How do you solve Length of the Longest Increasing Path on LeetCode?

Length of the Longest Increasing Path (LeetCode #3288) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Filtering coordinates based on the target is crucial to reduce unnecessary checks.

What is the time complexity of Length of the Longest Increasing Path?

The optimal solution for Length of the Longest Increasing Path runs in O(n log n) time and uses O(n) space. The time complexity is O(n log n) due to the sorting step, and O(n) for the dynamic programming part, making it efficient for larger inputs.

What is the brute force solution for Length of the Longest Increasing Path?

The brute force approach for Length of the Longest Increasing Path is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking all possible paths starting from the given coordinate and counting the length of each valid increasing path. This method is straightforward but inefficient for larger inputs. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Length of the Longest Increasing Path?

Length of the Longest Increasing Path uses the following concepts: Array, Binary Search, Sorting. The recommended patterns to study are: Dynamic Programming, Sorting, Greedy Algorithms.

What are the interview tips for Length of the Longest Increasing Path?

Always clarify the constraints and edge cases before diving into the solution. Think about how to optimize your brute force solution — often sorting or filtering can help. Practice explaining your thought process clearly, as communication is key in interviews.

What are common mistakes when solving Length of the Longest Increasing Path?

Failing to filter coordinates correctly before processing. Not considering the sorting order, which can lead to incorrect path lengths.

#3288

Length of the Longest Increasing Path

Hard

ArrayBinary SearchSortingDynamic ProgrammingSortingGreedy Algorithms

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(n)

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Intuition

Time O(n log n)Space O(n)

The optimal solution leverages sorting and dynamic programming to efficiently count the longest increasing path. By sorting the coordinates based on x and y values, we can ensure we only consider valid increasing paths.

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Algorithm

3 steps

1Step 1: Filter out coordinates that are not strictly less than coordinates[k].
2Step 2: Sort the remaining coordinates by x, and by y in descending order for ties.
3Step 3: Use dynamic programming to find the longest increasing path length.

solution.py18 lines

1# Full working Python code
2from typing import List
3
4def longestIncreasingPath(coordinates: List[List[int]], k: int) -> int:
5    target = coordinates[k]
6    filtered = [p for p in coordinates if p[0] < target[0] and p[1] < target[1]]
7    filtered.sort(key=lambda x: (x[0], -x[1]))
8    dp = [1] * len(filtered)
9    max_length = 0
10    for i in range(len(filtered)):
11        for j in range(i):
12            if filtered[j][1] < filtered[i][1]:
13                dp[i] = max(dp[i], dp[j] + 1)
14        max_length = max(max_length, dp[i])
15    return max_length + 1  # +1 for the target point
16
17# Example usage
18print(longestIncreasingPath([[3,1],[2,2],[4,1],[0,0],[5,3]], 1))

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Complexity note: The time complexity is O(n log n) due to the sorting step, and O(n) for the dynamic programming part, making it efficient for larger inputs.

1Filtering coordinates based on the target is crucial to reduce unnecessary checks.
2Sorting helps in efficiently finding increasing paths by ensuring we only consider valid pairs.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.