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| 1 | +/** |
| 2 | + * Inverted Index for BM25 search |
| 3 | + * |
| 4 | + * Optimizes search by pre-computing: |
| 5 | + * - Term → Document IDs mapping (inverted index) |
| 6 | + * - Document term frequencies |
| 7 | + * - IDF scores |
| 8 | + * |
| 9 | + * Time complexity: |
| 10 | + * - Build: O(n * m) where n = docs, m = avg tokens per doc |
| 11 | + * - Search: O(k * d) where k = query terms, d = avg docs per term |
| 12 | + * |
| 13 | + * vs. naive approach O(k * n * m) for every query |
| 14 | + */ |
| 15 | + |
| 16 | +import { tokenize, getTokenFrequencies } from "./tokenizer"; |
| 17 | + |
| 18 | +/** Posting entry: document ID + term frequency */ |
| 19 | +export interface Posting { |
| 20 | + docId: string; |
| 21 | + tf: number; // term frequency in this document |
| 22 | +} |
| 23 | + |
| 24 | +/** Inverted index entry for a term */ |
| 25 | +export interface IndexEntry { |
| 26 | + /** List of documents containing this term */ |
| 27 | + postings: Posting[]; |
| 28 | + /** Document frequency (number of docs containing this term) */ |
| 29 | + df: number; |
| 30 | + /** Pre-computed IDF score */ |
| 31 | + idf: number; |
| 32 | +} |
| 33 | + |
| 34 | +/** Document metadata */ |
| 35 | +export interface DocMeta { |
| 36 | + docId: string; |
| 37 | + /** Token count (document length) */ |
| 38 | + length: number; |
| 39 | +} |
| 40 | + |
| 41 | +/** Inverted index structure */ |
| 42 | +export interface InvertedIndex { |
| 43 | + /** Term → IndexEntry mapping */ |
| 44 | + termIndex: Map<string, IndexEntry>; |
| 45 | + /** Document metadata */ |
| 46 | + docMeta: Map<string, DocMeta>; |
| 47 | + /** Total number of documents */ |
| 48 | + totalDocs: number; |
| 49 | + /** Average document length */ |
| 50 | + avgDocLength: number; |
| 51 | +} |
| 52 | + |
| 53 | +/** |
| 54 | + * Build inverted index from documents |
| 55 | + * |
| 56 | + * @param documents - Array of { id, content } objects |
| 57 | + * @param tokenizeFn - Tokenization function (default: built-in tokenizer) |
| 58 | + * @returns Inverted index |
| 59 | + * |
| 60 | + * @example |
| 61 | + * const index = buildInvertedIndex([ |
| 62 | + * { id: "1", content: "Hello world" }, |
| 63 | + * { id: "2", content: "World of AI" } |
| 64 | + * ]); |
| 65 | + */ |
| 66 | +export function buildInvertedIndex( |
| 67 | + documents: Array<{ id: string; content: string }>, |
| 68 | + tokenizeFn: (text: string) => string[] = tokenize, |
| 69 | +): InvertedIndex { |
| 70 | + const termIndex = new Map<string, IndexEntry>(); |
| 71 | + const docMeta = new Map<string, DocMeta>(); |
| 72 | + let totalLength = 0; |
| 73 | + |
| 74 | + for (const doc of documents) { |
| 75 | + const tokens = tokenizeFn(doc.content); |
| 76 | + const tokenFreqs = getTokenFrequencies(tokens); |
| 77 | + |
| 78 | + // Store document metadata |
| 79 | + docMeta.set(doc.id, { docId: doc.id, length: tokens.length }); |
| 80 | + totalLength += tokens.length; |
| 81 | + |
| 82 | + // Update inverted index |
| 83 | + for (const [term, tf] of tokenFreqs) { |
| 84 | + let entry = termIndex.get(term); |
| 85 | + if (!entry) { |
| 86 | + entry = { postings: [], df: 0, idf: 0 }; |
| 87 | + termIndex.set(term, entry); |
| 88 | + } |
| 89 | + entry.postings.push({ docId: doc.id, tf }); |
| 90 | + entry.df++; |
| 91 | + } |
| 92 | + } |
| 93 | + |
| 94 | + const totalDocs = documents.length; |
| 95 | + const avgDocLength = totalDocs > 0 ? totalLength / totalDocs : 0; |
| 96 | + |
| 97 | + // Pre-compute IDF for all terms |
| 98 | + for (const entry of termIndex.values()) { |
| 99 | + // BM25 IDF formula: log((N - df + 0.5) / (df + 0.5) + 1) |
| 100 | + entry.idf = Math.log((totalDocs - entry.df + 0.5) / (entry.df + 0.5) + 1); |
| 101 | + } |
| 102 | + |
| 103 | + return { termIndex, docMeta, totalDocs, avgDocLength }; |
| 104 | +} |
| 105 | + |
| 106 | +/** |
| 107 | + * Search using inverted index with BM25 scoring |
| 108 | + * |
| 109 | + * @param index - Inverted index |
| 110 | + * @param queryTerms - Tokenized query terms |
| 111 | + * @param topK - Maximum number of results |
| 112 | + * @param k1 - BM25 term frequency saturation parameter (default: 1.5) |
