Odd String Difference - Solution & Explanation

Problem Overview: You receive an array of equal‑length strings. For each word, compute the difference between adjacent characters (for example "abcd" → [1,1,1]). Most words share the same difference pattern, but one word has a different pattern. Return that odd string.

Approach 1: Divide and Conquer with Recursive Method (Time: O(n * m), Space: O(m) recursion + pattern storage)

This method recursively splits the array of words into halves and evaluates the difference pattern of representative strings from each segment. For each word, compute its difference array by iterating over characters and subtracting adjacent ASCII values. The recursion compares pattern groups from left and right halves to detect which side contains the outlier pattern. Once a mismatch is identified, the recursion continues only on that segment until the odd string is isolated. This approach demonstrates how divide‑and‑conquer can reduce comparisons when you only need to locate a single anomaly among otherwise identical patterns.

Approach 2: Dynamic Programming for Optimal Substructure (Time: O(n * m), Space: O(n * m))

A more direct solution builds a reusable representation of each word’s difference pattern. Iterate through the array once and compute a signature string such as "1#1#1" from adjacent character differences. Store these signatures in a hash map where the key is the pattern and the value is the list or count of words sharing it. Because almost all strings share the same pattern, the map quickly reveals the single pattern with frequency one. Dynamic programming ideas apply because each difference value is derived from previously processed characters and reused as part of the signature structure. Hash lookups run in constant time, making this solution straightforward and efficient for typical constraints.

Both approaches rely on iterating through characters and constructing a difference representation. Understanding how to derive these patterns from a string and efficiently group them with a hash table is the core skill. The input itself is processed sequentially as an array of words.

Recommended for interviews: The hash‑based pattern grouping approach (Approach 2). It’s concise, runs in linear time relative to the total characters processed (O(n * m)), and clearly shows your ability to transform strings into comparable signatures. Discussing the divide‑and‑conquer idea first can demonstrate problem‑solving depth, but interviewers usually expect the hash map solution.