What is the time complexity of Guess the Word?

The optimal solution has a time complexity of O(N^2).

What data structures are used to solve Guess the Word?

This problem uses Array, Math, String, Interactive, Game Theory. Understanding these concepts is essential for solving this Hard problem efficiently.

What are the key insights for solving Guess the Word?

Insight 1: The most important insight is to reduce the search space effectively after each guess. This involves filtering the remaining candidate words based on the number of matches with the current guess. Insight 2: Choosing the 'best' guess in each iteration is crucial for efficient reduction of the search space. A good strategy involves minimizing the maximum number of words that could remain after making the guess.

Which companies ask LeetCode 843. Guess the Word in interviews?

This problem is frequently asked at Dropbox, Verily, Verkada.

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Guess the Word - LeetCode 843 Solution

Guess the Word - Complete Solution Guide

Guess the Word is LeetCode problem 843, a Hard level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given an array of unique strings words where words[i] is six letters long. One word of words was chosen as a secret word. You are also given the helper object Master . You may call Master.guess(word) where word is a six-letter-long string, and it must be from words . Master.guess(word) returns: -1 if word is not from words , or an integer representing the number of exact matches (value and position) of your guess to the secret word. There is a parameter allowedGuesses for each test case

Detailed Explanation

The "Guess the Word" problem is an interactive game where you need to guess a secret six-letter word from a given list of unique six-letter words. You are provided with a `Master` object that allows you to make guesses. The `Master.guess(word)` method returns the number of exact matches (same letter at the same position) between your guess and the secret word. The goal is to guess the secret word within a limited number of guesses (specified by `allowedGuesses`). The problem guarantees that the secret word exists in the given word list and that a reasonable strategy exists to find it without brute-forcing all possibilities.

Solution Approach

The provided solution employs a minimax-like heuristic approach. It iteratively guesses a word from the remaining candidate words. The word selected is the one that minimizes the maximum number of words that could potentially remain after a guess and match evaluation. Specifically, for each candidate word, it calculates how many words would remain for each possible match count (0 to 6). Then it picks the candidate with the minimum value of the largest group. The candidate is guessed, and the number of matches is obtained from the `Master` object. The candidate list is then filtered to only contain words that have the same number of matches as the guess.

Step-by-Step Algorithm

Step 1: Initialize the candidate list with the provided word list.
Step 2: Iterate up to 30 times (the maximum allowed guesses).
Step 3: If the candidate list is empty, return (secret word found or no word satisfies constraints).
Step 4: For each candidate word, calculate a score that represents the maximum number of words that would be left if we guessed that candidate and it has some number of matches with secret word.
Step 5: Select the candidate word with the minimum score (minimax heuristic).
Step 6: Make a guess using `master.guess(guess_word)`.
Step 7: If the guess matches the secret word (matches_count == 6), return.
Step 8: Filter the candidate list to only include words that have the same number of matches with the guessed word as the `master.guess` method returned.
Step 9: Repeat from step 2.

Key Insights

Insight 1: The most important insight is to reduce the search space effectively after each guess. This involves filtering the remaining candidate words based on the number of matches with the current guess.
Insight 2: Choosing the 'best' guess in each iteration is crucial for efficient reduction of the search space. A good strategy involves minimizing the maximum number of words that could remain after making the guess.
Insight 3: The constraint on the number of guesses (10 <= allowedGuesses <= 30) suggests that a heuristic approach, rather than a perfect algorithm, is sufficient and expected.

Complexity Analysis

Time Complexity: O(N^2)

Space Complexity: O(N)

Topics

This problem involves: Array, Math, String, Interactive, Game Theory.

Companies

Asked at: Dropbox, Verily, Verkada.

Guess the Word | LeetCode 843

Hard

Array Math String Interactive Game Theory

Time: O(N^2)Space: O(N)

Solution Code

Available in:

/**
 * // This is the Master's API interface.
 * // You should not implement it, or speculate about its implementation
 * interface Master {
 *     public int guess(String word) {}
 * }
 */
class Solution {
    public void findSecretWord(String[] words, Master master) {
        String[] candidates = words;
        
        for (int i = 0; i < 30; i++) {
            if (candidates == null || candidates.length == 0) {
                return;
            }

