Program to find maximum XOR for each query in Python

Suppose we have an array which is presorted called nums of size n and also have one value b. We want to perform the following query n times −

• Search for a non-negative value k < 2^m such that XOR of all elements in nums and k is maximized. So k is the answer to the ith query.

• Remove the last element from the current array nums.

• We have to find an array answer, where answer[i] is the answer to the ith query.

So, if the input is like nums = [0,1,1,3], m = 2, then the output will be [0,3,2,3], because

• nums = [0,1,1,3], k = 0 since 0 XOR 1 XOR 1 XOR 3 XOR 0 = 3.

• nums = [0,1,1], k = 3 since 0 XOR 1 XOR 1 XOR 3 = 3.

• nums = [0,1], k = 2 since 0 XOR 1 XOR 2 = 3.

• nums = [0], k = 3 since 0 XOR 3 = 3.

To solve this, we will follow these steps −

• x := 2^m - 1

• for i in range 0 to size of nums - 1, do

  • nums[i] := nums[i] XOR x

  • x := nums[i]

• return nums after reversal

Example

Let us see the following implementation to get better understanding −

def solve(nums, m):
   x=2**m-1
   for i in range(len(nums)):
      nums[i]^= x
      x = nums[i]
   return(nums[::-1])

nums = [0,1,1,3]
m = 2
print(solve(nums, m))

Input

[0,1,1,3], 2

Output

[0, 3, 2, 3]