Building a full-text search engine in TypeScript

Michele Riva

Michele Riva

Senior Software Architect @NearForm

Google Developer Expert

Microsoft MVP

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Why?

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What I cannot create, I do not understand

Richard Feynman

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A journey through algorithms and data structures

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There's no slow programming language, just bad DSA design

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What is "full-text" search?

sybase.com

Full-text search is a more advanced way to search a database.

Full-text search quickly finds all instances of a term (word) in a table without having to scan rows and without having to know which column a term is stored in.

Full-text search works by using text indexes.

A text index stores positional information for all terms found in the columns you create the text index on.

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What is "full-text" search?

sybase.com

Full-text search is a more advanced way to search a database.

Full-text search quickly finds all instances of a term (word) in a table without having to scan rows and without having to know which column a term is stored in.

Full-text search works by using text indexes.

A text index stores positional information for all terms found in the columns you create the text index on.

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What is "full-text" search?

sybase.com

Full-text search is a more advanced way to search a database.

Full-text search quickly finds all instances of a term (word) in a table without having to scan rows and without having to know which column a term is stored in.

Full-text search works by using text indexes.

A text index stores positional information for all terms found in the columns you create the text index on.

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What is "full-text" search?

sybase.com

Full-text search is a more advanced way to search a database.

Full-text search quickly finds all instances of a term (word) in a table without having to scan rows and without having to know which column a term is stored in.

Full-text search works by using text indexes.

A text index stores positional information for all terms found in the columns you create the text index on.

Popular full-text search engines

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"New generation" full-text search engines

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Sonic

Meilisearch

JavaScript-based full-text search engines

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Lunr.js

MiniSearch

Fuse.js

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Where to start?

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Understand what kind of data we want to store and retrieve

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[
  {
    "id": 1,
    "quote": "It's alive! It's alive!",
    "movie": "Frankenstein",
    "year": 1931
  },
  {
    "id": 2,
    "quote": "You've got to ask yourself one question: 'Do I feel lucky?' Well, do ya, punk?",
    "movie": "Dirty Harry",
    "year": 1971
  },
  {
    "id": 3,
    "quote": "Mama always said life was like a box of chocolates. You never know what you're gonna get.",
    "movie": "Forrest Gump",
    "year": 1994
  }
]

Example documents

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// "It's alive! It's alive!"
["Its", "alive", "Its", "alive"]

// "You've got to ask yourself one question: 'Do I feel lucky?' Well, do ya, punk?"
[
  "Youve", "got", "to", "ask", "yourself", "one", "question",
  "Do", "I", "feel", "lucky", "Well", "do", "ya", "punk"
]

// "Mama always said life was like a box of chocolates. You never know what you're gonna get."
[
  "Mama", "always", "said", "life", "was", "like", "a", "box", "of", 
  "chocolates", "You", "never", "know", "what", "youre", "gonna", "get"
]

Tokenizer

Break the sentences into individual tokens

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// "It's alive! It's alive!"
["its", "alive", "its", "alive"]

// "You've got to ask yourself one question: 'Do I feel lucky?' Well, do ya, punk?"
[
  "youve", "got", "to", "ask", "yourself", "one", "question",
  "do", "i", "feel", "lucky", "well", "do", "ya", "punk"
]

// "Mama always said life was like a box of chocolates. You never know what you're gonna get."
[
  "mama", "always", "said", "life", "was", "like", "a", "box", "of", 
  "chocolates", "you", "never", "know", "what", "youre", "gonna", "get"
]

Tokenizer

Lowercase all tokens

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// "It's alive! It's alive!"
["its", "alive"]

// "You've got to ask yourself one question: 'Do I feel lucky?' Well, do ya, punk?"
[
  "youve", "got", "to", "ask", "yourself", "one", "question",
  "do", "i", "feel", "lucky", "well", "ya", "punk"
]

// "Mama always said life was like a box of chocolates. You never know what you're gonna get."
[
  "mama", "always", "said", "life", "was", "like", "a", "box", "of", 
  "chocolates", "you", "never", "know", "what", "youre", "gonna", "get"
]

Tokenizer

Remove duplicates

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// "It's alive! It's alive!"
["alive"]

// "You've got to ask yourself one question: 'Do I feel lucky?' Well, do ya, punk?"
[
  "youve", /* "got", */ /* "to", */ "ask", "yourself", "one", "question",
  /* "do", */ /* "i", */ "feel", "lucky", "well", "ya", "punk"
]

// "Mama always said life was like a box of chocolates. You never know what you're gonna get."
[
  "mama", "always", "said", "life", /* "was", */, "like", /* "a", */ "box", /* "of", */
  "chocolates", "you", "never", "know", /* "what", */ "youre", /* "gonna", */ "get"
]

Tokenizer

Remove stop-words*

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What is a stop word?

