103 lines
3.5 KiB
Markdown
103 lines
3.5 KiB
Markdown
---
|
|
title: Equilibrium index
|
|
id: 5987fd532b954e0f21b5d3f6
|
|
challengeType: 5
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
<p>An equilibrium index of a sequence is an index into the sequence such that the sum of elements at lower indices is equal to the sum of elements at higher indices.</p>
|
|
<p>For example, in a sequence <big>$A$</big>:</p><p>:::: <big>$A_0 = -7$</big></p>
|
|
<p>:::: <big>$A_1 = 1$</big></p>
|
|
<p>:::: <big>$A_2 = 5$</big></p>
|
|
<p>:::: <big>$A_3 = 2$</big></p>
|
|
<p>:::: <big>$A_4 = -4$</big></p>
|
|
<p>:::: <big>$A_5 = 3$</big></p>
|
|
<p>:::: <big>$A_6 = 0$</big></p><p>3 is an equilibrium index, because:</p><p>:::: <big>$A_0 + A_1 + A_2 = A_4 + A_5 + A_6$</big></p><p>6 is also an equilibrium index, because:</p><p>:::: <big>$A_0 + A_1 + A_2 + A_3 + A_4 + A_5 = 0$</big></p><p>(sum of zero elements is zero)</p><p>7 is not an equilibrium index, because it is not a valid index of sequence <big>$A$</big>.</p>
|
|
<p>Write a function that, given a sequence, returns its equilibrium indices (if any).</p><p>Assume that the sequence may be very long.</p>
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>equilibrium</code> is a function.
|
|
testString: assert(typeof equilibrium === 'function', '<code>equilibrium</code> is a function.');
|
|
- text: <code>equilibrium([-7, 1, 5, 2, -4, 3, 0])</code> should return <code>[3,6]</code>.
|
|
testString: assert.deepEqual(equilibrium(equilibriumTests[0]), ans[0], '<code>equilibrium([-7, 1, 5, 2, -4, 3, 0])</code> should return <code>[3,6]</code>.');
|
|
- text: <code>equilibrium([2, 4, 6])</code> should return <code>[]</code>.
|
|
testString: assert.deepEqual(equilibrium(equilibriumTests[1]), ans[1], '<code>equilibrium([2, 4, 6])</code> should return <code>[]</code>.');
|
|
- text: <code>equilibrium([2, 9, 2])</code> should return <code>[1]</code>.
|
|
testString: assert.deepEqual(equilibrium(equilibriumTests[2]), ans[2], '<code>equilibrium([2, 9, 2])</code> should return <code>[1]</code>.');
|
|
- text: <code>equilibrium([1, -1, 1, -1, 1, -1, 1])</code> should return <code>[0,1,2,3,4,5,6]</code>.
|
|
testString: assert.deepEqual(equilibrium(equilibriumTests[3]), ans[3], '<code>equilibrium([1, -1, 1, -1, 1, -1, 1])</code> should return <code>[0,1,2,3,4,5,6]</code>.');
|
|
- text: <code>equilibrium([1])</code> should return <code>[0]</code>.
|
|
testString: assert.deepEqual(equilibrium(equilibriumTests[4]), ans[4], '<code>equilibrium([1])</code> should return <code>[0]</code>.');
|
|
- text: <code>equilibrium([])</code> should return <code>[]</code>.
|
|
testString: assert.deepEqual(equilibrium(equilibriumTests[5]), ans[5], '<code>equilibrium([])</code> should return <code>[]</code>.');
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function equilibrium (a) {
|
|
// Good luck!
|
|
}
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
### After Test
|
|
<div id='js-teardown'>
|
|
|
|
```js
|
|
const equilibriumTests =
|
|
[[-7, 1, 5, 2, -4, 3, 0], // 3, 6
|
|
[2, 4, 6], // empty
|
|
[2, 9, 2], // 1
|
|
[1, -1, 1, -1, 1, -1, 1], // 0,1,2,3,4,5,6
|
|
[1], // 0
|
|
[] // empty
|
|
];
|
|
const ans = [[3, 6], [], [1], [0, 1, 2, 3, 4, 5, 6], [0], []];
|
|
```
|
|
|
|
</div>
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
|
|
```js
|
|
function equilibrium(a) {
|
|
let N = a.length,
|
|
i,
|
|
l = [],
|
|
r = [],
|
|
e = [];
|
|
for (l[0] = a[0], r[N - 1] = a[N - 1], i = 1; i < N; i++)
|
|
{ l[i] = l[i - 1] + a[i], r[N - i - 1] = r[N - i] + a[N - i - 1]; }
|
|
for (i = 0; i < N; i++)
|
|
{ if (l[i] === r[i]) e.push(i); }
|
|
return e;
|
|
}
|
|
|
|
```
|
|
|
|
</section>
|