Merge pull request felipernb#118 from argonlaser/master

Added findDivisors

Author: felipernb

README.md

@@ -88,6 +88,7 @@ require('algorithms').Math;
 * extendedEuclidean
 * fastPower
 * fibonacci
+* findDivisors
 * fisherYates
 * gcd (Greatest common divisor)
 * greatestDifference

src/algorithms/math/find_divisors.js

@@ -0,0 +1,91 @@
+'use strict';
+
+/**
+ * Different implementations for finding the divisors
+ */
+
+/**
+ * Find all the divisors of a natural number
+ * This solution has a cost of O(n)
+ * This solution uses the naive method to print all divisors
+ *
+ * @param {number}
+ * @returns {number[]} - returns the divisors
+ */
+
+var findDivisorsGeneric = function(number) {
+  var index = 1;
+  var divisors = [];
+
+  for (index; index <= number; index++) {
+    if (number % index === 0) {
+      divisors.push(index);
+    }
+  }
+  return divisors;
+};
+
+/**
+ * Find all the divisors of a natural number
+ * This solution has a cost of O(sqrt(n))
+ * This method returns the divisors in an unsorted manner.
+ * All divisors of a number are present in pairs.
+ * Eg : For n=16: (1, 16), (2, 8), (4, 4). Include only one of the repeated divisors if any.
+ *
+ * @param {number}
+ * @returns {number[]} - returns the divisors
+ */
+
+var findDivisorsByPairingUnsorted = function(number) {
+  var index = 1;
+  var divisors = [];
+
+  for (index; index <= Math.sqrt(number); index++) {
+    if (number % index === 0) {
+      if (number / index === index)
+        divisors.push(index);
+      else {
+        divisors.push(index);
+        divisors.push(number / index);
+      }
+    }
+  }
+  return divisors;
+};
+
+/**
+ * Find all the divisors of a natural number
+ * This solution has a cost of O(sqrt(n))
+ * This method returns the array in a sorted manner
+ * All divisors of a number are present in pairs (divisorLessThanSqrt, divisorGreaterThanSqrt)
+ * Reverse the divisorGreaterThanSqrt array and append to divisorLessThanSqrt to sort the result
+ * Eg : For n=16: (1, 16), (2, 8), (4, 4). Include only one of the repeated divisors if any
+ *
+ * @param {number}
+ * @returns {number[]} - returns the divisors
+ */
+
+var findDivisorsByPairingSorted = function(number) {
+  var index = 1;
+  var divisors = [];
+  var divisorsLessThanSqrt = [];
+  var divisorsMoreThanSqrt = [];
+
+  for (index; index <= Math.sqrt(number); index++) {
+    if (number % index === 0) {
+      if (number / index === index)
+        divisorsLessThanSqrt.push(index);
+      else {
+        divisorsLessThanSqrt.push(index);
+        divisorsMoreThanSqrt.push(number / index);
+      }
+    }
+  }
+  divisors = divisorsLessThanSqrt.concat(divisorsMoreThanSqrt.reverse());
+  return divisors;
+};
+
+// Use findDivisorsGeneric as the default implementation
+findDivisorsGeneric.pairingUnsorted = findDivisorsByPairingUnsorted;
+findDivisorsGeneric.pairingSorted = findDivisorsByPairingSorted;
+module.exports = findDivisorsGeneric;

src/math.js

@@ -15,5 +15,6 @@ module.exports = {
   powerSet: require('./algorithms/math/power_set'),
   shannonEntropy: require('./algorithms/math/shannon_entropy'),
   collatzConjecture: require('./algorithms/math/collatz_conjecture'),
-  greatestDifference: require('./algorithms/math/greatest_difference')
+  greatestDifference: require('./algorithms/math/greatest_difference'),
+  findDivisors: require('./algorithms/math/find_divisors')
 };

src/test/algorithms/math/find_divisors.js

@@ -0,0 +1,52 @@
+'use strict';
+
+var math = require('../../..').Math;
+var findDivisors = math.findDivisors;
+var assert = require('assert');
+
+/**
+ * Deep equal for arrays
+ */
+function testArrayEqual(a, b) {
+  var arrayEqual = true;
+  a.sort();
+  b.sort();
+  a.forEach(function(elem, index) {
+    if (a[index] !== b[index]) {
+      arrayEqual = false;
+    }
+  });
+  return arrayEqual && a.length === b.length;
+}
+
+var testFindDivisors = function(findDivisors) {
+  assert(testArrayEqual([], findDivisors(-2)));
+  assert(testArrayEqual([], findDivisors(0)));
+  assert(testArrayEqual([1], findDivisors(1)));
+  assert(testArrayEqual([1, 2], findDivisors(2)));
+  assert(testArrayEqual([1, 3], findDivisors(3)));
+  assert(testArrayEqual([1, 2, 4], findDivisors(4)));
+  assert(testArrayEqual([1, 5], findDivisors(5)));
+  assert(testArrayEqual([1, 2, 4, 5, 10, 20, 25, 50, 100], findDivisors(100)));
+  assert(testArrayEqual([1, 2, 7, 13, 14, 26, 91, 182], findDivisors(182)));
+};
+
+describe('Find divisors', function() {
+  describe('#Generic()', function() {
+    it('should return the divisors of the number', function() {
+      testFindDivisors(findDivisors);
+    });
+  });
+
+  describe('#PairingUnsorted()', function() {
+    it('should return the divisors of the number', function() {
+      testFindDivisors(findDivisors.pairingUnsorted);
+    });
+  });
+
+  describe('#PairingSorted()', function() {
+    it('should return the divisors of the number', function() {
+      testFindDivisors(findDivisors.pairingSorted);
+    });
+  });
+});