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curriculum/challenges/english/10-coding-interview-prep/rosetta-code/equilibrium-index.md

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+---
+title: Equilibrium index
+id: 5987fd532b954e0f21b5d3f6
+challengeType: 5
+forumTopicId: 302255
+---
+
+## Description
+<section id='description'>
+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.
+For example, in a sequence  <big>$A$</big>:
+<ul style="list-style: none;">
+  <li><big>$A_0 = -7$</big></li>
+  <li><big>$A_1 =  1$</big></li>
+  <li><big>$A_2 =  5$</big></li>
+  <li><big>$A_3 =  2$</big></li>
+  <li><big>$A_4 = -4$</big></li>
+  <li><big>$A_5 =  3$</big></li>
+  <li><big>$A_6 =  0$</big></li>
+</ul>
+<code>3</code> is an equilibrium index, because:
+<ul style="list-style: none;">
+  <li><big>$A_0 + A_1 + A_2 = A_4 + A_5 + A_6$</big></li>
+</ul>
+<code>6</code> is also an equilibrium index, because:
+<ul style="list-style: none;">
+  <li><big>$A_0 + A_1 + A_2 + A_3 + A_4 + A_5 = 0$</big></li>
+</ul>
+(sum of zero elements is zero)
+<code>7</code> is not an equilibrium index, because it is not a valid index of sequence <big>$A$</big>.
+</section>
+
+## Instructions
+<section id='instructions'>
+Write a function that, given a sequence, returns its equilibrium indices (if any).
+Assume that the sequence may be very long.
+</section>
+
+## Tests
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>equilibrium</code> should be a function.
+    testString: assert(typeof equilibrium === '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]);
+  - text: <code>equilibrium([2, 4, 6])</code> should return <code>[]</code>.
+    testString: assert.deepEqual(equilibrium(equilibriumTests[1]), ans[1]);
+  - text: <code>equilibrium([2, 9, 2])</code> should return <code>[1]</code>.
+    testString: assert.deepEqual(equilibrium(equilibriumTests[2]), ans[2]);
+  - 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]);
+  - text: <code>equilibrium([1])</code> should return <code>[0]</code>.
+    testString: assert.deepEqual(equilibrium(equilibriumTests[4]), ans[4]);
+  - text: <code>equilibrium([])</code> should return <code>[]</code>.
+    testString: assert.deepEqual(equilibrium(equilibriumTests[5]), ans[5]);
+
+```
+
+</section>
+
+## Challenge Seed
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function equilibrium(a) {
+
+}
+```
+
+</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>