2018-09-30 22:01:58 +00:00
|
|
|
|
---
|
|
|
|
|
id: 5900f3e61000cf542c50fef9
|
|
|
|
|
challengeType: 5
|
|
|
|
|
title: 'Problem 122: Efficient exponentiation'
|
|
|
|
|
---
|
|
|
|
|
|
|
|
|
|
## Description
|
|
|
|
|
<section id='description'>
|
|
|
|
|
The most naive way of computing n15 requires fourteen multiplications:
|
|
|
|
|
n × n × ... × n = n15
|
|
|
|
|
But using a "binary" method you can compute it in six multiplications:
|
|
|
|
|
n × n = n2n2 × n2 = n4n4 × n4 = n8n8 × n4 = n12n12 × n2 = n14n14 × n = n15
|
|
|
|
|
However it is yet possible to compute it in only five multiplications:
|
|
|
|
|
n × n = n2n2 × n = n3n3 × n3 = n6n6 × n6 = n12n12 × n3 = n15
|
|
|
|
|
We shall define m(k) to be the minimum number of multiplications to compute nk; for example m(15) = 5.
|
|
|
|
|
For 1 ≤ k ≤ 200, find ∑ m(k).
|
|
|
|
|
</section>
|
|
|
|
|
|
|
|
|
|
## Instructions
|
|
|
|
|
<section id='instructions'>
|
|
|
|
|
|
|
|
|
|
</section>
|
|
|
|
|
|
|
|
|
|
## Tests
|
|
|
|
|
<section id='tests'>
|
|
|
|
|
|
|
|
|
|
```yml
|
2018-10-04 13:37:37 +00:00
|
|
|
|
tests:
|
|
|
|
|
- text: <code>euler122()</code> should return 1582.
|
2018-10-20 18:02:47 +00:00
|
|
|
|
testString: assert.strictEqual(euler122(), 1582, '<code>euler122()</code> should return 1582.');
|
2018-09-30 22:01:58 +00:00
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
</section>
|
|
|
|
|
|
|
|
|
|
## Challenge Seed
|
|
|
|
|
<section id='challengeSeed'>
|
|
|
|
|
|
|
|
|
|
<div id='js-seed'>
|
|
|
|
|
|
|
|
|
|
```js
|
|
|
|
|
function euler122() {
|
|
|
|
|
// Good luck!
|
|
|
|
|
return true;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
euler122();
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</section>
|
|
|
|
|
|
|
|
|
|
## Solution
|
|
|
|
|
<section id='solution'>
|
|
|
|
|
|
|
|
|
|
```js
|
|
|
|
|
// solution required
|
|
|
|
|
```
|
2019-07-18 15:24:12 +00:00
|
|
|
|
|
2018-09-30 22:01:58 +00:00
|
|
|
|
</section>
|