You are given an array of integers. Find the sum of XOR of all pairs formed by the elements of the array.Input FormatThe first line of input contains T - the number of test cases. It's followed by 2T lines, the first line contains N - the size of the array. The second line contains the elements of the array.Output FormatFor each test case, print the sum of XOR of all pairs formed by the elements of the array, separated by a new line.Constraints20 points1 <= T <= 1001 <= N <= 10000 <= A[i] <= 10580 points1 <= T <= 1001 <= N <= 1050 <= A[i] <= 105ExampleInput335 12 854 10 54 11 8615 35 25 10 15 12Output52560680ExplanationTest-Case 1(5 ^ 5) = 0(5 ^ 12) = 9(5 ^ 8) = 13(12 ^ 5) = 9(12 ^ 12) = 0(12 ^ 8) = 4(8 ^ 5) = 13(8 ^ 12) = 4(8 ^ 8) = 0The sum of all the above xor products = 52
Question
You are given an array of integers. Find the sum of XOR of all pairs formed by the elements of the array.Input FormatThe first line of input contains T - the number of test cases. It's followed by 2T lines, the first line contains N - the size of the array. The second line contains the elements of the array.Output FormatFor each test case, print the sum of XOR of all pairs formed by the elements of the array, separated by a new line.Constraints20 points1 <= T <= 1001 <= N <= 10000 <= A[i] <= 10580 points1 <= T <= 1001 <= N <= 1050 <= A[i] <= 105ExampleInput335 12 854 10 54 11 8615 35 25 10 15 12Output52560680ExplanationTest-Case 1(5 ^ 5) = 0(5 ^ 12) = 9(5 ^ 8) = 13(12 ^ 5) = 9(12 ^ 12) = 0(12 ^ 8) = 4(8 ^ 5) = 13(8 ^ 12) = 4(8 ^ 8) = 0The sum of all the above xor products = 52
Solution
This problem is asking you to find the sum of the XOR operation on all pairs of elements in an array.
Here is a step-by-step solution:
-
Initialize a variable
sumto 0. This will hold the sum of all XOR operations. -
Loop through the array. For each element, perform the XOR operation with every other element in the array.
-
Add the result of each XOR operation to
sum. -
After all pairs have been processed, print the value of
sum.
Here is a Python solution for the problem:
T = int(input())
for _ in range(T):
N = int(input())
arr = list(map(int, input().split()))
sum = 0
for i in range(N):
for j in range(i+1, N):
sum += arr[i] ^ arr[j]
print(sum)
This solution works by iterating over each pair of elements in the array only once (since a XOR b is the same as b XOR a), and adding the result of the XOR operation to the sum.
In the example provided, the sum of all XOR operations for the first test case is 52, and for the second test case is 60680.
Similar Questions
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