Stop words are a set of commonly used words in a language. Examples of stop words in English are “a”, “the”, “is”, “are” and etc. Stop words are commonly used in Text Mining and Natural Language Processing (NLP) to eliminate words that are so commonly used that they carry very little useful information.

https://www.opinosis-analytics.com/knowledge-base/stop-words-explained/

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// "It's alive! It's alive!"
["alive"]

// "You've got to ask yourself one question: 'Do I feel lucky?' Well, do ya, punk?"
[
  "youve", /* "got", */ /* "to", */ "ask", "yourself", "one", "question",
  /* "do", */ /* "i", */ "feel", "lucky", "well", "ya", "punk"
]

// "Mama always said life was like a box of chocolates. You never know what you're gonna get."
[
  "mama", "always", "said", "life", /* "was", */, "like", /* "a", */ "box", /* "of", */
  "chocolates", "you", "never", "know", /* "what", */ "youre", /* "gonna", */ "get"
]

Tokenizer

Remove stop-words*

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// "It's alive! It's alive!"
["alive"]

// "You've got to ask yourself one question: 'Do I feel lucky?' Well, do ya, punk?"
[
  "you" /* was "youve" */, "ask", "yourself", "one", "question",
  "feel", "luck" /* was "lucky" */, "well", /* "ya" becomes "you", duplicate */ "punk"
]

// "Mama always said life was like a box of chocolates. You never know what you're gonna get."
[
  "mom" /* was "mama" */, "always", "say" /* was "said" */, "life", "like", "box", 
  "chocolate" /* was "chocolates" */, "you", "never", "know", /*"you", was "youre", duplicate */, "get"
]

Tokenizer

Stemming*

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Snowball

https://snowballstem.org

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English 🇺🇸🇬🇧🇦🇺

http://snowball.tartarus.org/algorithms/english/stemmer.html

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German 🇩🇪

http://snowball.tartarus.org/algorithms/german/stemmer.html

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Italian 🇮🇹

http://snowball.tartarus.org/algorithms/italian/stemmer.html

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Finnish 🇫🇮

http://snowball.tartarus.org/algorithms/finnish/stemmer.html

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[
  {
    "id": 1,
    "quote": ["alive"],
    ...
  },
  {
    "id": 2,
    "quote": ["you", "ask", "yourself", "one", "question", "feel", "luck", "well", "punk"],
    ...
  },
  {
    "id": 3,
    "quote": ["mom", "always", "say", "life", "like", "box", "chocolate", "you", "never", "know", "get"],
    ...
  }
]

Final Result

Remaining tokens

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How do we want to store this data?

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Find document containing the word "chocolate" in linear time

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Find document containing the word "chocolate" in linear time

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Find document containing the word "chocolate" in linear time

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Find document containing the word "chocolate" in linear time

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Find document containing the word "chocolate" in linear time

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Find document containing the word "chocolate" in linear time

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Find document containing the word "chocolate" in linear time

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Time complexity is O(n)

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animal   = dog
book     = algorithms to live by
color    = green
language = javascript
city     = florence
food     = chocolate

HashMaps are used to store data in key-value pairs

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function hash(key: string, size: number): number {
  let hash = 0;
  
  for (let i = 0; i < key.length; i++) {
    let char = key[i];
    hash = (hash << 5) + char.charCodeAt(0);
    hash = (hash & hash) % size;
  }
  
  return hash;
}

Example of an hashing algorithm

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function hash(key: string, size: number): number {
  let hash = 0;
  
  for (let i = 0; i < key.length; i++) {
    let char = key[i];
    hash = (hash << 5) + char.charCodeAt(0);
    hash = (hash & hash) % size;
  }
  
  return hash;
}

const size = 10;

hash("food", size);           // => 2
hash("book", size);           // => 7
hash("hello, Berlin!", size); // => 9

Example of an hashing algorithm

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When asking for a key, we know the exact position of its value inside of the array.

