How do you solve Longest Harmonious Subsequence on LeetCode?

Longest Harmonious Subsequence (LeetCode #594) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Utilizing a frequency map can significantly reduce the complexity of the problem.

What is the brute force solution for Longest Harmonious Subsequence?

The brute force approach for Longest Harmonious Subsequence is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible subsequences of the array and checking each one to see if it is harmonious. This is straightforward but inefficient due to the exponential number of subsequences. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Longest Harmonious Subsequence?

Longest Harmonious Subsequence uses the following concepts: Array, Hash Table, Sliding Window, Sorting, Counting. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Longest Harmonious Subsequence?

Always think about how to optimize your solution after the brute force approach. Be ready to explain your thought process clearly and logically. Practice building frequency maps as they are commonly used in array problems.

What are common mistakes when solving Longest Harmonious Subsequence?

Not considering edge cases where no harmonious subsequence exists. Overlooking the need to check only adjacent numbers in the frequency map.

#594

Longest Harmonious Subsequence

Easy

ArrayHash TableSliding WindowSortingCountingHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n)Space O(n)

The optimal solution leverages a frequency map to count occurrences of each number. By checking adjacent numbers in this map, we can efficiently find the longest harmonious subsequence without generating all subsequences.

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Algorithm

4 steps

1Step 1: Create a frequency map to count occurrences of each number in the array.
2Step 2: Iterate through the keys in the frequency map.
3Step 3: For each key, check if the key + 1 exists in the map. If it does, calculate the length of the harmonious subsequence.
4Step 4: Keep track of the maximum length found.

solution.py10 lines

1# Full working Python code
2from collections import Counter
3
4def findLHS(nums):
5    freq = Counter(nums)
6    max_length = 0
7    for key in freq:
8        if key + 1 in freq:
9            max_length = max(max_length, freq[key] + freq[key + 1])
10    return max_length

ℹ

Complexity note: The time complexity is O(n) because we traverse the array once to build the frequency map and then iterate through the map, which is efficient. The space complexity is O(n) due to the storage of the frequency map.

1Utilizing a frequency map can significantly reduce the complexity of the problem.
2Harmonious subsequences can only be formed by adjacent numbers in the frequency map.

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