95 lines
3.2 KiB
Markdown
95 lines
3.2 KiB
Markdown
---
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title: Equilibrium index
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id: 5987fd532b954e0f21b5d3f6
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challengeType: 5
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---
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## Description
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<section id='description'>
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<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>
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<p>For example, in a sequence <big>$A$</big>:</p><p>:::: <big>$A_0 = -7$</big></p>
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<p>:::: <big>$A_1 = 1$</big></p>
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<p>:::: <big>$A_2 = 5$</big></p>
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<p>:::: <big>$A_3 = 2$</big></p>
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<p>:::: <big>$A_4 = -4$</big></p>
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<p>:::: <big>$A_5 = 3$</big></p>
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<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>
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<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>
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>equilibrium</code> is a function.
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testString: 'assert(typeof equilibrium === "function", "<code>equilibrium</code> is a function.");'
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- text: '<code>equilibrium([-7, 1, 5, 2, -4, 3, 0])</code> should return <code>[3,6]</code>.'
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testString: 'assert.deepEqual(equilibrium(tests[0]), ans[0], "<code>equilibrium([-7, 1, 5, 2, -4, 3, 0])</code> should return <code>[3,6]</code>.");'
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- text: '<code>equilibrium([2, 4, 6])</code> should return <code>[]</code>.'
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testString: 'assert.deepEqual(equilibrium(tests[1]), ans[1], "<code>equilibrium([2, 4, 6])</code> should return <code>[]</code>.");'
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- text: '<code>equilibrium([2, 9, 2])</code> should return <code>[1]</code>.'
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testString: 'assert.deepEqual(equilibrium(tests[2]), ans[2], "<code>equilibrium([2, 9, 2])</code> should return <code>[1]</code>.");'
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- text: '<code>equilibrium([1, -1, 1, -1, 1, -1, 1])</code> should return <code>[0,1,2,3,4,5,6]</code>.'
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testString: 'assert.deepEqual(equilibrium(tests[3]), ans[3], "<code>equilibrium([1, -1, 1, -1, 1, -1, 1])</code> should return <code>[0,1,2,3,4,5,6]</code>.");'
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- text: '<code>equilibrium([1])</code> should return <code>[0]</code>.'
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testString: 'assert.deepEqual(equilibrium(tests[4]), ans[4], "<code>equilibrium([1])</code> should return <code>[0]</code>.");'
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- text: '<code>equilibrium([])</code> should return <code>[]</code>.'
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testString: 'assert.deepEqual(equilibrium(tests[5]), ans[5], "<code>equilibrium([])</code> should return <code>[]</code>.");'
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function equilibrium (a) {
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// Good luck!
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}
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```
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</div>
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### After Test
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<div id='js-teardown'>
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```js
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console.info('after the test');
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function equilibrium(a) {
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let N = a.length,
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i,
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l = [],
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r = [],
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e = [];
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for (l[0] = a[0], r[N - 1] = a[N - 1], i = 1; i < N; i++)
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{ l[i] = l[i - 1] + a[i], r[N - i - 1] = r[N - i] + a[N - i - 1]; }
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for (i = 0; i < N; i++)
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{ if (l[i] === r[i]) e.push(i); }
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return e;
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}
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```
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</section>
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