Amazon SDE I 2025 Set Bits XOR Problem Quiz Quiz

Test your knowledge of the minimum XOR problem frequently asked in Amazon SDE I interviews. Challenge yourself with questions on bit manipulation, set bits, binary operations, and strategies to minimize XOR values while matching set bits.

1. Understanding the Problem Statement

   Given two integers a and b, what is the condition that the resulting integer x must satisfy besides minimizing x XOR a?

   1. x must be greater than both a and b
   2. x must have the same number of set bits as b
   3. x must be equal to b
   4. x must be a multiple of b

   Explanation: The main constraint is that x must have exactly the same number of set (1) bits as b, while making x XOR a as small as possible. Simply having x equal to b or being a multiple of b is not sufficient or required. x being greater than both a and b is unnecessary for the solution.

2. Counting Set Bits

   What is the most efficient built-in function to count the number of set bits in an integer in most modern programming languages?

   1. str(x).count('1')
   2. x.bit_length()
   3. x in binary
   4. bin(x).count('1')

   Explanation: The common and efficient way is to convert the integer to binary with bin(x), then count '1's using count('1'). str(x).count('1') counts digits in decimal, not binary. x in binary is not valid syntax, and x.bit_length() counts number of bits needed but not actual set bits.

3. Case 1: More Set Bits in A

   If integer a has more set bits than b, what operation should be performed to minimize x XOR a while adjusting the number of set bits in x?

   1. Turn off set bits in a starting from the least significant bit
   2. Set all bits to zero
   3. Add set bits to a at random positions
   4. Invert all bits of a

   Explanation: Starting with a, we need to reduce the set bits to match b’s count by turning off bits, starting from the least significant to minimize change. Adding set bits increases the count, which is not desirable. Setting bits to zero or inverting all bits would not result in the minimum xor or match set bit count.

4. Case 2: Fewer Set Bits in A

   When a has fewer set bits than required, what must be done to transform a into x?

   1. Remove set bits from a
   2. Multiply a and b
   3. Copy b's value to x
   4. Turn on unset bits in a until the count matches b

   Explanation: To match the higher number of set bits, we must enable (turn on) the unset bits of a while minimizing the changes. Removing set bits reduces the count, which is not the goal in this case. Copying b ignores the objective of minimizing x XOR a, and multiplication is not relevant.

5. Choosing Which Bits to Toggle

   In order to minimize x XOR a, which bits should be toggled first when adjusting set bits?

   1. Random bits should be toggled
   2. Toggle all bits at once
   3. Least significant bits should be toggled first
   4. Most significant bits should be toggled first

   Explanation: Flipping or toggling the least significant bits first causes the smallest possible increase in the value of XOR, thus minimizing the difference. Toggling the most significant or random bits may lead to a larger XOR. Toggling all bits does not maintain control over the set bit count.

6. Understanding XOR Minimization

   Why does starting with x = a generally help in minimizing x XOR a when adjusting set bits to match b?

   1. Because a always equals b
   2. Because multiplying a with b gives the correct answer
   3. Because the highest set bit is always in a
   4. Because a XOR a is 0, and fewer changes ensure minimal XOR

   Explanation: Since a XOR a equals zero, starting with a and making minimum necessary changes helps keep XOR as low as possible. There is no guarantee a equals b, so that option is incorrect. Multiplication does not apply, and the highest set bit's position is not always in a.

7. Bitwise Operations for Set Bit Manipulation

   When turning off the i-th bit in an integer x, which bitwise operation achieves this?

   1. x = x | (1 u003Cu003C i)
   2. x = x ^ 1
   3. x = x + (1 u003Cu003C i)
   4. x = x u0026 ~(1 u003Cu003C i)

   Explanation: To clear or turn off the i-th bit, you use bitwise AND with the complement of (1 u003Cu003C i). OR operation would turn the bit on, XOR simply toggles the least significant bit, and addition just increases the number without necessarily affecting the correct bit.

8. Algorithm Efficiency

   What is the maximum number of bit positions iterated over in this algorithm, considering 32-bit integers?

   1. 32
   2. 10
   3. 64
   4. 2

   Explanation: The algorithm loops over all 32 bit positions for 32-bit integers to check and change specific bits. 2 and 10 are too small and arbitrary, and 64 would be for a 64-bit integer type, not typically used here.

9. Result Verification

   After constructing x, what should we verify to ensure the solution is valid according to the problem's constraints?

   1. x equals a
   2. x has all bits set to one
   3. x is always less than b
   4. x has exactly as many set bits as b

   Explanation: The construction must ensure that the number of set bits in x matches b. x does not have to be the same as a or smaller than b. Setting all bits to one ignores the required set bit count.

10. Example Scenario

    If a = 3 (011 in binary) and b = 5 (101 in binary), what is the correct value for x following the rules of the problem?

    1. 3
    2. 5
    3. 2
    4. 7

    Explanation: Both a and b have two set bits, so x can be a itself to minimize the XOR value, resulting in x = 3. Choosing 5 or 2 does not minimize xor to the lowest value, while 7 has more set bits than required.