**For programmers practicing their coding skills, or preparing to take a Codility assessment, we provide a series of free lessons, challenges and demo problems in our programmers' home. **

**One of the most popular tasks is Equi and to date we have evaluated over 50,000 solutions to this problem!**

The most popular language used for solving this problem is Java, although C#, PHP and C++ are also very popular:

**The problem description is very short:**

The equilibrium index of a sequence is an index such that the sum of elements at lower indexes is equal to the sum of elements at higher indexes. 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

(The sum of zero elements is zero) 7 is not an equilibrium index - because it is not a valid index of sequence A. If you still have doubts, here is a precise definition: The integer k is an equilibrium index of a sequence A[0],A[1]..,A[n-1] if and only if

0<= kandsum(A[0..(k-1)])=sum(A[(k+1)..(n-1)]). Assume the sum of zero elements is equal to zero.Write a function

int equi(int A[], int n)that, given a sequence, returns its equilibrium index (any) or -1 if no equilibrium index exists. Assume that the sequence may be very long.

**The problem can be solved by using various approaches, the most common being simply to follow the equilibrium definition:**

int equi ( int A[], int n ) { int k, m, lsum, rsum; for(k = 0; k < n; ++k) { lsum = 0; rsum = 0; for(m = 0; m < k; ++m) lsum += A[m]; for(m = k + 1; m < n; ++m) rsum += A[m]; if (lsum == rsum) return k; } return -1; }

**Unfortunately, this approach has two disadvantages:**

- it fails on large input data sets, since the time complexity is
*O(n*^{2}) - it fails on large input values (for example if the input array contains values like MIN/MAX_INT) due to the arithmetic overflows

The solution analysis will detect such problems in submitted code:

We can fix the first problem with a better algorithm, and the second problem with a better data-type (for example, using long long type instead of int for sum computations). The key observation for better running time is to update the left/right sums in constant time instead of recomputing them from the scratch.

int equi(int arr[], int n) { if (n==0) return -1; long long sum = 0; int i; for(i=0;i<n;i++) sum+=(long long) arr[i]; long long sum_left = 0; for(i=0;i<n;i++) { long long sum_right = sum - sum_left - (long long) arr[i]; if (sum_left == sum_right) return i; sum_left += (long long) arr[i]; } return -1; }

**Using this solution, you can obtain a perfect score:**

**What's next?**

We have a live competition to write the shortest Equi solution - 54 bytes is smallest solution to date! If you're preparing for a Codility assessment, we offer two other demo problems which are free to take and can help you warm up:

Happy coding and good luck!

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