What is the time complexity of Sum of Values at Indices With K Set Bits?

The optimal solution has a time complexity of O(n).

What data structures are used to solve Sum of Values at Indices With K Set Bits?

This problem uses Array, Bit Manipulation. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Sum of Values at Indices With K Set Bits?

Insight 1: The core operation involves counting set bits (1s) in the binary representation of an integer. Efficient bit manipulation techniques are crucial for optimal performance. Insight 2: Iterating through the array and checking each index's binary representation for the required number of set bits is a straightforward approach. This can be implemented using a loop.

Which companies ask LeetCode 2859. Sum of Values at Indices With K Set Bits in interviews?

This problem is frequently asked at Accenture.

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Sum of Values at Indices With K Set Bits - LeetCode 2859 Solution

Sum of Values at Indices With K Set Bits - Complete Solution Guide

Sum of Values at Indices With K Set Bits is LeetCode problem 2859, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given a 0-indexed integer array nums and an integer k . Return an integer that denotes 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 present when it is written in binary. For example, the binary representation of 21 is 10101 , which has 3 set bits. Example 1: Input: nums = [5,10,1,5,2], k = 1 Output: 13 Explanation: The binary representation of the indices are: 0 = 000 2 1 = 001 2 2

Detailed Explanation

The problem asks you to calculate the sum of elements in a given integer array `nums`. However, you only sum the elements whose indices have exactly `k` set bits (1s) in their binary representation. The input is the array `nums` and the integer `k`. The output is a single integer representing the sum. For example, if `nums = [5, 10, 1, 5, 2]` and `k = 1`, the indices are 0, 1, 2, 3, 4. Their binary representations are 000, 001, 010, 011, 100. Only indices 1, 2, and 4 have exactly one set bit, so the output is nums[1] + nums[2] + nums[4] = 10 + 1 + 2 = 13.

Solution Approach

The provided solutions all employ a similar approach: iterate through the input array `nums`. For each index `i`, they determine the number of set bits in the binary representation of `i`. If this count equals `k`, the element at index `i` (i.e., `nums[i]`) is added to a running sum. Finally, the accumulated sum is returned.

Step-by-Step Algorithm

Step 1: Initialize a variable `sum` to 0. This variable will store the sum of elements.
Step 2: Iterate through the `nums` array using a loop (e.g., `for` loop). The loop variable `i` represents the index.
Step 3: For each index `i`, count the number of set bits in its binary representation. This can be done using bit manipulation (right-shifting and checking the least significant bit) or using built-in functions (like `Integer.bitCount()` in Java or `bin(i).count('1')` in Python).
Step 4: If the count of set bits is equal to `k`, add the element `nums[i]` to the `sum`.
Step 5: After iterating through all indices, return the final `sum`.

Key Insights

Insight 1: The core operation involves counting set bits (1s) in the binary representation of an integer. Efficient bit manipulation techniques are crucial for optimal performance.
Insight 2: Iterating through the array and checking each index's binary representation for the required number of set bits is a straightforward approach. This can be implemented using a loop.
Insight 3: Built-in functions like `Integer.bitCount()` (Java) or `bin(i).count('1')` (Python) can significantly simplify the process of counting set bits, improving readability and potentially efficiency.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Bit Manipulation.

Companies

Asked at: Accenture.

Sum of Values at Indices With K Set Bits | LeetCode 2859

Easy

Array Bit Manipulation

Time: O(n)Space: O(1)

Solution Code

Available in:

import java.util.List;

class Solution {
    public int sumIndicesWithKSetBits(List<Integer> nums, int k) {
        int sum = 0;
        for (int i = 0; i < nums.size(); i++) {
            if (Integer.bitCount(i) == k) {
                sum += nums.get(i);
            }
        }
        return sum;
    }
}

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Problem Info

Description

Problem 2859: Sum of Values at Indices With K Set Bits - Detailed explanation and solution approaches.

Topics

Array Bit Manipulation

Companies

Accenture

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:2859

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

5 steps

1
Step 1: Initialize a variable `sum` to 0. This variable will store the sum of elements.
2
Step 2: Iterate through the `nums` array using a loop (e.g., `for` loop). The loop variable `i` represents the index.
3
Step 3: For each index `i`, count the number of set bits in its binary representation. This can be done using bit manipulation (right-shifting and checking the least significant bit) or using built-in functions (like `Integer.bitCount()` in Java or `bin(i).count('1')` in Python).
4
Step 4: If the count of set bits is equal to `k`, add the element `nums[i]` to the `sum`.
5
Step 5: After iterating through all indices, return the final `sum`.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The algorithm uses a constant amount of extra space regardless of the input size. The variables `sum` and `count` (or their equivalents in different languages) occupy a fixed amount of memory. The loop iterates in-place without creating significant auxiliary data structures.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Precompute Set Bits

Create a separate array to store the number of set bits for each index beforehand. Then, iterate through `nums`, and use the precomputed array to efficiently check the number of set bits for each index without recalculating it.

Time: O(n + m*log(m)), where m is max indexSpace: O(n)

Trade-offs: This approach has slightly higher space complexity but could be faster if you need to perform the operation for the same array and multiple values of `k`.

✨

Key Insights

1Insight 1: The core operation involves counting set bits (1s) in the binary representation of an integer. Efficient bit manipulation techniques are crucial for optimal performance.
2Insight 2: Iterating through the array and checking each index's binary representation for the required number of set bits is a straightforward approach. This can be implemented using a loop.
3Insight 3: Built-in functions like `Integer.bitCount()` (Java) or `bin(i).count('1')` (Python) can significantly simplify the process of counting set bits, improving readability and potentially efficiency.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Edge Cases

Edge case 1: Empty input array (`nums` is empty). The solution handles this correctly by returning 0 because the sum is initially 0 and the loop won't execute.
Edge case 2: `k` is 0. The solution should correctly identify and sum only those numbers whose index has 0 set bits (only index 0).
Edge case 3: `k` is greater than the number of bits in the maximum index. The solution should correctly return 0 since no indices would satisfy the condition.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly counting set bits. Off-by-one errors or logical mistakes in bit manipulation can lead to inaccurate counts.

✗Common mistake 2: Not handling edge cases properly. Failing to consider an empty input array or edge cases related to `k` can lead to incorrect results or runtime errors.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Data analysis where you need to filter and aggregate data based on specific bit patterns in identifiers or indices.

🏦Real-world scenario 2: Network programming or embedded systems where efficient bit manipulation is crucial for handling flags, status codes, or optimizing memory usage.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Even for easy problems, discuss time and space complexity. Interviewers want to see you think analytically.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: November 7, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 13

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 6

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJun 29

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

What should I learn from easy problems?

Easy problems introduce core patterns that appear in harder problems. Master basic operations (iteration, conditionals, simple data structures), recognize common patterns (counting, searching, basic transformations), and practice explaining your thought process clearly.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Sum of Values at Indices With K Set Bits"?

For this easy-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether bit manipulation techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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