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  1. A zero-indexed array A consisting of N integers is given. An equilibrium index of this array is any integer P such that 0 ≤ P < N and the sum of elements of lower indices is equal to the sum of elements of higher indices, i.e.
  2. A[0] + A[1] + ... + A[P−1] = A[P+1] + ... + A[N−2] + A[N−1].
  3. Sum of zero elements is assumed to be equal to 0. This can happen if P = 0 or if P = N−1.
  4.  
  5. For example, consider the following array A consisting of N = 7 elements:
  6.  
  7. A[0] = -7   A[1] =  1   A[2] = 5
  8. A[3] =  2   A[4] = -4   A[5] = 3
  9. A[6] =  0
  10. P = 3 is an equilibrium index of this array, because:
  11.  
  12. A[0] + A[1] + A[2] = A[4] + A[5] + A[6]
  13. P = 6 is also an equilibrium index, because:
  14.  
  15. A[0] + A[1] + A[2] + A[3] + A[4] + A[5] = 0
  16. and there are no elements with indices greater than 6.
  17.  
  18. P = 7 is not an equilibrium index, because it does not fulfill the condition 0 ≤ P < N.
  19.  
  20. Write a function
  21.  
  22. class Solution { public int equi(int[] A); }
  23.  
  24. that, given a zero-indexed array A consisting of N integers, returns any of its equilibrium indices. The function should return −1 if no equilibrium index exists.
  25.  
  26. Assume that:
  27.  
  28. N is an integer within the range [0..10,000,000];
  29. each element of array A is an integer within the range [−2,147,483,648..2,147,483,647].
  30. For example, given array A such that
  31.  
  32. A[0] = -7   A[1] =  1   A[2] = 5
  33. A[3] =  2   A[4] = -4   A[5] = 3
  34. A[6] =  0
  35. the function may return 3 or 6, as explained above.
  36.  
  37. Complexity:
  38.  
  39. expected worst-case time complexity is O(N);
  40. expected worst-case space complexity is O(N), beyond input storage (not counting the storage required for input arguments).
  41. Elements of input arrays can be modified.
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