feat: Implementing Rabin-Karp algorithm for substring search

String/RabinKarp.js

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+/**
+ * Rabin-Karp algorithm for finding all occurrences of a pattern in a text.
+ * It uses hashing to efficiently find substrings.
+ * For More https://en.wikipedia.org/wiki/Rabin%E2%80%93Karp_algorithm
+ *
+ * Time Complexity:
+ * - Average: O(n + m)
+ * - Worst: O(n * m) due to potential hash collisions.
+ *
+ * Space Complexity: O(1) - only uses a fixed number of variables.
+ *
+ * @param {string} haystack - The text to search within.
+ * @param {string} needle - The substring to search for.
+ * @returns {number[]} - An array containing the starting indices of matches.
+ * @throws {RangeError} - If either input is an empty string.
+ *
+ * @example:
+ * const text = "abracadabra";
+ * const pattern = "abra";
+ * const result = rabinKarp(text, pattern);
+ * console.log(result); // Output: [0, 7]
+ *
+ * Explanation:
+ * The pattern "abra" occurs at index 0 and index 7 in the text "abracadabra".
+ *
+ * Here's how the algorithm works:
+ * 1. It computes the hash of the pattern and the hash of the first window of the text.
+ * 2. If the hashes match, it performs a character-by-character comparison to confirm a match.
+ * 3. The algorithm then slides over the text, recalculating the hash for each new window.
+ * 4. It continues until it has checked all possible windows in the text.
+ */
+export function rabinKarp(haystack, needle) {
+  if (!haystack || !needle) {
+    throw new RangeError('Input text and pattern cannot be empty.')
+  }
+
+  const base = 256 // Character set size (extended ASCII)
+  const prime = 101 // Prime number for hash computation
+  const needleLength = needle.length
+  const haystackLength = haystack.length
+  const matches = []
+
+  let needleHash = 0 // Hash value for the pattern
+  let haystackHash = 0 // Hash value for the current window in the text
+  let hashMultiplier = 1
+
+  // Calculate the multiplier used for the leading character in the hash
+  for (let i = 0; i < needleLength - 1; i++) {
+    hashMultiplier = (hashMultiplier * base) % prime
+  }
+
+  // Calculate the initial hash values for the pattern and the first window of the text
+  for (let i = 0; i < needleLength; i++) {
+    needleHash = (base * needleHash + needle.charCodeAt(i)) % prime
+    haystackHash = (base * haystackHash + haystack.charCodeAt(i)) % prime
+  }
+
+  // Slide over the text to check for matches
+  for (let i = 0; i <= haystackLength - needleLength; i++) {
+    // If the hash values match, check for character by character equality
+    if (needleHash === haystackHash) {
+      let j
+      for (j = 0; j < needleLength; j++) {
+        if (haystack[i + j] !== needle[j]) {
+          break
+        }
+      }
+      if (j === needleLength) {
+        matches.push(i) // Pattern found, add index to results
+      }
+    }
+
+    // Calculate the hash value for the next window
+    if (i < haystackLength - needleLength) {
+      haystackHash =
+        (base * (haystackHash - haystack.charCodeAt(i) * hashMultiplier) +
+          haystack.charCodeAt(i + needleLength)) %
+        prime
+
+      // Ensure the hash value is non-negative
+      if (haystackHash < 0) {
+        haystackHash += prime
+      }
+    }
+  }
+
+  return matches
+}

String/test/RabinKarp.test.js

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+import { rabinKarp } from '../RabinKarp'
+
+describe('Rabin-Karp Algorithm', () => {
+  it('should find occurrences of the pattern in the text', () => {
+    const haystack = 'abracadabra'
+    const needle = 'abra'
+    const result = rabinKarp(haystack, needle)
+    expect(result).toEqual([0, 7])
+  })
+
+  it('should return an empty array if the pattern is absent', () => {
+    const haystack = 'hello world'
+    const needle = 'test'
+    const result = rabinKarp(haystack, needle)
+    expect(result).toEqual([])
+  })
+
+  it('should throw RangeError for empty input', () => {
+    expect(() => rabinKarp('', 'pattern')).toThrow(RangeError)
+    expect(() => rabinKarp('text', '')).toThrow(RangeError)
+  })
+
+  it('should return empty for patterns longer than text', () => {
+    const haystack = 'short'
+    const needle = 'longerpattern'
+    const result = rabinKarp(haystack, needle)
+    expect(result).toEqual([])
+  })
+
+  it('should handle single-character patterns', () => {
+    const haystack = 'hello'
+    const needle = 'e'
+    const result = rabinKarp(haystack, needle)
+    expect(result).toEqual([1])
+  })
+})