Karp-Rabin String Matching

Author: tayllan

algorithms/string/karp_rabin.js

@@ -0,0 +1,131 @@
+/**
+ * Copyright (C) 2014 Tayllan Búrigo
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to
+ * deal in the Software without restriction, including without limitation the
+ * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
+ * sell copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
+ * IN THE SOFTWARE.
+ */
+'use strict';
+
+/**
+ * A prime number used to create
+ * the hash representation of a word
+ * 
+ * Bigger the prime number,
+ * bigger the hash value
+ */
+var base = 997;
+
+/**
+ * Calculates String Matching between two Strings
+ * Returns true if String 'b' is contained in String 'a'
+ *
+ * Average and Best Case Complexity: O(a.length + b.length)
+ * Worst Case Complexity: O(a.length * b.length)
+ *
+ * @param String
+ * @param String
+ * @return Boolean
+ */
+var karpRabin = function (a, b) {
+	var aLength = a.length;
+	var bLength = b.length;
+	var hashValue = hashFunction(b);
+	var newString = [];
+	
+	for (var i = 0; i < bLength; i++) {
+		newString.push(a.charAt(i));
+	}
+	
+	var newStringHashValue = hashFunction(newString.join(''));
+	
+	if (hashValue === newStringHashValue && checkEquality(b, newString.join(''))) {
+		return true;
+	}
+	else {
+		for (i = 1; i < aLength; i++) {
+			var previousCharacter = newString[0];
+			var nextCharacter = a.charAt(i);
+			
+			newStringHashValue = reHash(b.length, newStringHashValue, previousCharacter, nextCharacter);
+			newString.shift();
+			newString.push(nextCharacter);
+			
+			if (hashValue === newStringHashValue && checkEquality(b, newString.join(''))) {
+				return true;
+			}
+		}
+		
+		return false;
+	}
+};
+
+/**
+ * Checks if 'a' is equal to 'b'
+ * 
+ * @param String
+ * @param String
+ * @return Boolean
+ */
+var checkEquality = function (a, b) {
+	var aLength = a.length;
+	
+	for (var i = 0; i < aLength; i++) {
+		if (a.charAt(i) !== b.charAt(i)) {
+			return false;
+		}
+	}
+	
+	return true;
+};
+
+/**
+ * Creates the hash representation of 'word'
+ * 
+ * @param String
+ * @return Number
+ */
+var hashFunction = function (word) {
+	var hash = 0;
+	var wordLength = word.length;
+	
+	for (var i = 0, j = wordLength - 1; i < wordLength; i++, j--) {
+		hash += word.charCodeAt(i) * Math.pow(base, j);
+	}
+	
+	return hash;
+};
+
+/**
+ * Recalculates the hash representation of a word so that it isn't
+ * necessary to traverse the whole word again
+ * 
+ * @param Number
+ * @param Number
+ * @param Character
+ * @param Character
+ * @return Number
+ */
+var reHash = function (length, hash, previousCharacter, nextCharacter) {
+	hash -= previousCharacter.charCodeAt(0) * Math.pow(base, length - 1);
+	hash *= base;
+	hash += nextCharacter.charCodeAt(0);
+	
+	return hash;
+};
+
+module.exports = karpRabin;

main.js

@@ -42,7 +42,8 @@ var lib = {
     quicksort: require('./algorithms/sorting/quicksort')
   },
   String: {
-    editDistance: require('./algorithms/string/edit_distance')
+    editDistance: require('./algorithms/string/edit_distance'),
+    karpRabin: require('./algorithms/string/karp_rabin')
   },
   DataStructure: {
     BST: require('./data_structures/bst'),

test/algorithms/string/karp_rabin.js

@@ -0,0 +1,37 @@
+/**
+ * Copyright (C) 2014 Tayllan Búrigo
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to
+ * deal in the Software without restriction, including without limitation the
+ * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
+ * sell copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
+ * IN THE SOFTWARE.
+ */
+'use strict';
+
+var karp_rabin = require('../../../algorithms/string/karp_rabin'),
+	assert = require('assert');
+
+describe('Karp-Rabin', function () {
+  it('should verify if a string is contained in another string',
+    function () {
+      assert.equal(karp_rabin('', ''), true);
+      assert.equal(karp_rabin('a', 'b'), false);
+      assert.equal(karp_rabin('b', 'a'), false);
+      
+      // ' tes' is contained in 'super test'
+      assert.equal(karp_rabin('super test', ' tes'), true);
+    });
+});