Given three integers N, K and X, the task is to construct an array of length N, in which XOR of all elements of each contiguous sub-array of length K is X.
Input: N = 5, K = 1, X = 4
Output: 4 4 4 4 4
Each subarray of length 1 has Xor value equal to 4.
Input: N = 5, K = 2, X = 4
Output: 4 0 4 0 4
Each subarray of length 2 has Xor value equal to 4.
To solve the problem mentioned above, we need to follow the steps given below:
- Bitwise-XOR of any number, X with 0 is equal to the number itself. So, if we set the first element of the array A as X, and the next K – 1 elements as 0, then we will have the XOR of elements of first sub-array of length K, equal to X.
- If we set A[K] as A, then we will have XOR(A, …, A[K]) = X. Similarly, if we set A[K + 1] as A, then we will have XOR(A, …, A[K+1]) = X
- Continuing in this manner, we can observe that the general formula can be described as below:
A[i] = X, when i % K == 0
A[i] = 0, when i % K != 0 where i is in the range [0,N – 1]
Below is the implementation of the above approach:
4 0 4 0 4
Time Complexity: O(N)
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