Array vs Hash Map for Children

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/**
 * Complete Array-Based Trie Node with Performance Analysis
 */
class ArrayTrieNode {
    /**
     * Fixed-size array for children
     * Each index corresponds to a character position in the alphabet
     * null means no child exists for that character
     */
    children: (ArrayTrieNode | null)[];
    isEndOfWord: boolean = false;
    
    // Configurable alphabet
    private alphabetStart: number; // e.g., 'a'.charCodeAt(0) = 97
    
    constructor(alphabetSize: number = 26, alphabetStart: string = 'a') {
        // Allocate the full array immediately
        this.children = new Array(alphabetSize).fill(null);
        this.alphabetStart = alphabetStart.charCodeAt(0);
    }
    
    /**
     * Convert character to array index
     * This is the critical operation - must be O(1) and fast
     */
    private charToIndex(char: string): number {
        return char.charCodeAt(0) - this.alphabetStart;
    }
    
    /**
     * Get child for character
     * Time: O(1) - single array access
     * Memory access: Single cache line (usually)
     */
    getChild(char: string): ArrayTrieNode | null {
        const index = this.charToIndex(char);
        // Bounds check (can be omitted if input is guaranteed valid)
        if (index < 0 || index >= this.children.length) {
            return null;
        }
        return this.children[index];
    }
    
    /**
     * Set child for character
     * Time: O(1) - single array assignment
     */
    setChild(char: string, node: ArrayTrieNode): void {
        const index = this.charToIndex(char);
        this.children[index] = node;
    }
    
    /**
     * Check if child exists
     * Time: O(1)
     */
    hasChild(char: string): boolean {
        return this.getChild(char) !== null;
    }
    
    /**
     * Count actual children - requires full scan
     * Time: O(|Σ|) - must check every slot
     */
    countChildren(): number {
        let count = 0;
        for (const child of this.children) {
            if (child !== null) count++;
        }
        return count;
    }
    
    /**
     * Iterate over actual children with their characters
     * Time: O(|Σ|) - must scan all slots
     */
    *iterateChildren(): Generator<[string, ArrayTrieNode]> {
        for (let i = 0; i < this.children.length; i++) {
            if (this.children[i] !== null) {
                const char = String.fromCharCode(this.alphabetStart + i);
                yield [char, this.children[i]!];
            }
        }
    }
    
    /**
     * Check if this is a leaf node
     * Time: O(|Σ|) - must scan to confirm no children
     */
    isLeaf(): boolean {
        return this.children.every(child => child === null);
    }
    
    /**
     * Memory analysis for this node
     */
    static analyzeMemory(alphabetSize: number): {
        arrayBytes: number;
        overheadBytes: number;
        totalBytes: number;
        usefulBytesIfFull: number;
        wastedIfEmpty: number;
    } {
        const pointerSize = 8; // 64-bit pointers
        const objectOverhead = 24; // Typical JS object overhead
        const booleanSize = 4; // Boolean with padding
        const intSize = 4; // alphabetStart
        
        const arrayBytes = alphabetSize * pointerSize;
        const overheadBytes = objectOverhead + booleanSize + intSize;
        const totalBytes = arrayBytes + overheadBytes;
        
        return {
            arrayBytes,
            overheadBytes,
            totalBytes,
            usefulBytesIfFull: arrayBytes, // All pointers point to real nodes
            wastedIfEmpty: arrayBytes, // All null pointers
        };
    }
}
 
// Memory analysis for common alphabet sizes
console.log("26-char (lowercase):", ArrayTrieNode.analyzeMemory(26));
// { arrayBytes: 208, totalBytes: 240, wastedIfEmpty: 208 }
 
console.log("52-char (case-sensitive):", ArrayTrieNode.analyzeMemory(52));
// { arrayBytes: 416, totalBytes: 448, wastedIfEmpty: 416 }
 
console.log("128-char (ASCII):", ArrayTrieNode.analyzeMemory(128));
// { arrayBytes: 1024, totalBytes: 1056, wastedIfEmpty: 1024 }

