0953_verifying_an_alien_dictionary.html

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    <title>Verifying an Alien Dictionary - LeetCode 953</title>
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            <h1><span class="problem-number">#953</span> Verifying an Alien Dictionary</h1>
            <p>In an alien language, the alphabet order is different. Given a list of words and the alien alphabet order, check if the words are sorted lexicographically in this alien language.</p>
            <div class="problem-meta">
                <span class="meta-tag">📁 Array & Hashing</span>
                <span class="meta-tag">🔤 String</span>
                <span class="meta-tag">⏱️ O(n × m)</span>
            </div>
            <div class="file-ref">
                📄 Python: <a href="../python/0953_verifying_an_alien_dictionary/0953_verifying_an_alien_dictionary.py">0953_verifying_an_alien_dictionary.py</a>
            </div>
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        <div class="explanation-panel">
            <h4>💡 How It Works (Layman's Terms)</h4>
            <ul>
                <li><strong>Alien Alphabet:</strong> Instead of a-b-c-d..., aliens might use h-l-a-b... as their order</li>
                <li><strong>Lexicographic Order:</strong> Like dictionary order, but using the alien alphabet</li>
                <li><strong>Comparison:</strong> Compare adjacent words character by character</li>
                <li><strong>Rule 1:</strong> If first different character in word1 comes AFTER word2's in alien order → NOT sorted</li>
                <li><strong>Rule 2:</strong> If word1 is longer but word2 is a prefix of word1 (like "apple" vs "app") → NOT sorted</li>
            </ul>
        </div>


        <div class="visualization-section">
            <h3>🎬 Step-by-Step Visualization</h3>
            
            <div class="controls">
                <button class="btn btn-primary" id="stepBtn" onclick="step()">Step</button>
                <button class="btn btn-success" id="autoBtn" onclick="toggleAuto()">Auto Run</button>
                <button class="btn btn-warning" onclick="reset()">Reset</button>
            </div>

            <div class="status-message" id="statusMessage">
                Click "Step" or "Auto Run" to check if words are sorted in alien order
            </div>

            <div class="array-section">
                <div class="array-label">Alien Alphabet Order:</div>
                <div class="array-container" id="alphabetContainer" style="gap: 4px;"></div>
            </div>

            <div class="array-section">
                <div class="array-label">Words to Check:</div>
                <div class="array-container" id="wordsContainer"></div>
            </div>

            <div class="array-section">
                <div class="array-label">Character Comparison:</div>
                <div id="comparisonContainer" style="font-size: 1.3em; padding: 20px; background: #f5f5f5; border-radius: 10px;"></div>
            </div>

            <div class="info-box" id="resultBox" style="display: none;"></div>
        </div>

        <div class="code-section">
            <h3>💻 Python Solution</h3>
            <div class="code-block">
                <pre>from typing import List


"""
LeetCode Verifying An Alien Dictionary

Problem from LeetCode: https://leetcode.com/problems/verifying-an-alien-dictionary/

In an alien language, surprisingly, they also use English lowercase letters, but possibly in a different order. 
The order of the alphabet is some permutation of lowercase letters.

Given a sequence of words written in the alien language, and the order of the alphabet, 
return true if and only if the given words are sorted lexicographically in this alien language.

Example 1:
Input: words = ["hello","leetcode"], order = "hlabcdefgijkmnopqrstuvwxyz"
Output: true
Explanation: As 'h' comes before 'l' in this language, then the sequence is sorted.

Example 2:
Input: words = ["word","world","row"], order = "worldabcefghijkmnpqstuvxyz"
Output: false
Explanation: As 'd' comes after 'l' in this language, then words[0] &gt; words[1], hence the sequence is unsorted.

Example 3:
Input: words = ["apple","app"], order = "abcdefghijklmnopqrstuvwxyz"
Output: false
Explanation: The first three characters "app" match, and the second string is shorter (in size.) 
According to lexicographical rules "apple" &gt; "app", because 'l' &gt; '∅', where '∅' is defined as the blank character 
which is less than any other character.

Constraints:
- 1 &lt;= words.length &lt;= 100
- 1 &lt;= words[i].length &lt;= 20
- order.length == 26
- All characters in words[i] and order are English lowercase letters.
"""

class Solution:

    def is_alien_sorted(self, words: List[str], order: str) -&gt;bool:
        """
        Check if the words are sorted lexicographically by the alien language order.
        
