G-31. Word Ladder - 2 | Optimised Approach for Leetcode

This chapter explores an advanced, highly optimized competitive programming (CP) approach to solve the Word Ladder II problem without hitting LeetCode's stringent Time Limit Exceeded (TLE) constraints.

Note: If you are preparing for standard software engineering interviews, skip this approach. The standard BFS + sequence-storing approach taught in Word Ladder I & II is what interviewers expect. This optimization hack is purely designed to elevate your advanced algorithmic problem-solving and debugging intuition.

1. Why Do We Need an Optimised Approach? (The TLE Problem)

In the standard Word Ladder II solution, we store the full transformation sequence alongside every node directly inside the Breadth-First Search (BFS) queue:

• The Problem: As words transform through multiple branching paths, the number of valid intermediate sequences explodes combinatorially.
• The Consequence: Storing and duplicating full paths at every single BFS level consumes immense memory and computational overhead, resulting in Time Limit Exceeded (TLE) errors on LeetCode's stricter test cases.

Standard Approach (Queue stores sequences):
[ "hit" ] 
   |
[ "hit", "hot" ] 
   |
[ "hit", "hot", "dot" ], [ "hit", "hot", "lot" ] 
   |
(Memory & Time limit exhausted due to massive sequence replication!)

2. Core Mental Model: Breaking Down the Problem into Two Steps

To bypass the TLE wall, we decouple the problem into two distinct, highly efficient phases inspired by competitive programming strategies:

• Step 1 (Forward BFS + Hash Map): Run a standard BFS from the beginWord to the endWord, but instead of storing sequences, store only the minimum transformation step level for each word in an unordered map.
• Step 2 (Backward DFS + Backtracking): Starting from the endWord, trace backward to the beginWord using Depth-First Search (DFS) and strict level checks. Because we move backward from a fixed destination, we eliminate dead-end path explorations entirely.

3. Step 1: Forward BFS & Level Mapping

We use a standard queue-based BFS starting at the beginWord ("hit"). As we mutate characters from a to z to find valid dictionary words, we record their exact step level in a hash map (mpp).

Step 1 Execution Walkthrough

Let's trace beginWord = "hit", endWord = "cog", with a word list containing hot, dot, dog, lot, log.

4. Step 2: Backward DFS & Backtracking Intuition

Once Step 1 completes, our map holds the exact distance level of every reachable word. Now, we execute DFS from endWord ("cog" back to beginWord ("hit")).

Why Start from the End?

• Forward exploration branches wildly into dead ends (e.g., words that branch off and never reach the target).
• Backward tracing from the target restricts our choices strictly to paths where neighbor_level == current_level - 1. This cuts out unnecessary paths and guarantees we only explore valid shortest-path sequences.

5. Step-by-Step Backtracking Flow

When tracing backward from "cog" (Level 4), we look for neighbors at Level 3 ("log", "dog").

6. Complete Optimized C++ Implementation

Below is the complete, production-grade C++ solution incorporating pre-computed string sizes, reference-passed DFS sequences, and proper backtracking cleanup.

class Solution {
private:
    unordered_map<string, int> mpp;
    vector<vector<string>> ans;
    string bWord;

    void dfs(string word, vector<string>& seq) {
        // Base case: If we've traced back to the beginning word
        if (word == bWord) {
            vector<string> temp = seq;
            reverse(temp.begin(), temp.end());
            ans.push_back(temp);
            return;
        }

        int steps = mpp[word];
        int sz = word.size();

        for (int i = 0; i < sz; i++) {
            char original = word[i];
            for (char ch = 'a'; ch <= 'z'; ch++) {
                word[i] = ch;
                
                // Check if the mutated word exists in map and is exactly 1 step prior
                if (mpp.find(word) != mpp.end() && mpp[word] + 1 == steps) {
                    seq.push_back(word);
                    dfs(word, seq);
                    seq.pop_back(); // Backtrack
                }
            }
            word[i] = original; // Revert mutation
        }
    }

public:
    vector<vector<string>> findLadders(string beginWord, string endWord, vector<string>& wordList) {
        unordered_set<string> st(wordList.begin(), wordList.end());
        queue<string> q;
        
        bWord = beginWord;
        q.push(beginWord);
        mpp[beginWord] = 0;
        st.erase(beginWord);
        
        int sz = beginWord.size();

        // Step 1: Forward BFS to record distance levels
        while (!q.empty()) {
            string word = q.front();
            q.pop();
            
            int steps = mpp[word];
            
            // Optimization: Stop if we reach the end word level
            if (word == endWord) break;

            for (int i = 0; i < sz; i++) {
                char original = word[i];
                for (char ch = 'a'; ch <= 'z'; ch++) {
                    word[i] = ch;
                    if (st.count(word)) {
                        q.push(word);
                        st.erase(word);
                        mpp[word] = steps + 1;
                    }
                }
                word[i] = original;
            }
        }

        // Step 2: Backward DFS if endWord was reached
        if (mpp.find(endWord) != mpp.end()) {
            vector<string> seq;
            seq.push_back(endWord);
            dfs(endWord, seq);
        }

        return ans;
    }
};

7. Real-World Debugging & Production Pitfalls

• Forgetting to Revert String Mutations: When iterating through characters a to z, always restore word[i] = original after recursion returns; otherwise, subsequent iterations will inspect corrupted strings.
• TLE on LeetCode Due to Redundant size() Calls: Calling .size() inside nested loops can degrade performance in strict CP environments. Cache string lengths in local variables (int sz = beginWord.size()).
• Memory Leaks from Global State: In competitive programming setups, global or member data structures (mpp, ans, bWord) must be cleanly re-initialized or cleared if the class instance processes multiple test cases.

Summary and Key Takeaways

• Problem Statement Limitation: Standard BFS queue implementations storing full paths fail with TLE on LeetCode due to combinatorial sequence explosion.
• CP Optimization Strategy: Split the algorithm into two decoupled phases: Forward BFS for level mapping and Backward DFS for path backtracking.
• Map-Based Level Tracking: An unordered map (mpp) stores the minimum steps required to reach each valid dictionary word from the start.
• Backward Exploration Efficiency: Tracing from endWord to beginWord eliminates dead-end branches, drastically reducing execution time and memory overhead.
• Backtracking Mechanics: Use recursive push_back and pop_back along with exact level validation (mpp[word] + 1 == steps) to discover valid transformation paths.
• Interview Guidance: Use the simpler sequence-storing BFS approach during real technical interviews unless specifically asked to optimize for competitive programming constraints.