Hence, time complexity is O(1)

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But that's not enough to find "chocolate" inside of our array of documents in O(1)

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We need an inverted index

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{
  1 => ["alive"],
  2 => ["you", "ask", "yourself", "one", "question", "feel", "luck", "well", "punk"],
  3 => ["mom", "always", "say", "life", "like", "box", "chocolate", "you", "never", "know", "get"],
}

Regular HashMap

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{
  "alive"     => [1],
  "you"       => [2, 3],
  "ask"       => [1],
  "yourself"  => [2],
  "chocolate" => [3],
  "punk"      => [2],
  "one"       => [2],
  "question"  => [2],
  "feel"      => [2],
  "mom"       => [3],
  "always"    => [3],
  "say"       => [3],
  "know"      => [3],
  "luck"      => [2],
  "life"      => [3],
  "like"      => [3],
  "well"      => [2],
  "box"       => [3],
  "never"     => [3],
  "get"       => [3]
}

Inverted Index

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Optimizing space

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{
  "intersect"         => [10,32,12,2,3],
  "interstellar"      => [2,6,20,23,42],
  "intergalactic"     => [12,3,54,29,32],
  "international"     => [32,12,34,64,2],
  "intervene"         => [92,12,42,54,6],
  "internal"          => [102,32,543,6,1],

  "telecommunication" => [91,2,4,23],
  "television"        => [10,8,6,15,3,2],
  "telephone"         => [1,85,14,54,76]
}

Many tokens are sharing a common prefix

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Trees to the rescue!

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Prefix tree

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Private

Primark

Prime

Primate

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We can use a prefix tree as an "inverted index" to store the reference of a token with the document

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"primark" => [1, 3]
"primate" => [2, 4]
"prime"   => [1, 5]
"private" => [2, 6]
"art"     => [4, 5]
"artist"  => [4, 7]

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"primark" => [1, 3]
"primate" => [2, 4]
"prime"   => [1, 5]
"private" => [2, 6]
"art"     => [4, 5]
"artist"  => [4, 7]

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"Talk is cheap! Show me the code!"

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type Nullable<T> = T | null;

type Children = Map<string, TrieNode>;

type Docs = Set<string>;

type NodeContent = [string, Docs];

interface ITrieNode {
  key:       string;
  parent:    Nullable<TrieNode>;
  children:  Nullable<Children>;
  docs:      Docs;
  end:       boolean;
  
  getWord:   ()           => NodeContent;
  removeDoc: (id: string) => boolean;
}

trieNode.ts

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type FindResult = {
  [key: string]: Set<string>; 
}

interface ITrie {
  root:            TrieNode;
  
  insert:          (word: string, docId: string) => void;
  contains:        (word: string)                => boolean;
  find:            (prefix: string)              => FindResult;
  removeDocByWord: (word: string, docId: string) => boolean;
  remove:          (word: string)                => boolean;
}

trie.ts

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class TrieNode implements ITrieNode {
  public key;
  public parent   = null;
  public children = new Map();
  public docs     = new Set();
  public end      = false;
}

trieNode.ts

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class TrieNode implements ITrieNode {
  public key;
  public parent   = null;
  public children = {};
  public docs     = new Set();
  public end      = false;
  
  constructor(key: string) {
    this.key = key;
  }
}

trieNode.ts

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class TrieNode implements ITrieNode {
  public key;
  public parent   = null;
  public children = {};
  public docs     = new Set();
  public end      = false;
  
  constructor(key: string) {
    this.key = key;
  }
  
  getWord(): NodeContent {
    let node: TrieNode = this;
    let output = "";

    while (node !== null) {
      output = node.key + output;
      node = node.parent!;
    }

    return [output, this.docs];
  }
}

trieNode.ts

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class TrieNode implements ITrieNode {
  public key;
  public parent   = null;
  public children = {};
  public docs     = new Set();
  public end      = false;
  
  constructor(key: string) {
    this.key = key;
  }
  
  getWord() {
    let output = "";
    let node = this;
    
    while (node !== null) {
      output = node.key + output;
      node = node.parent!;
    }
    
    return [output, this.docs];
  }
  
  removeDoc(docID: string): boolean {
    return this.docs.delete(docID);
  }
}

trieNode.ts

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TC39 has standardized TCE

(tail-call elimination) with ES6

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class Trie implements ITrie {
  private root = new TrieNode("");
}

trie.ts

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insert(word: string, docId: string): void {
  const wordLength = word.length;
  let node = this.root;

  for (let i = 0; i < wordLength; i++) {
    const char = word[i];

    if (!node.children?.has(char)) {
      const newTrieNode = new TrieNode(char);
      newTrieNode.setParent(node);
      node.children!.set(char, newTrieNode);
    }

