Find all indices of Array having value same as average of other elements

Given an array arr[] of N integers, the task is to find all indices in the array, such that for each index i the arithmetic mean of all elements except arr[i] is equal to the value of the element at that index.

Examples :

Input: N = 5, arr[] = {1, 2, 3, 4, 5}
Output : {2}
Explanation : Upon removing array element at index 2 (i.e. 3),  
arithmetic mean of rest of the array equals (1 + 2 + 4 + 5) / 4 = 3, which is equal to the element at index 2. 
It can be seen that 2 is the only such index.

Input : N = 6, arr[] = {5, 5, 5, 5, 5, 5}
Output : {0, 1, 2, 3, 4, 5}

Approach: The problem can be solved by the following idea:

Calculate the total sum of the array and for each element (arr[i]) check if the average of all the other elements is same as arr[i].

Follow the steps to solve the problem:

• Find sum of all elements of the array and store in a variable say sum.
• Traverse the array and,
• At each iteration, find the sum of the array without current element by subtracting current element value from the sum. say, current_sum
• Find the mean of current_sum, by dividing it with N-1
• If mean is equal to the value at current index, push the index in answer vector, else continue.
• Return the answer vector.

Following is the code based on above approach :

0 1 2 3 4 

Time Complexity: O(N)
Auxiliary Space: O(N)