Sum of Values at Indices With K Set Bits

Sum of Values at Indices With K Set Bits

What is this problem about?

In the Sum of Values at Indices With K Set Bits interview question, you are given an array of integers and a non-negative integer k. Your task is to find the sum of all elements in the array whose index (not the value itself, but the position in the array) has exactly k set bits in its binary representation. A "set bit" is simply a bit with a value of 1. This problem combines basic array iteration with bit manipulation logic, making it a common entry-level technical question.

Why is this asked in interviews?

Accenture and other tech firms use this Sum of Values at Indices With K Set Bits coding problem to verify that a candidate can perform basic bitwise operations and understands binary indexing. It’s a test of attention to detail—ensuring you are checking the set bits of the index rather than the element's value. It also evaluates your ability to write clean loops and use built-in or manual methods for counting set bits efficiently.

Algorithmic pattern used

The algorithmic pattern used here is a combination of Array Iteration and Bit Manipulation. The logic is straightforward:

1. Initialize a running sum to 0.
2. Iterate through each index i from 0 to n-1.
3. For each index, count the number of set bits (1s) in its binary form.
4. If the count equals k, add the value at nums[i] to the sum. The time complexity is O(n * log(max_index)), where log(max_index) represents the number of bits in the index.

Example explanation

Consider the array [10, 20, 30, 40, 50] and k = 1. Indices are 0, 1, 2, 3, 4.

• Index 0 (binary 000): 0 set bits.
• Index 1 (binary 001): 1 set bit. (Match!)
• Index 2 (binary 010): 1 set bit. (Match!)
• Index 3 (binary 011): 2 set bits.
• Index 4 (binary 100): 1 set bit. (Match!) The elements at matching indices are nums[1], nums[2], and nums[4]. Sum = 20 + 30 + 50 = 100.

Common mistakes candidates make

A very frequent mistake is counting the bits in the element nums[i] instead of the index i. Another error is not knowing how to count bits efficiently. While many languages have built-in functions (like Integer.bitCount() in Java or bin(i).count('1') in Python), failing to explain how you would do it manually (e.g., using Brian Kernighan’s algorithm or simple bit shifting) might reflect poorly during a deep-dive interview.

Interview preparation tip

When preparing for the Sum of Values at Indices With K Set Bits coding problem, make sure you are comfortable with the basics of bitwise operators like &, |, and >>. Practice writing a function to count set bits manually. Knowing how to use n & (n - 1) to clear the least significant set bit is a classic trick that interviewers love to see. It’s also good to know the built-in bit-counting functions for your language of choice.