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/**
 * Complete Hash Map-Based Trie Node with Performance Analysis
 */
class HashMapTrieNode {
    /**
     * Hash map for children
     * Keys are single characters, values are child nodes
     * Only stores children that exist
     */
    children: Map<string, HashMapTrieNode>;
    isEndOfWord: boolean = false;
    
    constructor() {
        this.children = new Map();
    }
    
    /**
     * Get child for character
     * Time: O(1) average, O(k) worst case where k is bucket size
     * In practice: ~10-50ns due to hash computation and lookup
     */
    getChild(char: string): HashMapTrieNode | undefined {
        return this.children.get(char);
    }
    
    /**
     * Set child for character
     * Time: O(1) average, may trigger rehash (amortized O(1))
     */
    setChild(char: string, node: HashMapTrieNode): void {
        this.children.set(char, node);
    }
    
    /**
     * Check if child exists
     * Time: O(1) average
     */
    hasChild(char: string): boolean {
        return this.children.has(char);
    }
    
    /**
     * Delete a child
     * Time: O(1) average
     */
    deleteChild(char: string): boolean {
        return this.children.delete(char);
    }
    
    /**
     * Count actual children - direct property access
     * Time: O(1) - Map maintains size
     */
    countChildren(): number {
        return this.children.size;
    }
    
    /**
     * Iterate over actual children
     * Time: O(k) where k is actual children count
     * Much faster than array when sparse!
     */
    *iterateChildren(): Generator<[string, HashMapTrieNode]> {
        for (const entry of this.children) {
            yield entry;
        }
    }
    
    /**
     * Check if this is a leaf node
     * Time: O(1) - just check size
     */
    isLeaf(): boolean {
        return this.children.size === 0;
    }
    
    /**
     * Get all child characters (in insertion order for JS Map)
     */
    getChildChars(): string[] {
        return Array.from(this.children.keys());
    }
    
    /**
     * Memory analysis based on child count
     * Note: Actual memory varies significantly by JS engine
     */
    static analyzeMemory(childCount: number): {
        baseOverhead: number;
        perEntryBytes: number;
        totalBytes: number;
        vsArrayBytes: (alphabetSize: number) => number;
    } {
        // JavaScript Map overhead estimates (varies by engine)
        const objectOverhead = 24;
        const mapBaseOverhead = 48; // Empty Map object
        const booleanSize = 4;
        
        // Per-entry cost: key + value + internal pointers + hash metadata
        // Rough estimate: 40-60 bytes per entry
        const perEntryBytes = 48;
        
        const totalBytes = objectOverhead + mapBaseOverhead + booleanSize + 
                          (childCount * perEntryBytes);
        
        return {
            baseOverhead: objectOverhead + mapBaseOverhead + booleanSize,
            perEntryBytes,
            totalBytes,
            vsArrayBytes: (alphabetSize: number) => {
                const arrayTotal = objectOverhead + booleanSize + (alphabetSize * 8);
                return arrayTotal - totalBytes; // Positive = Map saves space
            }
        };
    }
}
 
// Compare memory at different child counts for 26-char alphabet
const scenarios = [
    { children: 1, desc: "Sparse (1 child)" },
    { children: 5, desc: "Low (5 children)" },
    { children: 13, desc: "Medium (13 children)" },
    { children: 20, desc: "High (20 children)" },
    { children: 26, desc: "Full (26 children)" },
];
 
console.log("Memory comparison: Hash Map vs Array (26-char alphabet)
");
for (const { children, desc } of scenarios) {
    const mapMem = HashMapTrieNode.analyzeMemory(children);
    const savings = mapMem.vsArrayBytes(26);
    console.log(`${desc}:`);
    console.log(`  Map: ~${mapMem.totalBytes} bytes`);
    console.log(`  Array: ~240 bytes (fixed)`);
    console.log(`  ${savings > 0 ? 'Map saves' : 'Array saves'}: ${Math.abs(savings)} bytes`);
}

