gistfile1.py

"""
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.
 
    A[0] + A[1] + ... + A[P-1] = A[P+1] + ... + A[N-2] + A[N-1].
 
Sum of zero elements is assumed to be equal to 0. This can happen if 
P = 0 or if P = N-1.
 
For example, consider the following array A consisting of N = 7 elements:
 
    A[0] = -7   A[1] =  1   A[2] = 5
    A[3] =  2   A[4] = -4   A[5] = 3
    A[6] =  0
 
P = 3 is an equilibrium index of this array, because:
 
        A[0] + A[1] + A[2] = A[4] + A[5] + A[6]
 
P = 6 is also an equilibrium index, because:
 
        A[0] + A[1] + A[2] + A[3] + A[4] + A[5] = 0
 
and there are no elements with indices greater than 6.
 
P = 7 is not an equilibrium index, because it does not fulfill the condition 
0 = P < N.
 
Write a function
 
    def equi(A) 
 
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.
 
Assume that:
 
        N is an integer within the range [0..10,000,000];
        each element of array A is an integer within the range 
        [-2,147,483,648..2,147,483,647].
 
For example, given array A such that
 
    A[0] = -7   A[1] =  1   A[2] = 5
    A[3] =  2   A[4] = -4   A[5] = 3
    A[6] =  0
 
the function may return 3 or 6, as explained above.
 
Complexity:
 
        expected worst-case time complexity is O(N);
        expected worst-case space complexity is O(N), beyond input storage (not 
        counting the storage required for input arguments).
 
Elements of input arrays can be modified.
 
"""
 
def equi (A):
    l = len(A)
    s = sum(A)
    ps = 0
    
    indicies = []
    
    for i in range(0, l):
        ps += A[i - 1] if i > 0 else 0
        
        if (i == 0 and (s - A[i]) == 0) or ((s - ps - A[i]) == ps):
            indicies.append(i)    
    
    return indicies if indicies else -1
 
test = [-7, 1, 5, 2, -4, 3, 0]
print equi(test)