How do you solve Find Substring With Given Hash Value on LeetCode?

Find Substring With Given Hash Value (LeetCode #2156) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Using a rolling hash allows for efficient updates instead of recalculating the hash from scratch.

What is the time complexity of Find Substring With Given Hash Value?

The optimal solution for Find Substring With Given Hash Value runs in O(n) time and uses O(1) space. The time complexity is O(n) because we only make a single pass through the string, updating the hash in constant time for each character.

What is the brute force solution for Find Substring With Given Hash Value?

The brute force approach for Find Substring With Given Hash Value is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible substring of length k in the given string and calculating its hash to see if it matches the given hash value. This is straightforward but inefficient for larger strings. The optimal Optimal Solution approach improves this to O(n).

What are the interview tips for Find Substring With Given Hash Value?

Always explain your thought process clearly when discussing your approach. Be prepared to discuss the trade-offs between different approaches, especially time and space complexity. Practice implementing rolling hashes, as they are a common technique in string manipulation problems.

What are common mistakes when solving Find Substring With Given Hash Value?

Forgetting to handle negative hash values when updating the hash. Not correctly implementing the power function, leading to incorrect hash calculations.

#2156

Find Substring With Given Hash Value

Hard

StringSliding WindowRolling HashHash FunctionRolling HashSliding Window

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n)Space O(1)

The optimal solution uses a rolling hash technique, which allows us to efficiently update the hash value as we slide over the string. Instead of recalculating the hash from scratch for each substring, we adjust the hash based on the characters that enter and exit the window.

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Algorithm

4 steps

1Step 1: Calculate the initial hash for the first substring of length k.
2Step 2: Use a loop to slide the window one character at a time from the start to the end of the string.
3Step 3: For each new position, update the hash by removing the contribution of the character that is sliding out and adding the contribution of the character that is sliding in.
4Step 4: If the updated hash matches hashValue, return the current substring.

solution.py16 lines

1def findSubstring(s, power, modulo, k, hashValue):
2    n = len(s)
3    current_hash = 0
4    for i in range(k):
5        current_hash = (current_hash + (ord(s[i]) - ord('a') + 1) * (power ** i)) % modulo
6    if current_hash == hashValue:
7        return s[:k]
8    power_k = power ** (k - 1)
9    for i in range(k, n):
10        current_hash = (current_hash - (ord(s[i - k]) - ord('a') + 1) * power_k) % modulo
11        current_hash = (current_hash * power + (ord(s[i]) - ord('a') + 1)) % modulo
12        if current_hash < 0:
13            current_hash += modulo
14        if current_hash == hashValue:
15            return s[i - k + 1:i + 1]
16    return ''

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Complexity note: The time complexity is O(n) because we only make a single pass through the string, updating the hash in constant time for each character.

1Using a rolling hash allows for efficient updates instead of recalculating the hash from scratch.
2Understanding the mathematical properties of modular arithmetic is crucial for hash calculations.

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