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/**
 * Side-by-side performance comparison
 * Run this to see actual numbers on your hardware
 */
function runComparison() {
    const ITERATIONS = 1_000_000;
    const ALPHABET = 'abcdefghijklmnopqrstuvwxyz';
    
    // Prepare test nodes
    const arrayNode = new ArrayTrieNode();
    const hashNode = new HashMapTrieNode();
    
    // Add some children
    for (const char of 'acdfhjmptx') { // 10 children
        arrayNode.setChild(char, new ArrayTrieNode());
        hashNode.setChild(char, new HashMapTrieNode());
    }
    
    // Benchmark: Random child lookups
    const lookupChars = ALPHABET.split('');
    
    // Array lookups
    let arrayStart = performance.now();
    for (let i = 0; i < ITERATIONS; i++) {
        const char = lookupChars[i % 26];
        arrayNode.getChild(char);
    }
    let arrayTime = performance.now() - arrayStart;
    
    // Hash map lookups
    let hashStart = performance.now();
    for (let i = 0; i < ITERATIONS; i++) {
        const char = lookupChars[i % 26];
        hashNode.getChild(char);
    }
    let hashTime = performance.now() - hashStart;
    
    console.log(`Child Lookup (${ITERATIONS.toLocaleString()} iterations):`);
    console.log(`  Array:    ${arrayTime.toFixed(2)}ms (${(arrayTime/ITERATIONS*1000000).toFixed(0)}ns/op)`);
    console.log(`  Hash Map: ${hashTime.toFixed(2)}ms (${(hashTime/ITERATIONS*1000000).toFixed(0)}ns/op)`);
    console.log(`  Ratio:    Hash Map is ${(hashTime/arrayTime).toFixed(1)}x slower
`);
    
    // Benchmark: Iterate all children
    const ITER_COUNT = 100_000;
    
    arrayStart = performance.now();
    for (let i = 0; i < ITER_COUNT; i++) {
        for (const _ of arrayNode.iterateChildren()) { /* consume */ }
    }
    arrayTime = performance.now() - arrayStart;
    
    hashStart = performance.now();
    for (let i = 0; i < ITER_COUNT; i++) {
        for (const _ of hashNode.iterateChildren()) { /* consume */ }
    }
    hashTime = performance.now() - hashStart;
    
    console.log(`Child Iteration (${ITER_COUNT.toLocaleString()} iterations):`);
    console.log(`  Array:    ${arrayTime.toFixed(2)}ms (scans all 26 slots)`);
    console.log(`  Hash Map: ${hashTime.toFixed(2)}ms (visits only 10 children)`);
    console.log(`  Ratio:    ${(arrayTime/hashTime).toFixed(1)}x difference
`);
    
    // Benchmark: Check if leaf
    const LEAF_COUNT = 1_000_000;
    
    arrayStart = performance.now();
    for (let i = 0; i < LEAF_COUNT; i++) {
        arrayNode.isLeaf();
    }
    arrayTime = performance.now() - arrayStart;
    
    hashStart = performance.now();
    for (let i = 0; i < LEAF_COUNT; i++) {
        hashNode.isLeaf();
    }
    hashTime = performance.now() - hashStart;
    
    console.log(`Leaf Check (${LEAF_COUNT.toLocaleString()} iterations):`);
    console.log(`  Array:    ${arrayTime.toFixed(2)}ms (O(|Σ|) scan)`);
    console.log(`  Hash Map: ${hashTime.toFixed(2)}ms (O(1) size check)`);
    console.log(`  Ratio:    Array is ${(arrayTime/hashTime).toFixed(1)}x slower`);
}
 
