Equilibrium index

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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.

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 $A$.

Test

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