            String guess_word = "";
            int min_score = Integer.MAX_VALUE;

            for (String w1 : candidates) {
                int[] groups = new int[7];
                for (String w2 : candidates) {
                    int m = match(w1, w2);
                    groups[m]++;
                }
                int score = 0;
                for (int group : groups) {
                    score = Math.max(score, group);
                }
                if (score < min_score) {
                    min_score = score;
                    guess_word = w1;
                }
            }
            
            int matches_count = master.guess(guess_word);
            
            if (matches_count == 6) {
                return;
            }
            
            String[] new_candidates = new String[candidates.length];
            int count = 0;
            for (String w : candidates) {
                if (match(guess_word, w) == matches_count) {
                    new_candidates[count++] = w;
                }
            }
            candidates = new String[count];
            System.arraycopy(new_candidates, 0, candidates, 0, count);
        }
    }
    
    private int match(String w1, String w2) {
        int matches = 0;
        for (int i = 0; i < w1.length(); i++) {
            if (w1.charAt(i) == w2.charAt(i)) {
                matches++;
            }
        }
        return matches;
    }
}

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Problem Info

Description

Problem 843: Guess the Word - Detailed explanation and solution approaches.

Topics

Array Math String Interactive Game Theory

Companies

DropboxVerilyVerkada

Stats

Difficulty:Hard

Languages:4

Companies:3

Problem #:843

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

9 steps

1
Step 1: Initialize the candidate list with the provided word list.
2
Step 2: Iterate up to 30 times (the maximum allowed guesses).
3
Step 3: If the candidate list is empty, return (secret word found or no word satisfies constraints).
4
Step 4: For each candidate word, calculate a score that represents the maximum number of words that would be left if we guessed that candidate and it has some number of matches with secret word.
5
Step 5: Select the candidate word with the minimum score (minimax heuristic).
6
Step 6: Make a guess using `master.guess(guess_word)`.
7
Step 7: If the guess matches the secret word (matches_count == 6), return.
8
Step 8: Filter the candidate list to only include words that have the same number of matches with the guessed word as the `master.guess` method returned.
9
Step 9: Repeat from step 2.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(N^2)

💾

Space Complexity

O(N)

📝

Why?

The time complexity is dominated by the nested loops used to calculate the scores in each iteration of the main loop. The space complexity is determined by the size of the `candidates` list, which can grow up to the initial size of the input word list.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Random Guessing

A simpler approach would be to randomly guess a word from the remaining candidate words in each iteration. However, this is less efficient and may not guarantee finding the secret word within the allowed number of guesses.

Time: O(N * allowedGuesses) on average, but can be much worse in the worst caseSpace: O(N)

Trade-offs: Easier to implement, but less likely to succeed compared to the minimax strategy. Suitable for smaller word lists but less reliable for larger ones.

✨

Key Insights

1Insight 1: The most important insight is to reduce the search space effectively after each guess. This involves filtering the remaining candidate words based on the number of matches with the current guess.
2Insight 2: Choosing the 'best' guess in each iteration is crucial for efficient reduction of the search space. A good strategy involves minimizing the maximum number of words that could remain after making the guess.
3Insight 3: The constraint on the number of guesses (10 <= allowedGuesses <= 30) suggests that a heuristic approach, rather than a perfect algorithm, is sufficient and expected.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

String

A sequence of characters. Like a word or sentence in programming!

Edge Cases

Edge case 1: Empty candidate list - The algorithm explicitly checks for an empty candidate list and returns, preventing potential errors. This can happen if the match constraints are too strict.
Edge case 2: Secret word is among the initial candidates - The algorithm should eventually guess the secret word if it's in the list. The minimax strategy ensures that a guess is made from the available words.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not correctly filtering the candidate list after each guess. It is crucial to only keep words that have the exact same number of matches with the guessed word as the `Master` object returned.

✗Common mistake 2: Choosing a poor heuristic for selecting the next guess. Random guessing or simply picking the first word in the candidate list often leads to inefficient search space reduction and may exceed the allowed number of guesses.

✗Common mistake 3: Not considering the case where candidate list becomes empty.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: This problem mimics scenarios where you need to identify an object or piece of information by asking questions with limited allowed trials. For example, identifying a faulty component in a system by running diagnostic tests.

🏦Real-world scenario 2: Search algorithms in databases often use heuristics to narrow down search results efficiently. The concept of reducing the search space based on feedback is widely used in information retrieval.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Hard problems often combine multiple techniques. Break the problem into sub-problems.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: October 2, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 14

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 7

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jun 30

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

Is it okay to not fully solve hard problems in interviews?

Yes! Interviewers care more about your problem-solving process than the final answer. Demonstrate: clear communication, systematic approach, ability to recognize when to pivot strategies, and graceful handling of hints. Partial progress with good reasoning is valued.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Guess the Word"?

For this hard-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether math techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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