// Run: runComparison();

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/**
 * Hybrid Strategy 1: Depth-Based Selection
 * Use arrays near root, hash maps deeper
 */
interface DepthAwareNode {
    depth: number;
    // Either array or map, never both
    arrayChildren?: (DepthAwareNode | null)[];
    mapChildren?: Map<string, DepthAwareNode>;
    isEndOfWord: boolean;
}
 
class DepthHybridTrie {
    private root: DepthAwareNode;
    private readonly arrayDepthThreshold: number;
    private readonly alphabetSize: number;
    
    constructor(alphabetSize: number = 26, arrayDepthThreshold: number = 3) {
        this.alphabetSize = alphabetSize;
        this.arrayDepthThreshold = arrayDepthThreshold;
        this.root = this.createNode(0);
    }
    
    private createNode(depth: number): DepthAwareNode {
        const useArray = depth < this.arrayDepthThreshold;
        
        return {
            depth,
            arrayChildren: useArray ? new Array(this.alphabetSize).fill(null) : undefined,
            mapChildren: useArray ? undefined : new Map(),
            isEndOfWord: false
        };
    }
    
    private charToIndex(char: string): number {
        return char.charCodeAt(0) - 97;
    }
    
    getChild(node: DepthAwareNode, char: string): DepthAwareNode | null {
        if (node.arrayChildren) {
            return node.arrayChildren[this.charToIndex(char)];
        }
        return node.mapChildren?.get(char) ?? null;
    }
    
    setChild(node: DepthAwareNode, char: string, child: DepthAwareNode): void {
        if (node.arrayChildren) {
            node.arrayChildren[this.charToIndex(char)] = child;
        } else {
            node.mapChildren!.set(char, child);
        }
    }
    
    insert(word: string): void {
        let current = this.root;
        
        for (let i = 0; i < word.length; i++) {
            const char = word[i];
            let child = this.getChild(current, char);
            
            if (!child) {
                child = this.createNode(current.depth + 1);
                this.setChild(current, char, child);
            }
            
            current = child;
        }
        
        current.isEndOfWord = true;
    }
}
 
/**
 * Hybrid Strategy 2: Adaptive Conversion
 * Start with hash map, convert to array when dense enough
 */
class AdaptiveNode {
    private static readonly CONVERSION_THRESHOLD = 0.4; // 40% density
    
    private mode: 'map' | 'array' = 'map';
    private mapChildren: Map<string, AdaptiveNode> = new Map();
    private arrayChildren: (AdaptiveNode | null)[] | null = null;
    
    isEndOfWord: boolean = false;
    
    getChild(char: string): AdaptiveNode | null {
        if (this.mode === 'array') {
            return this.arrayChildren![char.charCodeAt(0) - 97];
        }
        return this.mapChildren.get(char) ?? null;
    }
    
    setChild(char: string, node: AdaptiveNode): void {
        if (this.mode === 'array') {
            this.arrayChildren![char.charCodeAt(0) - 97] = node;
        } else {
            this.mapChildren.set(char, node);
            this.checkConversion();
        }
    }
    
    private checkConversion(): void {
        if (this.mode !== 'map') return;
        
        const density = this.mapChildren.size / 26;
        if (density >= AdaptiveNode.CONVERSION_THRESHOLD) {
            this.convertToArray();
        }
    }
    
    private convertToArray(): void {
        this.arrayChildren = new Array(26).fill(null);
        
        for (const [char, node] of this.mapChildren) {
            this.arrayChildren[char.charCodeAt(0) - 97] = node;
        }
        
        this.mapChildren.clear();
        this.mode = 'array';
    }
    
    getMode(): 'map' | 'array' {
        return this.mode;
    }
}
 
/**
 * Hybrid Strategy 3: Size-Tiered Storage
 * Different structures for different expected sizes
 */
class TieredNode {
    private tier: 'single' | 'few' | 'many';
    
