How do you solve Sum of Scores of Built Strings on LeetCode?

Sum of Scores of Built Strings (LeetCode #2223) 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: Understanding the relationship between prefixes and suffixes is crucial for this problem.

What is the brute force solution for Sum of Scores of Built Strings?

The brute force approach for Sum of Scores of Built Strings is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves comparing each substring with the final string to find the longest common prefix. This is straightforward but inefficient, as it checks each possible prefix individually. The optimal Optimal Solution approach improves this to O(n).

What are the interview tips for Sum of Scores of Built Strings?

Clearly explain your thought process and the trade-offs of different approaches. Practice implementing the Z-algorithm and understand its application in string problems. Be prepared to discuss time and space complexities for each approach you present.

What are common mistakes when solving Sum of Scores of Built Strings?

Not considering edge cases, such as strings with all identical characters. Overlooking the need to sum the scores correctly after calculating the longest prefixes.

#2223

Sum of Scores of Built Strings

Hard

StringBinary SearchRolling HashSuffix ArrayString MatchingHash FunctionString MatchingZ-algorithmDynamic Programming

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 approach uses the Z-algorithm to efficiently compute the longest common prefix lengths. The Z-array allows us to find the lengths of substrings that match the prefix of the string in linear time.

⚙️

Algorithm

4 steps

1Step 1: Construct the Z-array for the string s.
2Step 2: Initialize a variable 'total_score' to 0.
3Step 3: Iterate through the Z-array, adding the values to 'total_score' where the index is less than the length of the string.
4Step 4: Return 'total_score' as the result.

solution.py21 lines

1# Full working Python code
2
3def z_algorithm(s):
4    z = [0] * len(s)
5    left, right, n = 0, 0, len(s)
6    for i in range(1, n):
7        if i <= right:
8            z[i] = min(right - i + 1, z[i - left])
9        while i + z[i] < n and s[z[i]] == s[i + z[i]]:
10            z[i] += 1
11        if i + z[i] - 1 > right:
12            left, right = i, i + z[i] - 1
13    return z
14
15def sum_of_scores(s):
16    z = z_algorithm(s)
17    total_score = sum(z) + len(s)
18    return total_score
19
20# Example usage
21print(sum_of_scores('babab'))  # Output: 9

ℹ

Complexity note: The time complexity is O(n) because the Z-algorithm processes each character of the string a constant number of times, leading to linear growth in operations. The space complexity is O(n) due to the Z-array storage.

1Understanding the relationship between prefixes and suffixes is crucial for this problem.
2Using efficient algorithms like the Z-algorithm can drastically reduce computation time.

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