Polynomial Hash

Author: prasad-chavan1

Hashes/PolynomialHash.js

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+/**
+ * Polynomial Hash also known as Polynomial rolling hash function.
+ *
+ * Polynomial rolling hash function is a hash function that uses only multiplications and additions. 
+ * 
+ *
+ * NOTE: If two strings are equal, their hash values should also be equal. But the inverse need not be true.
+ *
+ * Wikipedia: https://en.wikipedia.org/wiki/Rolling_hash
+ */
+const DEFAULT_BASE = 37;
+const DEFAULT_MODULUS = 101;
+
+export default class PolynomialHash {
+    /**
+     * @param {number} [base] - Base number that is used to create the polynomial.
+     * @param {number} [modulus] - Modulus number that keeps the hash from overflowing.
+     */
+    constructor({ base = DEFAULT_BASE, modulus = DEFAULT_MODULUS } = {}) {
+        this.base = base;
+        this.modulus = modulus;
+    }
+
+    /**
+     * Function that creates hash representation of the word.
+     *
+     * Time complexity: O(word.length).
+     *
+     * @param {string} word - String that needs to be hashed.
+     * @return {number}
+     */
+    hash(word) {
+        const charCodes = Array.from(word).map((char) => this.charToNumber(char));
+
+        let hash = 0;
+        for (let charIndex = 0; charIndex < charCodes.length; charIndex += 1) {
+            hash *= this.base;
+            hash += charCodes[charIndex];
+            hash %= this.modulus;
+        }
+
+        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.
+     *
+     * Time complexity: O(1).
+     *
+     * @param {number} prevHash
+     * @param {string} prevWord
+     * @param {string} newWord
+     * @return {number}
+     */
+    roll(prevHash, prevWord, newWord) {
+        let hash = prevHash;
+
+        const prevValue = this.charToNumber(prevWord[0]);
+        const newValue = this.charToNumber(newWord[newWord.length - 1]);
+
+        let prevValueMultiplier = 1;
+        for (let i = 1; i < prevWord.length; i += 1) {
+            prevValueMultiplier *= this.base;
+            prevValueMultiplier %= this.modulus;
+        }
+
+        hash += this.modulus;
+        hash -= (prevValue * prevValueMultiplier) % this.modulus;
+
+        hash *= this.base;
+        hash += newValue;
+        hash %= this.modulus;
+
+        return hash;
+    }
+
+    /**
+     * Converts char to number.
+     *
+     * @param {string} char
+     * @return {number}
+     */
+    charToNumber(char) {
+        let charCode = char.codePointAt(0);
+
+        // Check if character has surrogate pair.
+        const surrogate = char.codePointAt(1);
+        if (surrogate !== undefined) {
+            const surrogateShift = 2 ** 16;
+            charCode += surrogate * surrogateShift;
+        }
+
+        return charCode;
+    }
+}

Hashes/test/PolynomialHash.test.js

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+import PolynomialHash from '../PolynomialHash';
+
+describe('PolynomialHash', () => {
+    it('should calculate new hash based on previous one', () => {
+        const bases = [3, 79, 101, 3251, 13229, 122743, 3583213];
+        const mods = [79, 101];
+        const frameSizes = [5, 20];
+
+        // @TODO: Provide Unicode support.
+        const text = 'Lorem Ipsum is simply dummy text of the printing and '
+            + 'typesetting industry. Lorem Ipsum has been the industry\'s standard '
+            + 'galley of type and \u{ffff} scrambled it to make a type specimen book. It '
+            + 'electronic 耀 typesetting, remaining essentially unchanged. It was '
+            // + 'popularised in the \u{20005} \u{20000}1960s with the release of Letraset sheets '
+            + 'publishing software like Aldus PageMaker 耀 including versions of Lorem.';
+
+        // Check hashing for different prime base.
+        bases.forEach((base) => {
+            mods.forEach((modulus) => {
+                const polynomialHash = new PolynomialHash({ base, modulus });
+
+                // Check hashing for different word lengths.
+                frameSizes.forEach((frameSize) => {
+                    let previousWord = text.substr(0, frameSize);
+                    let previousHash = polynomialHash.hash(previousWord);
+
+                    // Shift frame through the whole text.
+                    for (let frameShift = 1; frameShift < (text.length - frameSize); frameShift += 1) {
+                        const currentWord = text.substr(frameShift, frameSize);
+                        const currentHash = polynomialHash.hash(currentWord);
+                        const currentRollingHash = polynomialHash.roll(previousHash, previousWord, currentWord);
+
+                        // Check that rolling hash is the same as directly calculated hash.
+                        expect(currentRollingHash).toBe(currentHash);
+
+                        previousWord = currentWord;
+                        previousHash = currentHash;
+                    }
+                });
+            });
+        });
+    });
+
+    it('should generate numeric hashed less than 100', () => {
+        const polynomialHash = new PolynomialHash({ modulus: 100 });
+
+        expect(polynomialHash.hash('Some long text that is used as a key')).toBe(41);
+        expect(polynomialHash.hash('Test')).toBe(92);
+        expect(polynomialHash.hash('a')).toBe(97);
+        expect(polynomialHash.hash('b')).toBe(98);
+        expect(polynomialHash.hash('c')).toBe(99);
+        expect(polynomialHash.hash('d')).toBe(0);
+        expect(polynomialHash.hash('e')).toBe(1);
+        expect(polynomialHash.hash('ab')).toBe(87);
+
+        // @TODO: Provide Unicode support.
+        expect(polynomialHash.hash('\u{20000}')).toBe(92);
+    });
+});