    // Tier 1: Single child (common for word endings)
    private singleChar?: string;
    private singleChild?: TieredNode;
    
    // Tier 2: Few children (2-5) - small array of pairs
    private fewChildren?: { char: string; node: TieredNode }[];
    
    // Tier 3: Many children - full hash map
    private manyChildren?: Map<string, TieredNode>;
    
    isEndOfWord: boolean = false;
    
    constructor() {
        this.tier = 'single';
    }
    
    getChild(char: string): TieredNode | null {
        switch (this.tier) {
            case 'single':
                return this.singleChar === char ? this.singleChild! : null;
            
            case 'few':
                const found = this.fewChildren!.find(c => c.char === char);
                return found?.node ?? null;
            
            case 'many':
                return this.manyChildren!.get(char) ?? null;
        }
    }
    
    setChild(char: string, node: TieredNode): void {
        switch (this.tier) {
            case 'single':
                if (!this.singleChar) {
                    this.singleChar = char;
                    this.singleChild = node;
                } else {
                    // Upgrade to 'few' tier
                    this.fewChildren = [
                        { char: this.singleChar, node: this.singleChild! },
                        { char, node }
                    ];
                    this.singleChar = undefined;
                    this.singleChild = undefined;
                    this.tier = 'few';
                }
                break;
            
            case 'few':
                const existing = this.fewChildren!.findIndex(c => c.char === char);
                if (existing >= 0) {
                    this.fewChildren![existing].node = node;
                } else if (this.fewChildren!.length < 5) {
                    this.fewChildren!.push({ char, node });
                } else {
                    // Upgrade to 'many' tier
                    this.manyChildren = new Map();
                    for (const child of this.fewChildren!) {
                        this.manyChildren.set(child.char, child.node);
                    }
                    this.manyChildren.set(char, node);
                    this.fewChildren = undefined;
                    this.tier = 'many';
                }
                break;
            
            case 'many':
                this.manyChildren!.set(char, node);
                break;
        }
    }
    
    getTier(): string {
        return this.tier;
    }
}

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"""
Python-optimized trie node using dict and __slots__
"""
 
class OptimizedTrieNode:
    """
    Memory-efficient trie node using __slots__
    Reduces per-object overhead significantly
    """
    __slots__ = ('children', 'is_end_of_word')
    
    def __init__(self):
        self.children: dict[str, 'OptimizedTrieNode'] = {}
        self.is_end_of_word: bool = False
    
    def get_child(self, char: str) -> 'OptimizedTrieNode | None':
        return self.children.get(char)
    
    def set_child(self, char: str, node: 'OptimizedTrieNode') -> None:
        self.children[char] = node
    
    def has_child(self, char: str) -> bool:
        return char in self.children
 
 
class OptimizedTrie:
    """Complete trie using optimized nodes"""
    __slots__ = ('root',)
    
    def __init__(self):
        self.root = OptimizedTrieNode()
    
    def insert(self, word: str) -> None:
        node = self.root
        for char in word:
            if char not in node.children:
                node.children[char] = OptimizedTrieNode()
            node = node.children[char]
        node.is_end_of_word = True
    
    def search(self, word: str) -> bool:
        node = self.root
        for char in word:
            if char not in node.children:
                return False
            node = node.children[char]
        return node.is_end_of_word
    
    def starts_with(self, prefix: str) -> bool:
        node = self.root
        for char in prefix:
            if char not in node.children:
                return False
            node = node.children[char]
        return True
 
 
# Memory comparison
import sys
 
class StandardNode:
    def __init__(self):
        self.children = {}
        self.is_end_of_word = False
 
optimized = OptimizedTrieNode()
standard = StandardNode()
 
print(f"Optimized node size: {sys.getsizeof(optimized)} bytes")
print(f"Standard node size: {sys.getsizeof(standard)} bytes")
# Optimized is typically 30-50% smaller