Refactor Rabin-Karp (#110)

* Simplify Rabin-Karp functionality

* Created Rabin Fingerprinting module within util directory

* Updated Rabin-Karp search to use rolling hash module
Incorporate tests from @dubzzz

Author: Bruce-Feldman

src/algorithms/string/rabin-karp/__test__/rabinKarp.test.js

@@ -1,24 +1,20 @@
-import { rabinKarp, hashWord, reHashWord } from '../rabinKarp';
+import rabinKarp from '../rabinKarp';
 
 describe('rabinKarp', () => {
-  it('should correctly calculates hash and re-hash', () => {
-    expect(hashWord('a')).toBe(97);
-    expect(hashWord('b')).toBe(98);
-    expect(hashWord('abc')).toBe(941094);
-    expect(hashWord('bcd')).toBe(950601);
-    expect(reHashWord(hashWord('abc'), 'abc', 'bcd')).toBe(950601);
-    expect(reHashWord(hashWord('abc'), 'abc', 'bcd')).toBe(hashWord('bcd'));
-  });
-
   it('should find substring in a string', () => {
     expect(rabinKarp('', '')).toBe(0);
     expect(rabinKarp('a', '')).toBe(0);
     expect(rabinKarp('a', 'a')).toBe(0);
+    expect(rabinKarp('ab', 'b')).toBe(1);
     expect(rabinKarp('abcbcglx', 'abca')).toBe(-1);
     expect(rabinKarp('abcbcglx', 'bcgl')).toBe(3);
     expect(rabinKarp('abcxabcdabxabcdabcdabcy', 'abcdabcy')).toBe(15);
     expect(rabinKarp('abcxabcdabxabcdabcdabcy', 'abcdabca')).toBe(-1);
     expect(rabinKarp('abcxabcdabxaabcdabcabcdabcdabcy', 'abcdabca')).toBe(12);
     expect(rabinKarp('abcxabcdabxaabaabaaaabcdabcdabcy', 'aabaabaaa')).toBe(11);
+    expect(rabinKarp('^ !/\'#\'pp', ' !/\'#\'pp')).toBe(1);
+    expect(rabinKarp('a\u{ffff}', '\u{ffff}')).toBe(1);
+    expect(rabinKarp('a\u{10000}', '\u{10000}')).toBe(1);
+    expect(rabinKarp('\u0000耀\u0000', '耀\u0000')).toBe(1);
   });
 });

src/algorithms/string/rabin-karp/rabinKarp.js

@@ -1,88 +1,33 @@
-/**
- * A prime number used to create
- * the hash representation of a word
- *
- * Bigger the prime number,
- * bigger the hash value
- */
-const PRIME = 97;
-
-/**
- * Function that creates hash representation of the word.
- *
- * @param {string} word
- * @return {number}
- */
-export function hashWord(word) {
-  let hash = 0;
-
-  for (let charIndex = 0; charIndex < word.length; charIndex += 1) {
-    hash += word[charIndex].charCodeAt(0) * (PRIME ** charIndex);
-  }
-
-  return hash;
-}
-
-/**
- * Function that creates hash representation of the word
- * based on previous word (shifted by one character left) hash value.
- *
- * Recalculates the hash representation of a word so that it isn't
- * necessary to traverse the whole word again
- *
- * @param {number} prevHash
- * @param {string} prevWord
- * @param {string} newWord
- * @return {number}
- */
-export function reHashWord(prevHash, prevWord, newWord) {
-  const newWordLastIndex = newWord.length - 1;
-  let newHash = prevHash - prevWord[0].charCodeAt(0);
-  newHash /= PRIME;
-  newHash += newWord[newWordLastIndex].charCodeAt(0) * (PRIME ** newWordLastIndex);
-
-  return newHash;
-}
+import RabinFingerprint from '../../../utils/hash/rolling/Rabin_Fingerprint';
 
 /**
  * @param {string} text
  * @param {string} word
  * @return {number}
  */
-export function rabinKarp(text, word) {
-  // Calculate word hash that we will use for comparison with other substring hashes.
-  const wordHash = hashWord(word);
-
-  let prevSegment = null;
-  let currentSegmentHash = null;
-
-  // Go through all substring of the text that may match
-  for (let charIndex = 0; charIndex <= text.length - word.length; charIndex += 1) {
-    const currentSegment = text.substring(charIndex, charIndex + word.length);
-
-    // Calculate the hash of current substring.
-    if (currentSegmentHash === null) {
-      currentSegmentHash = hashWord(currentSegment);
-    } else {
-      currentSegmentHash = reHashWord(currentSegmentHash, prevSegment, currentSegment);
-    }
-
-    prevSegment = currentSegment;
-
-    // Compare the hash of current substring and seeking string.
-    if (wordHash === currentSegmentHash) {
-      // In case if hashes match let's check substring char by char.
-      let numberOfMatches = 0;
-
-      for (let deepCharIndex = 0; deepCharIndex < word.length; deepCharIndex += 1) {
-        if (word[deepCharIndex] === text[charIndex + deepCharIndex]) {
-          numberOfMatches += 1;
-        }
-      }
+export default function rabinKarp(text, word) {
+  const toNum = function toNum(character) {
+    const surrogate = character.codePointAt(1);
+    return ((surrogate === undefined) ? 0 : surrogate) + (character.codePointAt(0) * (2 ** 16));
+  };
+  const arrEq = (a1, a2) => ((a1.length === a2.length) && a1.every((val, idx) => val === a2[idx]));
+
+  const wordArr = [...word].map(toNum);
+  const textArr = [...text].map(toNum);
+
+  // The prime generation function could depend on the inputs for collision guarantees.
+  const hasher = new RabinFingerprint(() => 229);
+  const cmpVal = hasher.init(wordArr);
+
+  let currHash = hasher.init(textArr.slice(0, wordArr.length));
+  if ((currHash === cmpVal) && arrEq(wordArr, textArr.slice(0, wordArr.length))) {
+    return 0;
+  }
 
