Find original array from a given encrypted array of size n. Encrypted array is obtained by replacing each element of the original array by the sum of the remaining array elements.

Examples : 

Input :  arr[] = {10, 14, 12, 13, 11}
Output : {5, 1, 3, 2, 4}
Original array {5, 1, 3, 2, 4}
Encrypted array is obtained as:
= {1+3+2+4, 5+3+2+4, 5+1+2+4, 5+1+3+4, 5+1+3+2}
= {10, 14, 12, 13, 11}
Each element of original array is replaced by the 
sum of the remaining array elements.  

Input : arr[] = {95, 107, 103, 88, 110, 87}
Output : {23, 11, 15, 30, 8, 31}

Approach is purely based on arithmetic observations which are illustrated below:  

Let n = 4, and
the original array be ori[] = {a, b, c, d}
encrypted array is given as:
arr[] = {b+c+d, a+c+d, a+b+d, a+b+c}

Elements of encrypted array are :
arr[0] = (b+c+d), arr[1] = (a+c+d), 
arr[2] = (a+b+d), arr[3] = (a+b+c)
add up all the elements
sum =  arr[0] + arr[1] + arr[2] + arr[3]
       = (b+c+d) + (a+c+d) + (a+b+d) + (a+b+c)
       = 3(a+b+c+d) 
Sum of elements of ori[] = sum / n-1
                        = sum/3 
                        = (a+b+c+d)
Thus, for a given encrypted array arr[] of size n, the sum of 
the elements of the original array ori[] can be calculated as:
sum =  (arr[0]+arr[1]+....+arr[n-1]) / (n-1)

Then, elements of ori[] are calculated as:
ori[0] = sum - arr[0]
ori[1] = sum - arr[1] 
        .
        .
ori[n-1] = sum - arr[n-1]                  

Below is the implementation of above steps.  

# Python 3 implementation to find
# original array from the encrypted
# array

# Finds and prints the elements of
# the original array
def findAndPrintOriginalArray(arr, n):

	# total sum of elements
	# of encrypted array
	arr_sum = 0
	for i in range(0, n):
		arr_sum += arr[i]

	# total sum of elements
	# of original array
	arr_sum = int(arr_sum / (n - 1))

	# calculating and displaying
	# elements of original array
	for i in range(0, n):
		print((arr_sum - arr[i]),
					end = " ")

# Driver program to test above
arr = [10, 14, 12, 13, 11]
n = len(arr)
findAndPrintOriginalArray(arr, n)

# This code is contributed By Smitha

Output : 

5 1 3 2 4

Time complexity: O(N)

Auxiliary Space: O(1)