131 lines
2.6 KiB
Markdown
131 lines
2.6 KiB
Markdown
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---
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id: 5987fd532b954e0f21b5d3f6
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title: Equilibrium index
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challengeType: 5
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forumTopicId: 302255
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dashedName: equilibrium-index
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---
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# --description--
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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.
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For example, in a sequence $A$:
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<ul style='list-style: none;'>
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<li><big>$A_0 = -7$</big></li>
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<li><big>$A_1 = 1$</big></li>
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<li><big>$A_2 = 5$</big></li>
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<li><big>$A_3 = 2$</big></li>
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<li><big>$A_4 = -4$</big></li>
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<li><big>$A_5 = 3$</big></li>
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<li><big>$A_6 = 0$</big></li>
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</ul>
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`3` is an equilibrium index, because:
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<ul style='list-style: none;'>
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<li><big>$A_0 + A_1 + A_2 = A_4 + A_5 + A_6$</big></li>
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</ul>
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`6` is also an equilibrium index, because:
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<ul style='list-style: none;'>
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<li><big>$A_0 + A_1 + A_2 + A_3 + A_4 + A_5 = 0$</big></li>
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</ul>
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(sum of zero elements is zero)
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`7` is not an equilibrium index, because it is not a valid index of sequence $A$.
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# --instructions--
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Write a function that, given a sequence, returns its equilibrium indices (if any).
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Assume that the sequence may be very long.
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# --hints--
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`equilibrium` should be a function.
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```js
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assert(typeof equilibrium === 'function');
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```
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`equilibrium([-7, 1, 5, 2, -4, 3, 0])` should return `[3,6]`.
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```js
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assert.deepEqual(equilibrium(equilibriumTests[0]), ans[0]);
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```
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`equilibrium([2, 4, 6])` should return `[]`.
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```js
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assert.deepEqual(equilibrium(equilibriumTests[1]), ans[1]);
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```
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`equilibrium([2, 9, 2])` should return `[1]`.
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```js
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assert.deepEqual(equilibrium(equilibriumTests[2]), ans[2]);
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```
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`equilibrium([1, -1, 1, -1, 1, -1, 1])` should return `[0,1,2,3,4,5,6]`.
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```js
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assert.deepEqual(equilibrium(equilibriumTests[3]), ans[3]);
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```
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`equilibrium([1])` should return `[0]`.
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```js
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assert.deepEqual(equilibrium(equilibriumTests[4]), ans[4]);
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```
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`equilibrium([])` should return `[]`.
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```js
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assert.deepEqual(equilibrium(equilibriumTests[5]), ans[5]);
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```
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# --seed--
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## --after-user-code--
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```js
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const equilibriumTests =
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[[-7, 1, 5, 2, -4, 3, 0], // 3, 6
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[2, 4, 6], // empty
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[2, 9, 2], // 1
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[1, -1, 1, -1, 1, -1, 1], // 0,1,2,3,4,5,6
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[1], // 0
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[] // empty
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];
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const ans = [[3, 6], [], [1], [0, 1, 2, 3, 4, 5, 6], [0], []];
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```
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## --seed-contents--
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```js
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function equilibrium(a) {
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}
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```
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# --solutions--
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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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