-      if (numberOfMatches === word.length) {
-        return charIndex;
-      }
+  for (let i = 0; i < (textArr.length - wordArr.length); i += 1) {
+    currHash = hasher.roll(textArr[i], textArr[i + wordArr.length]);
+    if ((currHash === cmpVal) && arrEq(wordArr, textArr.slice(i + 1, i + wordArr.length + 1))) {
+      return i + 1;
     }
   }
 

src/utils/hash/rolling/Rabin_Fingerprint.js

@@ -0,0 +1,51 @@
+/**
+ * Generates fingerprints using Rabin scheme with x = 2 (for potential compiler optimizations).
+ * Guaranteed not to over or underflow if function assumptions are met.
+ */
+export default class RabinFingerprint {
+  /**
+   * @param { function() : number } [primeGenerator]
+   * @assumes Output from any function call is prime less than Number.MAX_SAFE_INTEGER / 2.
+   */
+  constructor(primeGenerator) {
+    this.prime = primeGenerator();
+  }
+
+  /**
+   * @param { array[number] } [values]
+   * @returns {number} - The hash value after digesting input.
+   * @assumes All array elements are non-negative.
+   * @note First element in array is considered to be oldest value.
+   */
+  init(values) {
+    this.val = 0;
+    this.len = values.length;
+
+    for (let i = 0; i < values.length; i += 1) {
+      this.val = (((this.val * 2) % this.prime) + (values[i] % this.prime)) % this.prime;
+    }
+
+    return this.val;
+  }
+
+  /*
+   * @param {number} [oldValue]
+   * @param {number} [newValue]
+   * @returns {number} - The hash value after removing the oldest value & inserting the newest.
+   * @assumes Instance has already been initialized.
+   * @assumes oldValue is the oldest value still processed by the hash.
+   * @assumes newValue is non-negative.
+   */
+  roll(oldValue, newValue) {
+    let oldVal = oldValue % this.prime;
+    for (let i = 1; i < this.len; i += 1) {
+      oldVal = (oldVal * 2) % this.prime;
+    }
+    this.val = (this.val + this.prime - (oldVal % this.prime)) % this.prime;
+
+    const newVal = newValue % this.prime;
+    this.val = (((this.val * 2) % this.prime) + (newVal % this.prime)) % this.prime;
+
+    return this.val;
+  }
+}

src/utils/hash/rolling/__test__/Rabin_Fingerprint.test.js

@@ -0,0 +1,59 @@
+import RabinFingerprint from '../Rabin_Fingerprint';
+
+describe('Rabin fingerprint Hash Family', () => {
+  it('should hash deterministically', () => {
+    const primeVals = [3, 5, 19, 53, 97, 401, 7039, 193939];
+    for (let primeIdx = 0; primeIdx < primeVals.length; primeIdx += 1) {
+      const primeVal = primeVals[primeIdx];
+      const hasher = new RabinFingerprint(() => primeVal);
+
+      // Test basic values
+      expect(hasher.init([])).toEqual(0);
+      expect(hasher.init([1])).toEqual(1);
+
+      // Test overflow
+      const largeVal = Number.MAX_SAFE_INTEGER;
+      expect(hasher.init([primeVal])).toEqual(0);
+      expect(hasher.init([largeVal])).toEqual(largeVal % primeVal);
+
+      const numLargeVal = 2; // 2 ^ numLargeVal fits in javascript number
+      const largeValues = new Array(numLargeVal).fill(largeVal);
+
+      const expVal = ((largeVal % primeVal) * ((2 ** numLargeVal) - 1)) % primeVal;
+      expect(hasher.init(largeValues)).toEqual(expVal);
+
+      // Test using Fermat's little theorem
+      const fermatValues = new Array(primeVal).fill(primeVal);
+      const numFermatTests = 100;
+      for (let i = 0; i < numFermatTests; i += 1) {
+        const randomValue = Math.floor(Math.random() * largeVal);
+        fermatValues[0] = randomValue;
+        expect(hasher.init(fermatValues)).toEqual(randomValue % primeVal);
+      }
+    }
+  });
+
+  it('should roll appropriately', () => {
+    const primeVals = [3, 5, 19, 53, 97, 401, 7039, 193939];
+
+    for (let primeIdx = 0; primeIdx < primeVals.length; primeIdx += 1) {
+      const primeVal = primeVals[primeIdx];
+      const hasher = new RabinFingerprint(() => primeVal);
+
+      // Test basic values
+      const largeVal = Number.MAX_SAFE_INTEGER;
+      expect(hasher.init([0])).toEqual(0);
+      expect(hasher.roll(0, 1)).toEqual(1);
+      expect(hasher.roll(1, primeVal)).toEqual(0);
+      expect(hasher.roll(primeVal, largeVal)).toEqual(largeVal % primeVal);
+
+      const numRollTest = 100;
+      let previousValue = largeVal;
+      for (let i = 0; i < numRollTest; i += 1) {
+        const randomVal = Math.floor(Math.random() * largeVal);
+        expect(hasher.roll(previousValue, randomVal)).toEqual(randomVal % primeVal);
+        previousValue = randomVal;
+      }
+    }
+  });
+});