Find the Difference

Find the Difference

What is this problem about?

The Find the Difference interview question is a character-tracking task. You are given two strings, $s$ and $t$. String $t$ is generated by shuffling string $s$ and then adding one additional character at a random position. Your goal is to identify and return that single added character.

Why is this asked in interviews?

Companies like Microsoft and Amazon ask the Find the Difference coding problem to assess a candidate's basic data structure knowledge. While a hash map is a valid solution, interviewers often look for the $O(1)$ space Bit Manipulation approach. It’s a great introductory problem to test optimization awareness within a String interview pattern.

Algorithmic pattern used

This problem can be solved with three different patterns:

1. Hash Table: Count character frequencies in $s$ and compare with frequencies in $t$.
2. ASCII Sum: Calculate the sum of ASCII values of all characters in $t$ and subtract the sum of ASCII values in $s$. The remainder is the character code of the extra letter.
3. XOR (Optimized): XOR all characters in both $s$ and $t$. Since XORing a character with itself results in 0, all paired characters cancel out, leaving only the added character.

Example explanation

$s = "abcd"$, $t = "abcde"$

• ASCII Sum:
• Sum(s) = 'a' + 'b' + 'c' + 'd'
• Sum(t) = 'a' + 'b' + 'c' + 'd' + 'e'
• Result = Sum(t) - Sum(s) = 'e'.
• XOR:
• ('a'^'b'^'c'^'d') ^ ('a'^'b'^'c'^'d'^'e')
• Paired chars become 0: 0 ^ 0 ^ 0 ^ 0 ^ 'e' = 'e'.

Common mistakes candidates make

• Sorting: Using sorting ($O(N \log N)$) instead of linear search ($O(N)$).
• String Concatenation: Trying to remove characters one-by-one from $t$, which can be $O(N^2)$ depending on the language.
• Ignoring Case: Not confirming if the strings are case-sensitive.

Interview preparation tip

Whenever you have a problem involving finding a "unique" or "odd-one-out" element in a set of pairs, think XOR. It is the most efficient Bit Manipulation interview pattern for these scenarios.