Count Pairs of Equal Substrings With Minimum Difference

Count Pairs of Equal Substrings With Minimum Difference

What is this problem about?

The "Count Pairs of Equal Substrings With Minimum Difference interview question" is a string alignment challenge. You are given two strings, $s1$ and $s2$. You need to find pairs of indices $(i, j)$ such that the character $s1[i]$ is equal to $s2[j]$. Among all such pairs, you are specifically interested in those where the difference between the indices $(i - j)$ is minimized. Your goal is to count how many such "minimal difference" pairs exist.

Why is this asked in interviews?

Google uses the "Count Pairs of Equal Substrings With Minimum Difference coding problem" to test a candidate's ability to optimize search operations using hash tables. It evaluates if you can identify that comparing every character in $s1$ with every character in $s2$ ($O(N imes M)$) is unnecessary. It’s a test of "Hash Table interview pattern" and "Greedy" logic.

Algorithmic pattern used

This problem relies on Hash Tables and Prefix/Suffix Tracking.

1. First Occurrences: For string $s1$, we want the first occurrence of each character to minimize $i$. Store these in a map: first_pos[char] = index.
2. Last Occurrences: For string $s2$, we want the last occurrence of each character to maximize $j$, which in turn minimizes the difference $i - j$. Store these in last_pos[char] = index.
3. Minimize Difference: Iterate through all characters 'a' through 'z'. If a character exists in both maps, calculate diff = first_pos[char] - last_pos[char].
4. Count: Keep track of the global minimum diff found so far and count how many characters achieve it.

Example explanation

$s1 = "abacaba"$, $s2 = "abacaba"$

• First occurrences in $s1$: {a:0, b:1, c:3}
• Last occurrences in $s2$: {a:6, b:5, c:3}
• Differences:
  • 'a': $0 - 6 = -6$
  • 'b': $1 - 5 = -4$
  • 'c': $3 - 3 = 0$ The minimum difference is -6 (for 'a'). There is only 1 such pair.

Common mistakes candidates make

• Brute Force: Checking all $N imes M$ pairs of indices.
• Incorrect logic for "Minimum": Trying to minimize $|i - j|$ instead of $i - j$. The problem usually specifies the direction or specific index subtraction order.
• Ignoring characters: Forgetting that only equal characters can form a pair.

Interview preparation tip

When asked to find a "minimum difference" in a string or array, always consider if pre-calculating the first or last occurrence of elements helps. This "Greedy interview pattern" is a standard way to avoid nested loops.