Alien Dictionary
A hard Graph problem included in Love Babbar 450, Striver A2Z. Below: the roles whose interviews prioritise this topic, and how to practise it.
- Topic
- Graph
- Sheets
- 2
- Core for
- 11 roles
- Platform
- LeetCode
The problem
Given a list of words from an alien language's dictionary where the words are sorted lexicographically, derive the order of letters in that language. Return an empty string if the order is invalid.
Example 1
- Input
- words = ["wrt","wrf","er","ett","rftt"]
- Output
- "wertf"
- Why
- From consecutive pairs we derive w->e, e->r, r->t, t->f, giving order wertf.
Example 2
- Input
- words = ["z","x","z"]
- Output
- ""
- Why
- The order implies z < x and x < z, which is a cycle, so the order is invalid.
Constraints
- 1 <= words.length <= 100
- 1 <= words[i].length <= 100
- words[i] consists of lowercase English letters
How to think about it
Updated 2026-09-09In a sorted dictionary, the relative order of the alphabet is established by the very first character where two adjacent words diverge. Comparing adjacent pairs extract directed edges `c1 -> c2`. Deriving the full alphabet order is then a topological sort across all unique characters, where any cycle or invalid prefix order indicates an impossible dictionary.
Approaches, worst first
Pairwise DAG DFS post-order
time O(C) · space O(1)
Derive directed constraints between divergent character pairs in adjacent words. Perform depth-first search with node coloring to detect cycles and push characters to a reverse topological order list. Backtracking recursion requires additional call stack frames and explicit recursion state sets.
Character DAG, Kahn topological sortWrite this one
time O(C) · space O(1)
Collect all unique characters into in-degree maps. Compare each adjacent word pair: find the first differing index and add a directed edge `word1[j] -> word2[j]`. Enqueue in-degree 0 characters, peel dependencies, and verify whether result string length matches total unique characters.
Where people lose marks · 3
- Prefix rule violation: if `word2` is a strict prefix of `word1` (e.g. `['abc', 'ab']`), the sorted order is fundamentally invalid and must return `''` immediately.
- Characters that never appear in any edge relation must still appear in the final alphabet string; seed in-degree entries for every character present across all words.
- Comparing all word pairs instead of only consecutive adjacent pairs adds redundant edges without providing any additional constraint.
The theory behind it
Graph — the ground this problem stands on. All Graph problems
What Graph is
A graph is a network of individual points, called vertices or nodes, connected by lines called edges. Think of a subway transit map, an electrical circuit, or a web of social friends. Unlike a tree, a graph has no designated top node and no parent-child hierarchy. Connections can run one-way or both ways, and paths can loop back on themselves to form closed cycles.
When to reach for it
Reach for graph algorithms when inputs describe relationships, networks, flights between cities, course prerequisites, or clone networks. Signals include finding the shortest route across unweighted connections, ordering tasks that depend on earlier tasks, counting isolated clusters, or checking whether a path contains an infinite loop. Whenever problems present pairs of related entities and ask for reachability, distances, or dependencies, graph representations apply.
How the pattern works
First convert edge lists into an adjacency list, mapping each node to an array of its neighbors. Choose your exploration strategy based on the goal: use a queue and breadth-first search to find the shortest path in unweighted networks, or use recursion and depth-first search to explore full paths and detect cycles. Because graphs can have loops, always track visited nodes in a set or boolean array. Add nodes to the visited set at the moment they enter the queue so they are never visited twice.
What each operation costs
| Operation | Time |
|---|---|
| visit all nodes and edges via search | O(v + e) |
| topological sort using in-degree counts | O(v + e) |
| shortest path using dijkstra with a min-heap | O((v + e) log v) |
What usually goes wrong with Graph
- Adding a node to the visited set when popping from the queue instead of when pushing, which lets neighboring nodes enqueue duplicate entries and wastes memory.
- Failing to check for cycles in directed graphs when finding prerequisite orders, causing topological sort routines to hang or return incomplete lists.
- Assuming an input graph is fully connected and scanning from only a single starting node, missing disconnected islands and isolated components.
Which roles need this problem
Graph is a core topic for these 11 roles — if you're targeting one of them, this problem is early in your path, not optional.
Secondary for 6 more roles, including Performance Engineer, Search Engineer, Information Retrieval Engineer.
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