mirror of
https://github.moeyy.xyz/https://github.com/trekhleb/javascript-algorithms.git
synced 2024-11-10 11:09:43 +08:00
Adding math algorithm to compute power and its tests (#172)
* Adding math algorithm to compute power and its tests * adding more test cases, updating compute power js * Updating ReadMe for power computation algorithm
This commit is contained in:
parent
518dc57388
commit
8676c1b9fe
35
src/algorithms/math/compute-power/README.md
Normal file
35
src/algorithms/math/compute-power/README.md
Normal file
@ -0,0 +1,35 @@
|
||||
# Power(a,b)
|
||||
|
||||
This computes power of (a,b)
|
||||
eg: power(2,3) = 8
|
||||
power(10,0) = 1
|
||||
|
||||
The algorithm uses divide and conquer approach to compute power.
|
||||
Currently the algorithm work for two positive integers X and Y
|
||||
Lets say there are two numbers X and Y.
|
||||
At each step of the algorithm:
|
||||
1. if Y is even
|
||||
then power(X, Y/2) * power(X, Y/2) is computed
|
||||
2. if Y is odd
|
||||
then X * power(X, Y/2) * power(X, Y/2) is computed
|
||||
|
||||
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).
|
||||
And then res is multiplied by self.
|
||||
|
||||
Illustration through example
|
||||
power (2,5)
|
||||
- 2 * power(2,2) * power(2,2)
|
||||
power(2,2)
|
||||
- power(2,1) * power(2,1)
|
||||
power(2,1)
|
||||
- return 2
|
||||
|
||||
Going up the tree once the end values are computed
|
||||
power(2,1) = 2
|
||||
power(2,2) = power(2,1) * power(2,1) = 2 * 2 = 4
|
||||
power(2,5) = 2 * power(2,2) * power(2,2) = 2 * 4 * 4 = 32
|
||||
|
||||
|
||||
Complexity relation: T(n) = T(n/2) + 1
|
||||
|
||||
Time complexity of the algorithm: O(logn)
|
@ -0,0 +1,16 @@
|
||||
import computePower from '../power';
|
||||
|
||||
describe('computePower', () => {
|
||||
it('should compute Power', () => {
|
||||
expect(computePower(1, 1)).toBe(1);
|
||||
expect(computePower(2, 0)).toBe(1);
|
||||
expect(computePower(3, 4)).toBe(81);
|
||||
expect(computePower(190, 2)).toBe(36100);
|
||||
expect(computePower(16, 16)).toBe(18446744073709552000);
|
||||
expect(computePower(100, 9)).toBe(1000000000000000000);
|
||||
expect(computePower(9, 16)).toBe(1853020188851841);
|
||||
expect(computePower(11, 5)).toBe(161051);
|
||||
expect(computePower(13, 11)).toBe(1792160394037);
|
||||
expect(computePower(7, 21)).toBe(558545864083284000);
|
||||
});
|
||||
});
|
23
src/algorithms/math/compute-power/power.js
Normal file
23
src/algorithms/math/compute-power/power.js
Normal file
@ -0,0 +1,23 @@
|
||||
/**
|
||||
* @param {number1} number
|
||||
* @param {number2} number
|
||||
* @return {number1^number2}
|
||||
*/
|
||||
|
||||
// recursive implementation to compute power
|
||||
export default function computePower(number1, number2) {
|
||||
let val = 0;
|
||||
let res = 0;
|
||||
if (number2 === 0) { // if number2 is 0
|
||||
val = 1;
|
||||
} else if (number2 === 1) { // if number2 is 1 return number 1 as it is
|
||||
val = number1;
|
||||
} else if (number2 % 2 === 0) { // if number2 is even
|
||||
res = computePower(number1, number2 / 2);
|
||||
val = res * res;
|
||||
} else { // if number2 is odd
|
||||
res = computePower(number1, Math.floor(number2 / 2));
|
||||
val = res * res * number1;
|
||||
}
|
||||
return val;
|
||||
}
|
Loading…
Reference in New Issue
Block a user