Word Ladder II
A hard Graph problem included in Striver A2Z. Below: the roles whose interviews prioritise this topic, and how to practise it.
- Topic
- Graph
- Sheets
- 1
- Core for
- 11 roles
- Platform
- LeetCode
The problem
Given a beginWord, endWord, and a wordList, find all shortest transformation sequences from beginWord to endWord. Each sequence must change exactly one letter at each step, and every intermediate word must be in the wordList. Return all such sequences.
Example 1
- Input
- beginWord = "hit", endWord = "cog", wordList = ["hot","dot","dog","lot","log","cog"]
- Output
- [["hit","hot","dot","dog","cog"],["hit","hot","lot","log","cog"]]
- Why
- Two shortest paths of length 5 each exist from hit to cog.
Example 2
- Input
- beginWord = "hit", endWord = "cog", wordList = ["hot","dot","dog","lot","log"]
- Output
- []
- Why
- No sequence exists because endWord is not in the wordList.
Constraints
- 1 <= beginWord.length <= 10
- endWord.length == beginWord.length
- 1 <= wordList.length <= 5000
How to think about it
Updated 2026-09-09Finding all shortest paths requires two distinct phases: BFS to discover the exact shortest distance to every intermediate word, followed by DFS backtracking to reconstruct the paths. Crucially, during BFS, words visited at the current level must only be removed from the candidate pool after the ENTIRE level finishes, allowing multiple parallel shortest parents to be recorded.
Approaches, worst first
Queue storing complete path arrays
time O(N * 26 * L^2 + P * L) · space O(P * L)
Enqueue full transformation sequences directly in a BFS queue. For each popped path, mutate the last word into dictionary words and push newly created complete arrays. Storing thousands of entire path copies in queue memory causes severe allocation bloat compared to backtracking along a parent DAG.
BFS level-graph with DFS path backtrackingWrite this one
time O(N * 26 * L^2 + P * L) · space O(N * L)
Run level-order BFS tracking shortest distance to each word and constructing a parent DAG `parents[word]`. Erase words from dictionary at the end of each BFS level. Once endWord is found, run DFS backtracking starting from endWord backwards to beginWord along parent pointers.
Where people lose marks · 3
- Removing words from the dictionary immediately upon first enqueue prevents other equally short paths from linking to the same node in the parent DAG.
- Attempting to carry full path lists inside the BFS queue consumes gigabytes of memory; only store parent DAG references during BFS and reconstruct paths via DFS.
- If endWord is not present in wordList, return an empty list `[]` immediately.
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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