What is the optimal time complexity of solving Longest Increasing Path In Matrix?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Longest Increasing Path In Matrix?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Longest Increasing Path In Matrix?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Longest Increasing Path In Matrix?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Longest Increasing Path In Matrix

Learn how to solve the 'Longest Increasing Path In Matrix' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Medium

Given an m x n integers matrix, return the length of the longest increasing path in matrix.

From each cell, you can either move in four directions: left, right, up, or down. You may not move diagonally or move outside the boundary (i.e., wrap-around is not allowed).

Write a function longestIncreasingPath(matrix: List[List[int]]) -> int.

Constraints

•m == len(matrix)
•n == len(matrix[0])
•1 <= m, n <= 200
•0 <= matrix[i][j] <= 2^31 - 1

Examples

Example 1

Input

matrix = [[9,9,4],[6,6,8],[2,1,1]]

Output

Explanation

The longest increasing path is [1, 2, 6, 9].

Example 2

Input

matrix = [[3,4,5],[3,2,6],[2,2,1]]

Output

Explanation

The longest increasing path is [3, 4, 5, 6]. Moving diagonally is not allowed.

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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