| 113 | + * @param b - BM25 document length normalization parameter (default: 0.75) |
| 114 | + * @returns Array of { docId, score } sorted by score descending |
| 115 | + */ |
| 116 | +export function searchInvertedIndex( |
| 117 | + index: InvertedIndex, |
| 118 | + queryTerms: string[], |
| 119 | + topK: number, |
| 120 | + k1 = 1.5, |
| 121 | + b = 0.75, |
| 122 | +): Array<{ docId: string; score: number }> { |
| 123 | + if (queryTerms.length === 0 || index.totalDocs === 0) { |
| 124 | + return []; |
| 125 | + } |
| 126 | + |
| 127 | + // Accumulate scores for each document |
| 128 | + const scores = new Map<string, number>(); |
| 129 | + |
| 130 | + for (const term of queryTerms) { |
| 131 | + const entry = index.termIndex.get(term); |
| 132 | + if (!entry) continue; // Term not in index |
| 133 | + |
| 134 | + const { idf, postings } = entry; |
| 135 | + |
| 136 | + for (const posting of postings) { |
| 137 | + const docLength = index.docMeta.get(posting.docId)?.length ?? 0; |
| 138 | + |
| 139 | + // BM25 score for this term in this document |
| 140 | + const tf = posting.tf; |
| 141 | + const normalizedTf = (tf * (k1 + 1)) / (tf + k1 * (1 - b + b * (docLength / index.avgDocLength))); |
| 142 | + const termScore = idf * normalizedTf; |
| 143 | + |
| 144 | + scores.set(posting.docId, (scores.get(posting.docId) || 0) + termScore); |
| 145 | + } |
| 146 | + } |
| 147 | + |
| 148 | + // Sort by score and return top K |
| 149 | + return Array.from(scores.entries()) |
| 150 | + .map(([docId, score]) => ({ docId, score })) |
| 151 | + .sort((a, b) => b.score - a.score) |
| 152 | + .slice(0, topK); |
| 153 | +} |
| 154 | + |
| 155 | +/** |
| 156 | + * Get document IDs that contain ANY of the query terms (for filtering) |
| 157 | + */ |
| 158 | +export function getMatchingDocIds( |
| 159 | + index: InvertedIndex, |
| 160 | + queryTerms: string[], |
| 161 | +): Set<string> { |
| 162 | + const matchingDocs = new Set<string>(); |
| 163 | + |
| 164 | + for (const term of queryTerms) { |
| 165 | + const entry = index.termIndex.get(term); |
| 166 | + if (!entry) continue; |
| 167 | + |
| 168 | + for (const posting of entry.postings) { |
| 169 | + matchingDocs.add(posting.docId); |
| 170 | + } |
| 171 | + } |
| 172 | + |
| 173 | + return matchingDocs; |
| 174 | +} |
| 175 | + |
| 176 | +/** |
| 177 | + * Get document IDs that contain ALL of the query terms (AND query) |
| 178 | + */ |
| 179 | +export function getIntersectingDocIds( |
| 180 | + index: InvertedIndex, |
| 181 | + queryTerms: string[], |
| 182 | +): Set<string> { |
| 183 | + if (queryTerms.length === 0) return new Set(); |
| 184 | + |
| 185 | + // Get docs for first term |
| 186 | + const firstEntry = index.termIndex.get(queryTerms[0]); |
| 187 | + if (!firstEntry) return new Set(); |
| 188 | + |
| 189 | + let result = new Set(firstEntry.postings.map((p) => p.docId)); |
| 190 | + |
| 191 | + // Intersect with docs for remaining terms |
| 192 | + for (let i = 1; i < queryTerms.length; i++) { |
| 193 | + const entry = index.termIndex.get(queryTerms[i]); |
| 194 | + if (!entry) return new Set(); // No docs contain this term |
| 195 | + |
| 196 | + const termDocs = new Set(entry.postings.map((p) => p.docId)); |
| 197 | + result = new Set([...result].filter((id) => termDocs.has(id))); |
| 198 | + |
| 199 | + if (result.size === 0) return new Set(); |
| 200 | + } |
| 201 | + |
| 202 | + return result; |
| 203 | +} |
| 204 | + |
| 205 | +/** |
| 206 | + * Get index statistics |
| 207 | + */ |
| 208 | +export function getIndexStats(index: InvertedIndex): { |
| 209 | + totalDocs: number; |
| 210 | + totalTerms: number; |
| 211 | + avgDocLength: number; |
| 212 | + avgTermsPerDoc: number; |
| 213 | +} { |
| 214 | + let totalTermsInDocs = 0; |
| 215 | + for (const meta of index.docMeta.values()) { |
| 216 | + totalTermsInDocs += meta.length; |
| 217 | + } |
| 218 | + |
| 219 | + return { |
| 220 | + totalDocs: index.totalDocs, |
| 221 | + totalTerms: index.termIndex.size, |
| 222 | + avgDocLength: index.avgDocLength, |
| 223 | + avgTermsPerDoc: index.totalDocs > 0 ? totalTermsInDocs / index.totalDocs : 0, |
| 224 | + }; |
| 225 | +} |
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