Add isPowerOfTwo functions.

Author: trekhleb

README.md

@@ -50,6 +50,7 @@ a set of rules that precisely define a sequence of operations.
   * [Least Common Multiple](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/least-common-multiple) (LCM)
   * [Integer Partition](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/integer-partition)
   * [Sieve of Eratosthenes](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/sieve-of-eratosthenes) - finding all prime numbers up to any given limit
+  * [Is Power of Two](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/is-power-of-two) - check if the number is power of two (naive and bitwise algorithms)
 * **Sets**
   * [Cartesian Product](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/cartesian-product) - product of multiple sets
   * [Power Set](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/power-set) - all subsets of a set

src/algorithms/math/is-power-of-two/README.md

@@ -0,0 +1,52 @@
+# Is a power of two
+
+Given a positive integer, write a function to find if it is 
+a power of two or not.
+
+**Naive solution**
+
+In naive solution we just keep dividing the number by two
+unless the number becomes `1` and every time we do so we
+check that remainder after division is always `0`. Otherwise
+the number can't be a power of two.
+
+**Bitwise solution**
+
+Powers of two in binary form always have just one bit.
+The only exception is with a signed integer (e.g. an 8-bit
+signed integer with a value of -128 looks like: `10000000`)
+
+```
+1: 0001
+2: 0010
+4: 0100
+8: 1000
+```
+
+So after checking that the number is greater than zero, 
+we can use a bitwise hack to test that one and only one 
+bit is set.
+
+```
+number & (number - 1)
+```
+
+For example for number `8` that operations will look like:
+
+```
+  1000
+- 0001
+  ----
+  0111
+  
+  1000
+& 0111
+  ----
+  0000    
+```
+
+## References
+
+- [GeeksForGeeks](https://www.geeksforgeeks.org/program-to-find-whether-a-no-is-power-of-two/)
+- [Bitwise Solution on Stanford](http://www.graphics.stanford.edu/~seander/bithacks.html#DetermineIfPowerOf2)
+- [Binary number subtraction on YouTube](https://www.youtube.com/watch?v=S9LJknZTyos&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=66)

src/algorithms/math/is-power-of-two/__test__/isPowerOfTwo.test.js

@@ -0,0 +1,30 @@
+import isPowerOfTwo from '../isPowerOfTwo';
+
+describe('isPowerOfTwo', () => {
+  it('should throw an exception when trying to apply function to negative number', () => {
+    const isNegativePowerOfTwo = () => {
+      isPowerOfTwo(-1);
+    };
+
+    expect(isNegativePowerOfTwo).toThrowError();
+  });
+
+  it('should check if the number is made by multiplying twos', () => {
+    expect(isPowerOfTwo(0)).toBeFalsy();
+    expect(isPowerOfTwo(1)).toBeFalsy();
+    expect(isPowerOfTwo(2)).toBeTruthy();
+    expect(isPowerOfTwo(3)).toBeFalsy();
+    expect(isPowerOfTwo(4)).toBeTruthy();
+    expect(isPowerOfTwo(5)).toBeFalsy();
+    expect(isPowerOfTwo(6)).toBeFalsy();
+    expect(isPowerOfTwo(7)).toBeFalsy();
+    expect(isPowerOfTwo(8)).toBeTruthy();
+    expect(isPowerOfTwo(10)).toBeFalsy();
+    expect(isPowerOfTwo(12)).toBeFalsy();
+    expect(isPowerOfTwo(16)).toBeTruthy();
+    expect(isPowerOfTwo(31)).toBeFalsy();
+    expect(isPowerOfTwo(64)).toBeTruthy();
+    expect(isPowerOfTwo(1024)).toBeTruthy();
+    expect(isPowerOfTwo(1023)).toBeFalsy();
+  });
+});

src/algorithms/math/is-power-of-two/__test__/isPowerOfTwoBitwise.test.js

@@ -0,0 +1,30 @@
+import isPowerOfTwoBitwise from '../isPowerOfTwoBitwise';
+
+describe('isPowerOfTwoBitwise', () => {
+  it('should throw an exception when trying to apply function to negative number', () => {
+    const isNegativePowerOfTwo = () => {
+      isPowerOfTwoBitwise(-1);
+    };
+
+    expect(isNegativePowerOfTwo).toThrowError();
+  });
+
+  it('should check if the number is made by multiplying twos', () => {
+    expect(isPowerOfTwoBitwise(0)).toBeFalsy();
+    expect(isPowerOfTwoBitwise(1)).toBeFalsy();
+    expect(isPowerOfTwoBitwise(2)).toBeTruthy();
+    expect(isPowerOfTwoBitwise(3)).toBeFalsy();
+    expect(isPowerOfTwoBitwise(4)).toBeTruthy();
+    expect(isPowerOfTwoBitwise(5)).toBeFalsy();
+    expect(isPowerOfTwoBitwise(6)).toBeFalsy();
+    expect(isPowerOfTwoBitwise(7)).toBeFalsy();
+    expect(isPowerOfTwoBitwise(8)).toBeTruthy();
+    expect(isPowerOfTwoBitwise(10)).toBeFalsy();
+    expect(isPowerOfTwoBitwise(12)).toBeFalsy();
+    expect(isPowerOfTwoBitwise(16)).toBeTruthy();
+    expect(isPowerOfTwoBitwise(31)).toBeFalsy();
+    expect(isPowerOfTwoBitwise(64)).toBeTruthy();
+    expect(isPowerOfTwoBitwise(1024)).toBeTruthy();
+    expect(isPowerOfTwoBitwise(1023)).toBeFalsy();
+  });
+});

src/algorithms/math/is-power-of-two/isPowerOfTwo.js

@@ -0,0 +1,30 @@
+/**
+ * @param {number} number
+ * @return {boolean}
+ */
+export default function isPowerOfTwo(number) {
+  // Don't work with negative numbers.
+  if (number < 0) {
+    throw new Error('Please provide positive number');
+  }
+
+  // 0 and 1 are not powers of two.
+  if (number <= 1) {
+    return false;
+  }
+
+  // Let's find out if we can divide the number by two
+  // many times without remainder.
+  let dividedNumber = number;
+  while (dividedNumber !== 1) {
+    if (dividedNumber % 2 !== 0) {
+      // For every case when remainder isn't zero we can say that this number
+      // couldn't be a result of power of two.
+      return false;
+    }
+
+    dividedNumber /= 2;
+  }
+
+  return true;
+}

src/algorithms/math/is-power-of-two/isPowerOfTwoBitwise.js

@@ -0,0 +1,31 @@
+/**
+ * @param {number} number
+ * @return {boolean}
+ */
+export default function isPowerOfTwoBitwise(number) {
+  // Don't work with negative numbers.
+  if (number < 0) {
+    throw new Error('Please provide positive number');
+  }
+
+  // 0 and 1 are not powers of two.
+  if (number <= 1) {
+    return false;
+  }
+
+  /*
+   * Powers of two in binary look like this:
+   * 1: 0001
+   * 2: 0010
+   * 4: 0100
+   * 8: 1000
+   *
+   * Note that there is always exactly 1 bit set. The only exception is with a signed integer.
+   * e.g. An 8-bit signed integer with a value of -128 looks like:
+   * 10000000
+   *
+   * So after checking that the number is greater than zero, we can use a clever little bit
+   * hack to test that one and only one bit is set.
+   */
+  return (number & (number - 1)) === 0;
+}