    node = node.children!.get(char)!;

    if (i === wordLength - 1) {
      node.setEnd(true);
      node.docs.add(docId);
    }
  }
}

trie.ts

  find(prefix: string): FindResult {
    let node = this.root;
    const output: FindResult = {};

    for (const char of prefix) {
      if (node?.children?.has(char)) {
        node = node.children.get(char)!;
      } else {
        return output;
      }
    }

    findAllWords(node, output);

    function findAllWords(_node: TrieNode, _output: FindResult) {
      if (_node.end) {
        const [word, docIDs] = _node.getWord();

        if (!(word in _output)) {
          _output[word] = new Set();
        }

        if (docIDs?.size) {
          for (const doc of docIDs) {
            _output[word].add(doc);
          }
        }
      }

      for (const childNode of _node.children?.values() ?? []) {
        findAllWords(childNode, _output);
      }
    }

    return output;
  }

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 Tokenizer

 Prefix-tree

❌ Typo-tolerance

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trie.find("wrld");

// Resuls:

[
  {
    id: 1,
    quote: "Hello, World!"
  },
  {
    id: 2,
    quote: "What a wonderful world"
  }
]

Dynamic programming

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Dynamic Programming

An algorithmic technique for solving an optimization problem by breaking it down into simpler subproblems and utilizing the fact that the optimal solution to the overall problem depends upon the optimal solution to its subproblems.

https://educative.io

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Levenshtein distance

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Levenshtein distance

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The Levenshtein algorithm calculates the least number of edit operations that are necessary to modify one string to obtain another string.

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const word1 = "moon";
const word2 = "lions";

levenshtein(word1, word2); // => 3

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Allowed operations

Insert

Delete

Replace

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Edit distance of "Moon" and "Lions"

1)

MOON

LIONS

REPLACE

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Edit distance of "Moon" and "Lions"

1)

MOON

LIONS

REPLACE

2)

LOON

LIONS

REPLACE

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Edit distance of "Moon" and "Lions"

1)

MOON

LIONS

REPLACE

2)

LOON

LIONS

REPLACE

3)

LION

LIONS

INSERT

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Λ L I O N S
Λ
M
O
O
N

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Λ L I O N S
Λ
M
O
O
N

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MO -> L

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1

D(2,2)

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Λ L I O N S
Λ
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N

MOO -> O

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Λ L I O N S
Λ 0
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"" -> ""

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Λ L I O N S
Λ 0 1
M
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N

"" -> "L"

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Λ L I O N S
Λ 0 1 2
M
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"" -> "LI"

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Λ L I O N S
Λ 0 1 2 3
M
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O
N

"" -> "LIO"

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Λ L I O N S
Λ 0 1 2 3 4
M
O
O
N

"" -> "LION"

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Λ L I O N S
Λ 0 1 2 3 4 5
M
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N

"" -> "LIONS"

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Λ L I O N S
Λ 0 1 2 3 4 5
M 1
O
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"M" -> ""

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Λ L I O N S
Λ 0 1 2 3 4 5
M 1
O 2
O
N

"MO" -> ""

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Λ L I O N S
Λ 0 1 2 3 4 5
M 1
O 2
O 3
N

"MOO" -> ""

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Λ L I O N S
Λ 0 1 2 3 4 5
M 1
O 2
O 3
N 4

"MOON" -> ""

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Λ L I O N S
Λ 0 1 2 3 4 5
M 1
O 2
O 3
N 4

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D(2,1)

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Λ L I O N S
Λ 0 1 2 3 4 5
M 1
O 2
O 3
N 4

+1

2

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Λ L I O N S
Λ 0 1 2 3 4 5
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Λ L I O N S
Λ 0 1 2 3 4 5
M 1
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Λ L I O N S
Λ 0 1 2 3 4 5
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N 4

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Λ L I O N S
Λ 0 1 2 3 4 5
M 1 1
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Λ L I O N S
Λ 0 1 2 3 4 5
M 1 1 2 3 4 5
O 2
O 3
N 4

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Λ L I O N S
Λ 0 1 2 3 4 5
M 1 1 2 3 4 5
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O 3
N 4

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Λ L I O N S
Λ 0 1 2 3 4 5
M 1 1 2 3 4 5
O 2 2 2
O 3
N 4

2

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D(4,2) = D(3,1)

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Λ L I O N S
Λ 0 1 2 3 4 5
M 1 1 2 3 4 5
O 2 2 2 2 3 4
O 3 3 3 2 3 4
N 4 4 4 3 2 3

