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 $A$:
:::: $A_0 = -7$
:::: $A_1 = 1$
:::: $A_2 = 5$
:::: $A_3 = 2$
:::: $A_4 = -4$
:::: $A_5 = 3$
:::: $A_6 = 0$
3 is an equilibrium index, because:
:::: $A_0 + A_1 + A_2 = A_4 + A_5 + A_6$
6 is also an equilibrium index, because:
:::: $A_0 + A_1 + A_2 + A_3 + A_4 + A_5 = 0$
(sum of zero elements is zero)
7 is not an equilibrium index, because it is not a valid index of sequence $A$.
Write a function that, given a sequence, returns its equilibrium indices (if any).
Assume that the sequence may be very long.
equilibrium
is a function.
testString: assert(typeof equilibrium === 'function', 'equilibrium
is a function.');
- text: equilibrium([-7, 1, 5, 2, -4, 3, 0])
should return [3,6]
.
testString: assert.deepEqual(equilibrium(equilibriumTests[0]), ans[0], 'equilibrium([-7, 1, 5, 2, -4, 3, 0])
should return [3,6]
.');
- text: equilibrium([2, 4, 6])
should return []
.
testString: assert.deepEqual(equilibrium(equilibriumTests[1]), ans[1], 'equilibrium([2, 4, 6])
should return []
.');
- text: equilibrium([2, 9, 2])
should return [1]
.
testString: assert.deepEqual(equilibrium(equilibriumTests[2]), ans[2], 'equilibrium([2, 9, 2])
should return [1]
.');
- text: equilibrium([1, -1, 1, -1, 1, -1, 1])
should return [0,1,2,3,4,5,6]
.
testString: assert.deepEqual(equilibrium(equilibriumTests[3]), ans[3], 'equilibrium([1, -1, 1, -1, 1, -1, 1])
should return [0,1,2,3,4,5,6]
.');
- text: equilibrium([1])
should return [0]
.
testString: assert.deepEqual(equilibrium(equilibriumTests[4]), ans[4], 'equilibrium([1])
should return [0]
.');
- text: equilibrium([])
should return []
.
testString: assert.deepEqual(equilibrium(equilibriumTests[5]), ans[5], 'equilibrium([])
should return []
.');
```