How do you solve Longest Ideal Subsequence on LeetCode?

Longest Ideal Subsequence (LeetCode #2370) 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: The problem can be approached using dynamic programming to build solutions incrementally.

What is the brute force solution for Longest Ideal Subsequence?

The brute force approach for Longest Ideal 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 string and checking which ones are ideal. 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 Ideal Subsequence?

Longest Ideal Subsequence uses the following concepts: Hash Table, String, Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Array.

What are the interview tips for Longest Ideal Subsequence?

Always clarify the problem constraints and edge cases before jumping into coding. Explain your thought process while coding to demonstrate your understanding. Practice writing clean and efficient code, as readability is important in interviews.

What are common mistakes when solving Longest Ideal Subsequence?

Failing to consider the bounds of the alphabet when checking adjacent characters. Not properly updating the dp array, leading to incorrect subsequence lengths.

#2370

Longest Ideal Subsequence

Medium

Hash TableStringDynamic ProgrammingDynamic ProgrammingArray

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)

We can use dynamic programming to build the solution incrementally. By maintaining an array that tracks the longest ideal subsequence ending at each character, we can efficiently compute the result.

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Algorithm

5 steps

1Step 1: Initialize a dp array where dp[i] represents the length of the longest ideal subsequence ending with character s[i].
2Step 2: Iterate through each character in the string s.
3Step 3: For each character, check previous characters to see if they can be part of an ideal subsequence (i.e., their difference is <= k).
4Step 4: Update dp[i] based on the maximum length found from valid previous characters.
5Step 5: The result will be the maximum value in the dp array.

solution.py12 lines

1# Full working Python code
2def longestIdealSubsequence(s, k):
3    dp = [0] * 26
4    max_length = 0
5    for char in s:
6        index = ord(char) - ord('a')
7        current_length = 1
8        for j in range(max(0, index - k), min(25, index + k) + 1):
9            current_length = max(current_length, dp[j] + 1)
10        dp[index] = max(dp[index], current_length)
11        max_length = max(max_length, dp[index])
12    return max_length

ℹ

Complexity note: The time complexity is O(n) because we iterate through the string once and check a fixed range of characters (at most 26) for each character in the string.

1The problem can be approached using dynamic programming to build solutions incrementally.
2Understanding the relationship between characters and their indices in the alphabet is crucial for checking the ideal conditions.

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