algoadvance

You are given a 0-indexed integer array nums and an integer k.

Return the sum of the elements of nums at indices where the number of 1s in the binary representation of the index is k.

Clarifying Questions

1. Can nums contain negative numbers?
   • Yes, nums can contain negative numbers.
2. What is the range of values for k?
   • k is a non-negative integer and will be less than or equal to the number of bits used to represent the indices of nums.
3. What are the constraints on the length of nums?
   • The length of nums can be up to (2^{20}).

Strategy

1. Bit Counting: For each index, we need to count the number of 1 bits set in its binary representation.
2. Sum Calculation: If the count of set bits equals k, add the element at that index to the sum.
3. We can use Python’s built-in bit manipulation functions to make counting the 1s more efficient.

Code

def sum_indices_with_k_set_bits(nums, k):
    def count_set_bits(n):
        return bin(n).count('1')
    
    total_sum = 0
    
    for i in range(len(nums)):
        if count_set_bits(i) == k:
            total_sum += nums[i]
            
    return total_sum

Explanation

1. Helper Function:
   • count_set_bits(n): Returns the number of 1s in the binary representation of n by using bin(n).count('1').
2. Sum Calculation:
   • Initialize total_sum to 0.
   • Loop through each index i in the array nums.
   • For each index, use count_set_bits(i) to get the number of set bits.
   • If this count equals k, add nums[i] to total_sum.
3. Return Result:
   • After loop finishes, return the computed total_sum.

Time Complexity

• Count Set Bits: bin(i).count('1') runs in (O(\log i)), but practically it is very fast.
• For Loop Over Indices: We iterate over each element of the array once, making the loop (O(n)) if the length of nums is n.
• Overall, the time complexity is (O(n \log n)), where n is the length of nums, but the logarithmic factor is small in practice given Python’s efficient handling of integers.

This solution ensures that we are efficiently calculating the sum by leveraging Python’s optimized bit manipulation tools.

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