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Commit 8676c1b

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HatimLokhandwalatrekhleb
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Adding math algorithm to compute power and its tests (trekhleb#172)
* Adding math algorithm to compute power and its tests * adding more test cases, updating compute power js * Updating ReadMe for power computation algorithm
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# Power(a,b)
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This computes power of (a,b)
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eg: power(2,3) = 8
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power(10,0) = 1
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The algorithm uses divide and conquer approach to compute power.
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Currently the algorithm work for two positive integers X and Y
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Lets say there are two numbers X and Y.
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At each step of the algorithm:
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1. if Y is even
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then power(X, Y/2) * power(X, Y/2) is computed
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2. if Y is odd
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then X * power(X, Y/2) * power(X, Y/2) is computed
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At each step since power(X,Y/2) is called twice, this is optimised by saving the result of power(X, Y/2) in a variable (lets say res).
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And then res is multiplied by self.
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Illustration through example
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power (2,5)
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- 2 * power(2,2) * power(2,2)
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power(2,2)
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- power(2,1) * power(2,1)
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power(2,1)
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- return 2
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Going up the tree once the end values are computed
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power(2,1) = 2
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power(2,2) = power(2,1) * power(2,1) = 2 * 2 = 4
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power(2,5) = 2 * power(2,2) * power(2,2) = 2 * 4 * 4 = 32
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Complexity relation: T(n) = T(n/2) + 1
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Time complexity of the algorithm: O(logn)
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import computePower from '../power';
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describe('computePower', () => {
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it('should compute Power', () => {
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expect(computePower(1, 1)).toBe(1);
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expect(computePower(2, 0)).toBe(1);
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expect(computePower(3, 4)).toBe(81);
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expect(computePower(190, 2)).toBe(36100);
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expect(computePower(16, 16)).toBe(18446744073709552000);
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expect(computePower(100, 9)).toBe(1000000000000000000);
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expect(computePower(9, 16)).toBe(1853020188851841);
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expect(computePower(11, 5)).toBe(161051);
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expect(computePower(13, 11)).toBe(1792160394037);
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expect(computePower(7, 21)).toBe(558545864083284000);
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});
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});
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/**
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* @param {number1} number
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* @param {number2} number
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* @return {number1^number2}
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*/
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// recursive implementation to compute power
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export default function computePower(number1, number2) {
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let val = 0;
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let res = 0;
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if (number2 === 0) { // if number2 is 0
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val = 1;
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} else if (number2 === 1) { // if number2 is 1 return number 1 as it is
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val = number1;
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} else if (number2 % 2 === 0) { // if number2 is even
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res = computePower(number1, number2 / 2);
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val = res * res;
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} else { // if number2 is odd
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res = computePower(number1, Math.floor(number2 / 2));
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val = res * res * number1;
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}
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return val;
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}

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