-dimensional dynamic programming

A table exposes how two changing prefixes or positions depend on smaller cases.

Approach: Dynamic Programming (2D)

Click play to start

Step 0 / 0

Press play to start the visualization.

1×

Core Insight

A table exposes how two changing prefixes or positions depend on smaller cases.

Common Pitfall

Initialize the first row and column before using neighboring cells.

Description

Count unique paths from top-left to bottom-right in m×n grid.

Constraints

Time Complexity: O(m·n)
Space Complexity: O(m·n)

Solution — Dynamic Programming (2D)

TimeO(m·n) SpaceO(m·n)

Implementation Plan

Translate the invariant into these small, testable moves.

Define the row and column meaning.
Initialize base cases.
Fill cells in dependency order.
Read the answer from the target cell.

def uniquePaths(m, n):
    row = [1] * n
    for i in range(m - 1):
        newRow = [1] * n
        for j in range(n - 2, -1, -1):
            newRow[j] = newRow[j + 1] + row[j]
        row = newRow
    return row[0]

Longest Common Subsequence

Unique Paths

Steps

Description

Constraints

Tags

Solution — Dynamic Programming (2D)