        Args:
            words: List of words to check
            order: The alien language alphabet order
            
        Returns:
            bool: True if the words are sorted according to the alien order, False otherwise
        """
        order_map = {char: i for i, char in enumerate(order)}
        for i in range(len(words) - 1):
            word1, word2 = words[i], words[i + 1]
            for j in range(len(word1)):
                if j &gt;= len(word2):
                    return False
                if word1[j] != word2[j]:
                    if order_map[word2[j]] &lt; order_map[word1[j]]:
                        return False
                    break
        return True

    def isAlienSorted_alt(self, words: List[str], order: str) -&gt;bool:
        """
        Alternative implementation using a key function for comparisons.
        
        Args:
            words: List of words to check
            order: The alien language alphabet order
            
        Returns:
            bool: True if the words are sorted, False otherwise
        """
        order_map = {char: i for i, char in enumerate(order)}
        for w1, w2 in zip(words, words[1:]):
            if len(w1) &gt; len(w2) and w1[:len(w2)] == w2:
                return False
            for c1, c2 in zip(w1, w2):
                if c1 != c2:
                    if order_map[c1] &gt; order_map[c2]:
                        return False
                    break
        return True


if __name__ == '__main__':
    # Example usage based on LeetCode sample
    solution = Solution()
    
    # Example 1
    words = ["hello","leetcode"]
    order = "hlabcdefgijkmnopqrstuvwxyz"
    result = solution.is_alien_sorted(words, order)
    print(f"Example 1: {result}")  # Expected: True
    
    # Example 2
    words = ["word","world","row"]
    order = "worldabcefghijkmnpqstuvxyz"
    result = solution.is_alien_sorted(words, order)
    print(f"Example 2: {result}")  # Expected: False
    
    # Example 3
    words = ["apple","app"]
    order = "abcdefghijklmnopqrstuvwxyz"
    result = solution.is_alien_sorted(words, order)
    print(f"Example 3: {result}")  # Expected: False
</pre>
            </div>
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    </div>

    <script>
        const alienOrder = "hlabcdefgijkmnopqrstuvwxyz";
        const words = ["hello", "leetcode"];
        const orderMap = {};
        alienOrder.split('').forEach((c, i) => orderMap[c] = i);

        let currentPair = 0;
        let charIndex = 0;
        let phase = 'init';
        let autoInterval = null;

        function init() {
            renderAlphabet();
            renderWords();
            document.getElementById('comparisonContainer').innerHTML = 'Comparison will appear here...';
            document.getElementById('resultBox').style.display = 'none';
        }

        function renderAlphabet() {
            const container = document.getElementById('alphabetContainer');
            container.innerHTML = '';
            alienOrder.split('').forEach((char, idx) => {
                const box = document.createElement('div');
                box.className = 'array-box small';
                box.id = `alpha-${char}`;
                box.style.width = '35px';
                box.style.height = '35px';
                box.style.fontSize = '1em';
                box.innerHTML = `${char}<span class="index-label">${idx}</span>`;
                container.appendChild(box);
            });
        }

        function renderWords() {
            const container = document.getElementById('wordsContainer');
            container.innerHTML = '';
            words.forEach((word, idx) => {
                const box = document.createElement('div');
                box.className = 'array-box';
                box.id = `word-${idx}`;
                box.style.width = 'auto';
                box.style.minWidth = '100px';
                box.style.padding = '10px 20px';
                box.innerHTML = `"${word}"<span class="index-label">[${idx}]</span>`;
                container.appendChild(box);
            });
        }

        function highlightChar(char) {
            document.querySelectorAll('[id^="alpha-"]').forEach(b => b.classList.remove('highlight'));
            if (char && document.getElementById(`alpha-${char}`)) {
                document.getElementById(`alpha-${char}`).classList.add('highlight');
            }
        }

        function step() {
            if (phase === 'init') {
                phase = 'comparing';
                currentPair = 0;
                charIndex = 0;
                document.getElementById('statusMessage').textContent = 
                    `Comparing adjacent pairs: "${words[0]}" vs "${words[1]}"`;
                document.getElementById(`word-0`).classList.add('current');
                document.getElementById(`word-1`).classList.add('current');
            } else if (phase === 'comparing') {
                if (currentPair >= words.length - 1) {
                    phase = 'done';
                    document.getElementById('resultBox').style.display = 'block';
                    document.getElementById('resultBox').className = 'info-box secondary';
                    document.getElementById('resultBox').textContent = '✅ All pairs are in correct order! Words are SORTED.';
                    document.getElementById('statusMessage').textContent = 'Verification complete!';
                    document.getElementById('stepBtn').disabled = true;
                    stopAuto();
                    return;
                }

