What is the time complexity of Longest Palindrome After Substring Concatenation II?

The optimal solution for Longest Palindrome After Substring Concatenation II runs in O(n) time and uses O(n) space. We preprocess each string in linear time, leading to O(n) complexity. Space is used to store palindrome lengths.

What is the brute force solution for Longest Palindrome After Substring Concatenation II?

The brute force approach for Longest Palindrome After Substring Concatenation II is Brute Force, with O(n²) time complexity and O(1) space complexity. Generate all possible concatenations of substrings from s and t, then check each for palindrome properties. This approach is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Longest Palindrome After Substring Concatenation II?

Longest Palindrome After Substring Concatenation II uses the following concepts: Two Pointers, String, Dynamic Programming. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Longest Palindrome After Substring Concatenation II?

Explain your thought process clearly. Consider edge cases early. Optimize your solution progressively.

What are common mistakes when solving Longest Palindrome After Substring Concatenation II?

Not considering empty substrings. Overlooking single character palindromes.

#3504

Longest Palindrome After Substring Concatenation II

Hard

Two PointersStringDynamic ProgrammingHash MapArray

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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)

Utilize dynamic programming to find the longest palindromic substring in s and t, then combine results. This reduces unnecessary checks.

⚙️

Algorithm

3 steps

1Step 1: Preprocess s and t to find the longest palindromic substrings that start and end at each index.
2Step 2: Use these preprocessed results to calculate the maximum palindrome length by combining valid starting and ending characters.
3Step 3: Return the maximum length found.

solution.py15 lines

1def longestPalindrome(s, t):
2    def longest_palindrome_from(s):
3        n = len(s)
4        p = [0] * n
5        for i in range(n):
6            l, r = i, i
7            while l >= 0 and r < n and s[l] == s[r]:
8                p[i] += 1
9                l -= 1
10                r += 1
11        return p
12    p_s = longest_palindrome_from(s)
13    p_t = longest_palindrome_from(t)
14    max_len = max(p_s) + max(p_t)
15    return max_len

ℹ

Complexity note: We preprocess each string in linear time, leading to O(n) complexity. Space is used to store palindrome lengths.

1Single characters are palindromes.
2Combining palindromic substrings maximizes length.

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