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Λ L I O N S
Λ 0 1 2 3 4 5
M 1 1 2 3 4 5
O 2 2 2 2 3 4
O 3 3 3 2 3 4
N 4 4 4 3 2

3

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Λ L I O N S
Λ 0 1 2 3 4 5
M 1 1 2 3 4 5
O 2 2 2 2 3 4
O 3 3 3 2 3 4
N 4 4 4 3 2

0

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1

2

3

4

5

6

2

3

4

1

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Edit distance of "Moon" and "Lions"

1)

MOON

LIONS

REPLACE

2)

LOON

LIONS

REPLACE

3)

LION

LIONS

INSERT

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Λ P O S E R
Λ 0 1 2 3 4 5
H 1 1 2 3 4 5
O 2 2 1 2 3 4
R 3 3 2 2 3 3
S 4 4 3 2 3 4
E 5 5 4 3 2

Levenshtein distance of Horse - Poser

3

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Levenshtein distance of Race - Raise

Λ R A I S E
Λ 0 1 2 3 4 5
R 1 0 1 2 3 4
I 2 1 0 1 2 3
C 3 2 1 1 2 3
E 4 3 2 2 2

2

MicheleRivaCode

export function levenshtein(a: string, b: string): number {
  if (!a.length) return b.length;
  if (!b.length) return a.length;

  let tmp;

  if (a.length > b.length) {
    tmp = a;
    a = b;
    b = tmp;
  }

  const row = Array.from({ length: a.length + 1 }, (_, i) => i);
  let val = 0;

  for (let i = 1; i <= b.length; i++) {
    let prev = i;

    for (let j = 1; j <= a.length; j++) {
      if (b[i - 1] === a[j - 1]) {
        val = row[j - 1];
      } else {
        val = Math.min(row[j - 1] + 1, Math.min(prev + 1, row[j] + 1));
      }

      row[j - 1] = prev;
      prev = val;
    }
    row[a.length] = prev;
  }

  return row[a.length];
}

We can perform these operations on both strings and trees

MicheleRivaCode

Tree Edit Distance (and Levenshtein Distance)

Simple fast algorithms for the editing distance between trees and related problems

Kaizhong Zhang and Dennis Shasha

https://shorturl.at/otBMY

MicheleRivaCode

MicheleRivaCode

import { Lyra } from '@nearform/lyra';

const db = new Lyra({
  schema: {
    author: 'string',
    quote: 'string'
  }
});

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await db.insert({
  quote: 'It is during our darkest moments that we must focus to see the light.',
  author: 'Aristotle'
});

await db.insert({
  quote: 'If you really look closely, most overnight successes took a long time.',
  author: 'Steve Jobs'
});

await db.insert({
  quote: 'If you are not willing to risk the usual, you will have to settle for the ordinary.',
  author: 'Jim Rohn'
});

await db.insert({
  quote: 'You miss 100% of the shots you don\'t take',
  author: 'Wayne Gretzky - Michael Scott'
});

MicheleRivaCode

const searchResult = await db.search({
  term: 'if',
  properties: ['quote']
});

// Result

{
  elapsed: '99μs',
  hits: [
    {
      id: 'ckAOPGTA5qLXx0MgNr1Zy',
      quote: 'If you really look closely, most overnight successes took a long time.',
      author: 'Steve Jobs'
    },
    {
      id: 'fyl-_1veP78IO-wszP86Z',
      quote: 'If you are not willing to risk the usual, you will have to settle for the ordinary.',
      author: 'Jim Rohn'
    }
  ],
  count: 2
}

MicheleRivaCode

const searchResult = await db.search({
  term: 'Michael',
  properties: '*'
});

// Result

{
  elapsed: '111μs',
  hits: [
    {
      id: 'L1tpqQxc0c2djrSN2a6TJ',
      quote: "You miss 100% of the shots you don't take",
      author: 'Wayne Gretzky - Michael Scott'
    }
  ],
  count: 1
}

MicheleRivaCode

MicheleRivaCode

npm i @nearform/lyra

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MicheleRivaCode

Real-World Next.js

Build scalable, high performances and modern web applications using Next.js, the React framework for production

MicheleRivaCode

MicheleRivaCode

@MicheleRiva

@MicheleRivaCode

/in/MicheleRiva95

www.micheleriva.dev

Building a full-text search engine in TypeScript

By Michele Riva

Building a full-text search engine in TypeScript

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