                const word1 = words[currentPair];
                const word2 = words[currentPair + 1];

                if (charIndex >= word1.length) {
                    // word1 is done, it's valid (word1 <= word2 in length or found difference)
                    document.getElementById('comparisonContainer').innerHTML = 
                        `✓ "${word1}" ≤ "${word2}" — All characters matched and word1 ended first or is equal prefix`;
                    currentPair++;
                    charIndex = 0;
                    document.querySelectorAll('[id^="word-"]').forEach(b => b.classList.remove('current'));
                    if (currentPair < words.length - 1) {
                        document.getElementById(`word-${currentPair}`).classList.add('current');
                        document.getElementById(`word-${currentPair + 1}`).classList.add('current');
                    }
                    document.getElementById('statusMessage').textContent = 
                        currentPair < words.length - 1 ? 
                        `Moving to next pair: "${words[currentPair]}" vs "${words[currentPair + 1]}"` :
                        'All pairs checked!';
                    return;
                }

                if (charIndex >= word2.length) {
                    // word2 is shorter but word1 still has chars → NOT sorted
                    phase = 'done';
                    document.getElementById('comparisonContainer').innerHTML = 
                        `❌ "${word1}" > "${word2}" — word2 is a prefix of word1!`;
                    document.getElementById('resultBox').style.display = 'block';
                    document.getElementById('resultBox').className = 'info-box highlight';
                    document.getElementById('resultBox').textContent = '❌ NOT SORTED! word2 is prefix of word1.';
                    document.getElementById('stepBtn').disabled = true;
                    stopAuto();
                    return;
                }

                const c1 = word1[charIndex];
                const c2 = word2[charIndex];
                const pos1 = orderMap[c1];
                const pos2 = orderMap[c2];

                highlightChar(c1);

                if (c1 === c2) {
                    document.getElementById('comparisonContainer').innerHTML = 
                        `Comparing char[${charIndex}]: '${c1}' (pos ${pos1}) = '${c2}' (pos ${pos2}) → Same, continue...`;
                    document.getElementById('statusMessage').textContent = 
                        `Characters match at index ${charIndex}, checking next character...`;
                    charIndex++;
                } else if (pos1 < pos2) {
                    document.getElementById('comparisonContainer').innerHTML = 
                        `Comparing char[${charIndex}]: '${c1}' (pos ${pos1}) < '${c2}' (pos ${pos2}) → ✓ Correct order!`;
                    document.getElementById('statusMessage').textContent = 
                        `'${c1}' comes before '${c2}' in alien order. This pair is valid!`;
                    // Move to next pair
                    currentPair++;
                    charIndex = 0;
                    document.querySelectorAll('[id^="word-"]').forEach(b => b.classList.remove('current'));
                    if (currentPair < words.length - 1) {
                        document.getElementById(`word-${currentPair}`).classList.add('current');
                        document.getElementById(`word-${currentPair + 1}`).classList.add('current');
                    }
                } else {
                    document.getElementById('comparisonContainer').innerHTML = 
                        `Comparing char[${charIndex}]: '${c1}' (pos ${pos1}) > '${c2}' (pos ${pos2}) → ❌ Wrong order!`;
                    phase = 'done';
                    document.getElementById('resultBox').style.display = 'block';
                    document.getElementById('resultBox').className = 'info-box highlight';
                    document.getElementById('resultBox').textContent = `❌ NOT SORTED! '${c1}' comes after '${c2}' in alien order.`;
                    document.getElementById('stepBtn').disabled = true;
                    stopAuto();
                }
            }
        }

        function toggleAuto() {
            if (autoInterval) {
                stopAuto();
            } else {
                document.getElementById('autoBtn').textContent = 'Pause';
                autoInterval = setInterval(() => {
                    if (phase === 'done') {
                        stopAuto();
                    } else {
                        step();
                    }
                }, 1200);
            }
        }

        function stopAuto() {
            if (autoInterval) {
                clearInterval(autoInterval);
                autoInterval = null;
            }
            document.getElementById('autoBtn').textContent = 'Auto Run';
        }

        function reset() {
            stopAuto();
            phase = 'init';
            currentPair = 0;
            charIndex = 0;
            document.getElementById('stepBtn').disabled = false;
            document.getElementById('statusMessage').textContent = 
                'Click "Step" or "Auto Run" to check if words are sorted in alien order';
            document.querySelectorAll('.array-box').forEach(b => {
                b.classList.remove('highlight', 'current', 'complete');
            });
            init();
        }

        init();
    </script>
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