Mystical Numbers Codechef Solution | May CHALLENGE


Mystical Numbers Codechef Solution

A number MM is said to be a Mystical Number with respect to a number XX if (M⊕X)>(M&X)(M⊕X)>(M&X).

You are given an array AA of size NN. You are also given QQ queries. Each query consists of three integers LL, RR, and XX.

For each query, find the count of Mystical Numbers in the subarray A[L:R]A[L:R] with respect to the number XX.


  • ⊕⊕ represents the Bitwise XOR operation and && represents the Bitwise AND operation.
  • A[L:R]A[L:R] denotes the subarray A[L],A[L+1],…,A[R]A[L],A[L+1],…,A[R].

Input Format

  • The first line contains a single integer TT – the number of test cases. Then the test cases follow.
  • The first line of each test case contains an integer NN – the size of the array AA.
  • The second line of each test case contains NN space-separated integers A1,A2,…,ANA1,A2,…,AN denoting the array AA.
  • The third line of each test case contains an integer QQ – denoting the number of queries.
  • The ithith of the next QQ lines contains three space-separated integers LL , RR and XX.

Output Format

For each testcase,

  • For each query, print in a new line, the count of Mystical Numbers among A[L],A[L+1],…,A[R]A[L],A[L+1],…,A[R] with respect to the number XX.


  • 1≤T≤1001≤T≤100
  • 1≤N≤2⋅1051≤N≤2⋅105
  • 0≤Ai<2310≤Ai<231
  • 1≤Q≤2⋅1051≤Q≤2⋅105
  • 1≤L≤R≤N1≤L≤R≤N
  • 0≤X<2310≤X<231
  • Sum of NN over all test cases does not exceed 2⋅1052⋅105.
  • Sum of QQ over all test cases does not exceed 2⋅1052⋅105.

Sample Input 1 

1 2 3 4 5
1 5 4
2 5 2

Sample Output 1 



Test case 11:

  • Query 11: L=1,R=5,X=4L=1,R=5,X=4.
    • A1⊕X=5,A1&X=0A1⊕X=5,A1&X=0.
    • A2⊕X=6,A2&X=0A2⊕X=6,A2&X=0.
    • A3⊕X=7,A3&X=0A3⊕X=7,A3&X=0.
    • A4⊕X=0,A4&X=4A4⊕X=0,A4&X=4.
    • A5⊕X=1,A5&X=4A5⊕X=1,A5&X=4.

Mystical numbers are A1,A2,A1,A2, and A3A3 with respect to 44. Therefore, the answer to this query is 33.

  • Query 22: L=2,R=5,X=2L=2,R=5,X=2.
    • A2⊕X=0,A2&X=2A2⊕X=0,A2&X=2.
    • A3⊕X=1,A3&X=2A3⊕X=1,A3&X=2.
    • A4⊕X=6,A4&X=0A4⊕X=6,A4&X=0.
    • A5⊕X=7,A5&X=0A5⊕X=7,A5&X=0.

Mystical numbers are A4A4 and A5A5 with respect to 22. Therefore , the answer to this query is 22.

Mystical Numbers Codechef  SOLUTION

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