Merge pull request #37 from quietshu/master

Extended Euclidean algorithm

Author: felipernb

Diff for: algorithms/math/extended_euclidean.js

@@ -0,0 +1,62 @@
+/**
+ * Copyright (C) 2014 Shu Ding
+ *
+ * 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';
+
+/**
+ * Extended Euclidean algorithm to calculate the solve of 
+ *   ax + by = gcd(a, b)
+ * gcd(a, b) is the greatest common divisor of integers a and b.
+ *
+ * @param Number
+ * @param Number
+ *
+ * @return {Number, Number}
+ */
+var extEuclid = function (a, b) {
+    var s = 0, oldS = 1;
+    var t = 1, oldT = 0;
+    var r = b, oldR = a;
+    var quotient, temp;
+    while (r !== 0) {
+        quotient = Math.floor(oldR / r);
+
+        temp = r;
+        r = oldR - quotient * r;
+        oldR = temp;
+
+        temp = s;
+        s = oldS - quotient * s;
+        oldS = temp;
+
+        temp = t;
+        t = oldT - quotient * t;
+        oldT = temp;
+    }
+
+    return {
+        x: oldS,
+        y: oldT
+    };
+};
+
+module.exports = extEuclid;

Diff for: main.js

@@ -30,7 +30,8 @@ var lib = {
   Math: {
     fibonacci: require('./algorithms/math/fibonacci'),
     fisherYates: require('./algorithms/math/fisher_yates'),
-    gcd: require('./algorithms/math/gcd')
+    gcd: require('./algorithms/math/gcd'),
+    extendedEuclidean: require('./algorithms/math/extended_euclidean')
   },
   Search: {
     bfs: require('./algorithms/searching/bfs'),

Diff for: test/algorithms/math/extended_euclidean.js

@@ -0,0 +1,41 @@
+/**
+ * Copyright (C) 2014 Shu Ding
+ *
+ * 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 extEuclid = require('../../../algorithms/math/extended_euclidean'),
+    assert = require('assert');
+
+describe('extEuclid', function () {
+  it('should calculate the solve to Bézout\'s identity', function () {
+    var solve = extEuclid(1, 0);
+    assert.equal(solve.x, 1);
+    assert.equal(solve.y, 0);
+
+    solve = extEuclid(25, 35);
+    assert.equal(solve.x, 3);
+    assert.equal(solve.y, -2);
+
+    solve = extEuclid(-55, 22);
+    assert.equal(solve.x, 1);
+    assert.equal(solve.y, 3);
+  });
+});