Sum of Values at Indices With K Set Bits

To solve this problem, iterate through the array indices, checking each index’s binary representation. Count the number of set bits (1's) in the binary form and sum the corresponding values at those indices where the count matches k. Focus on the array manipulation combined with bit counting techniques for optimal performance.

Problem Statement

You are given a 0-indexed integer array nums and an integer k. Your task is to return the sum of elements in nums whose corresponding indices have exactly k set bits in their binary representation.

The set bits in an integer are the 1's in its binary representation. For example, the binary representation of 5 is 101, which has two set bits. Iterate through the indices in nums and check the binary representation of each index to identify those with exactly k set bits.

Examples

Example 1

Input: nums = [5,10,1,5,2], k = 1

Output: 13

The binary representation of the indices are: 0 = 0002 1 = 0012 2 = 0102 3 = 0112 4 = 1002 Indices 1, 2, and 4 have k = 1 set bits in their binary representation. Hence, the answer is nums[1] + nums[2] + nums[4] = 13.

Example 2

Input: nums = [4,3,2,1], k = 2

Output: 1

The binary representation of the indices are: 0 = 002 1 = 012 2 = 102 3 = 112 Only index 3 has k = 2 set bits in its binary representation. Hence, the answer is nums[3] = 1.

Constraints

• 1 <= nums.length <= 1000
• 1 <= nums[i] <= 105
• 0 <= k <= 10

Solution Approach

Iterate Through Array Indices

Start by iterating through each index of the array. For every index, count the number of set bits (1's) in its binary representation using built-in bit manipulation functions like bin(i).count('1'). If the number of set bits equals k, add the value at that index to the sum.

Efficient Bit Counting

Bit counting can be optimized by using bitwise operations. Instead of converting an integer to a binary string, you can use the bitwise AND operation to check each bit. This reduces overhead and speeds up the solution, especially when handling larger arrays.

Edge Case Handling

Consider edge cases such as when k is 0 (where no set bits are allowed). Also, handle cases where the array is small or all elements have binary representations with the same number of set bits.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity depends on the method used for bit counting. If each bit is counted individually for each index, the time complexity will be O(n * log(m)), where n is the array length and m is the number of bits in the maximum index. If bitwise operations are used, the complexity can be reduced to O(n). The space complexity is O(1) as we only need a few variables for counting and summing.

What Interviewers Usually Probe

• Check if the candidate correctly handles the bit counting and edge cases.
• Evaluate their approach to time and space optimization for larger arrays.
• Look for a clean and efficient solution using bitwise operations over string manipulation.

Common Pitfalls or Variants

Common pitfalls

• Overcomplicating the solution by using string manipulations instead of bitwise operations.
• Forgetting to handle edge cases such as k = 0 or very large indices.
• Neglecting to optimize for large input sizes, which may cause time or space inefficiencies.

Follow-up variants

• Modify the problem to sum values at indices with more than k set bits.
• Consider variations where the indices with exactly k set bits need to meet additional conditions (e.g., even or odd numbers).
• Instead of counting set bits, change the task to sum values at indices where the binary representation has exactly n 1's and n 0's.

FAQ

What is the best approach for the Sum of Values at Indices With K Set Bits problem?

The best approach is to iterate through the indices, counting set bits for each index. Using bitwise operations will improve the solution's efficiency.

How do I count set bits in a number?

You can count set bits by converting the number to its binary representation and counting the number of 1's, or by using bitwise operations for more efficiency.

Can this problem be optimized for large arrays?

Yes, using bitwise operations for counting set bits and avoiding unnecessary string conversions can significantly improve performance for larger arrays.

What should I do if k equals 0?

If k equals 0, you need to sum values at indices where the binary representation of the index has zero set bits (e.g., index 0).

What is the time complexity of the solution?

The time complexity is O(n * log(m)) where n is the array length and m is the number of bits in the largest index, though bitwise operations can optimize this to O(n).