LeetCode #2451 — EASY

Odd String Difference

Build confidence with an intuition-first walkthrough focused on array fundamentals.

The Problem

Problem Statement

You are given an array of equal-length strings words. Assume that the length of each string is n.

Each string words[i] can be converted into a difference integer array difference[i] of length n - 1 where difference[i][j] = words[i][j+1] - words[i][j] where 0 <= j <= n - 2. Note that the difference between two letters is the difference between their positions in the alphabet i.e. the position of 'a' is 0, 'b' is 1, and 'z' is 25.

For example, for the string "acb", the difference integer array is [2 - 0, 1 - 2] = [2, -1].

All the strings in words have the same difference integer array, except one. You should find that string.

Return the string in words that has different difference integer array.

Example 1:

Input: words = ["adc","wzy","abc"]
Output: "abc"
Explanation: 
- The difference integer array of "adc" is [3 - 0, 2 - 3] = [3, -1].
- The difference integer array of "wzy" is [25 - 22, 24 - 25]= [3, -1].
- The difference integer array of "abc" is [1 - 0, 2 - 1] = [1, 1]. 
The odd array out is [1, 1], so we return the corresponding string, "abc".

Example 2:

Input: words = ["aaa","bob","ccc","ddd"]
Output: "bob"
Explanation: All the integer arrays are [0, 0] except for "bob", which corresponds to [13, -13].

Constraints:

3 <= words.length <= 100
n == words[i].length
2 <= n <= 20
words[i] consists of lowercase English letters.

Step 01

Brute Force Baseline

Problem summary: You are given an array of equal-length strings words. Assume that the length of each string is n. Each string words[i] can be converted into a difference integer array difference[i] of length n - 1 where difference[i][j] = words[i][j+1] - words[i][j] where 0 <= j <= n - 2. Note that the difference between two letters is the difference between their positions in the alphabet i.e. the position of 'a' is 0, 'b' is 1, and 'z' is 25. For example, for the string "acb", the difference integer array is [2 - 0, 1 - 2] = [2, -1]. All the strings in words have the same difference integer array, except one. You should find that string. Return the string in words that has different difference integer array.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Hash Map

Example 1

["adc","wzy","abc"]

Example 2

["aaa","bob","ccc","ddd"]

Core Insight

What unlocks the optimal approach

Find the difference integer array for each string.
Compare them to find the odd one out.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2451: Odd String Difference
class Solution {
    public String oddString(String[] words) {
        var d = new HashMap<String, List<String>>();
        for (var s : words) {
            int m = s.length();
            var cs = new char[m - 1];
            for (int i = 0; i < m - 1; ++i) {
                cs[i] = (char) (s.charAt(i + 1) - s.charAt(i));
            }
            var t = String.valueOf(cs);
            d.putIfAbsent(t, new ArrayList<>());
            d.get(t).add(s);
        }
        for (var ss : d.values()) {
            if (ss.size() == 1) {
                return ss.get(0);
            }
        }
        return "";
    }
}

// Accepted solution for LeetCode #2451: Odd String Difference
func oddString(words []string) string {
	d := map[string][]string{}
	for _, s := range words {
		m := len(s)
		cs := make([]byte, m-1)
		for i := 0; i < m-1; i++ {
			cs[i] = s[i+1] - s[i]
		}
		t := string(cs)
		d[t] = append(d[t], s)
	}
	for _, ss := range d {
		if len(ss) == 1 {
			return ss[0]
		}
	}
	return ""
}

# Accepted solution for LeetCode #2451: Odd String Difference
class Solution:
    def oddString(self, words: List[str]) -> str:
        d = defaultdict(list)
        for s in words:
            t = tuple(ord(b) - ord(a) for a, b in pairwise(s))
            d[t].append(s)
        return next(ss[0] for ss in d.values() if len(ss) == 1)

// Accepted solution for LeetCode #2451: Odd String Difference
use std::collections::HashMap;
impl Solution {
    pub fn odd_string(words: Vec<String>) -> String {
        let n = words[0].len();
        let mut map: HashMap<String, (bool, usize)> = HashMap::new();
        for (i, word) in words.iter().enumerate() {
            let mut k = String::new();
            for j in 1..n {
                k.push_str(&(word.as_bytes()[j] - word.as_bytes()[j - 1]).to_string());
                k.push(',');
            }
            let new_is_only = !map.contains_key(&k);
            map.insert(k, (new_is_only, i));
        }
        for (is_only, i) in map.values() {
            if *is_only {
                return words[*i].clone();
            }
        }
        String::new()
    }
}

// Accepted solution for LeetCode #2451: Odd String Difference
function oddString(words: string[]): string {
    const d: Map<string, string[]> = new Map();
    for (const s of words) {
        const cs: number[] = [];
        for (let i = 0; i < s.length - 1; ++i) {
            cs.push(s[i + 1].charCodeAt(0) - s[i].charCodeAt(0));
        }
        const t = cs.join(',');
        if (!d.has(t)) {
            d.set(t, []);
        }
        d.get(t)!.push(s);
    }
    for (const [_, ss] of d) {
        if (ss.length === 1) {
            return ss[0];
        }
    }
    return '';
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(m × n)

Space

O(m + n)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED

O(n) time

O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.

Mutating counts without cleanup

Wrong move: Zero-count keys stay in map and break distinct/count constraints.

Usually fails on: Window/map size checks are consistently off by one.

Fix: Delete keys when count reaches zero.