What is the time complexity of Find Subsequence of Length K With the Largest Sum?

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

What data structures are used to solve Find Subsequence of Length K With the Largest Sum?

This problem uses Array, Hash Table, Sorting, Heap (Priority Queue). Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Find Subsequence of Length K With the Largest Sum?

Insight 1: Sorting is crucial. We need to identify the `k` largest numbers to maximize the sum. Simple iteration won't efficiently find the optimal solution. Insight 2: Maintaining original indices is essential. After selecting the `k` largest numbers, we must reconstruct the subsequence in the original order by tracking the original indices of those numbers.

Which companies ask LeetCode 2099. Find Subsequence of Length K With the Largest Sum in interviews?

This problem is frequently asked at Accenture, Oracle.

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Find Subsequence of Length K With the Largest Sum - LeetCode 2099 Solution

Find Subsequence of Length K With the Largest Sum - Complete Solution Guide

Find Subsequence of Length K With the Largest Sum is LeetCode problem 2099, 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 an integer array nums and an integer k . You want to find a subsequence of nums of length k that has the largest sum. Return any such subsequence as an integer array of length k . A subsequence is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements. Example 1: Input: nums = [2,1,3,3], k = 2 Output: [3,3] Explanation: The subsequence has the largest sum of 3 + 3 = 6. Example 2: Input: nums = [-1,-2,3,4]

Detailed Explanation

The problem asks you to find a subsequence (a subset of elements maintaining their original order) of length `k` from the input array `nums` such that the sum of the elements in this subsequence is maximized. The input includes an integer array `nums` and an integer `k` representing the desired length of the subsequence. The output is an integer array representing the subsequence with the largest sum. Note that multiple subsequences might have the same largest sum; any one of them is a valid output.

Solution Approach

The provided solutions utilize a common approach: First, they sort the numbers to easily identify the `k` largest elements. However, a naive sort would lose the original indices, so they either use pairs (number, index) or a separate index tracking method. After finding the `k` largest numbers, based on their original indices, they reconstruct the subsequence maintaining the original order present in the input array.

Step-by-Step Algorithm

Step 1: Create a data structure to associate each number with its original index. This can be a pair (number, index) or a separate index array.
Step 2: Sort the data structure in descending order based on the numbers. This places the largest numbers at the beginning.
Step 3: Select the first `k` elements from the sorted data structure.
Step 4: Sort these `k` selected elements based on their original indices in ascending order to restore the original sequence.
Step 5: Extract the numbers from the sorted (by index) `k` elements to create the final subsequence and return this array.

Key Insights

Insight 1: Sorting is crucial. We need to identify the `k` largest numbers to maximize the sum. Simple iteration won't efficiently find the optimal solution.
Insight 2: Maintaining original indices is essential. After selecting the `k` largest numbers, we must reconstruct the subsequence in the original order by tracking the original indices of those numbers.
Insight 3: The solution can be optimized by using a sorting algorithm with O(n log n) time complexity, as opposed to a brute-force approach which would be far less efficient.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(n)

Topics

This problem involves: Array, Hash Table, Sorting, Heap (Priority Queue).

Companies

Asked at: Accenture, Oracle.

Find Subsequence of Length K With the Largest Sum | LeetCode 2099

Easy

Array Hash Table Sorting Heap (Priority Queue)

Time: O(n log n)Space: O(n)

Solution Code

Available in:

import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;

class Solution {
    public int[] maxSubsequence(int[] nums, int k) {
        int n = nums.length;
        int[] copy = Arrays.copyOf(nums, n);
        Arrays.sort(copy);

        Map<Integer, Integer> count = new HashMap<>();
        for (int i = n - k; i < n; i++) {
            count.put(copy[i], count.getOrDefault(copy[i], 0) + 1);
        }

        int[] result = new int[k];
        int index = 0;
        for (int num : nums) {
            if (count.containsKey(num) && count.get(num) > 0) {
                result[index++] = num;
                count.put(num, count.get(num) - 1);
                if (index == k) {
                    break;
                }
            }
        }

        return result;
    }
}

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Problem Info

Description

Problem 2099: Find Subsequence of Length K With the Largest Sum - Detailed explanation and solution approaches.

Topics

Array Hash Table Sorting Heap (Priority Queue)

Companies

AccentureOracle

Stats

Difficulty:Easy

Languages:4

Companies:2

Problem #:2099

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: Create a data structure to associate each number with its original index. This can be a pair (number, index) or a separate index array.
2
Step 2: Sort the data structure in descending order based on the numbers. This places the largest numbers at the beginning.
3
Step 3: Select the first `k` elements from the sorted data structure.
4
Step 4: Sort these `k` selected elements based on their original indices in ascending order to restore the original sequence.
5
Step 5: Extract the numbers from the sorted (by index) `k` elements to create the final subsequence and return this array.

💡

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 log n)

✨ Log-linear - Great for sorting algorithms!

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The dominant operation is sorting, which takes O(n log n) time in most cases. The additional space used for storing indices or pairs is proportional to the input size `n`, leading to O(n) space complexity. In-place sorting would reduce the space complexity but might not be practically implemented as it can be less efficient than other methods. The Python3 solution is particularly efficient due to Python's built-in sorting efficiency and its list comprehension.

📖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

Using a Min-Heap

Maintain a min-heap of size `k`. Iterate through the array, adding each element to the heap. If the heap size exceeds `k`, remove the smallest element. After iterating, extract elements from the heap and reconstruct the subsequence based on their original indices.

Time: O(n log k)Space: O(k)

Trade-offs: This approach is more efficient than sorting the entire array if `k` is significantly smaller than `n`. However, it involves more complex heap management.

✨

Key Insights

1Insight 1: Sorting is crucial. We need to identify the `k` largest numbers to maximize the sum. Simple iteration won't efficiently find the optimal solution.
2Insight 2: Maintaining original indices is essential. After selecting the `k` largest numbers, we must reconstruct the subsequence in the original order by tracking the original indices of those numbers.
3Insight 3: The solution can be optimized by using a sorting algorithm with O(n log n) time complexity, as opposed to a brute-force approach which would be far less efficient.

📚

Key Terms Explained

For Students

Array

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

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: `k` equals `nums.length`. In this case, the entire array is the subsequence, and the solution handles this correctly by returning the original array. This is efficiently handled by the sorting approach which directly returns the top K if k equals n.
Edge case 2: The input array contains duplicate numbers. The solution correctly handles this by selecting the `k` largest numbers, even if duplicates exist. The preservation of original order ensures correct output, regardless of duplicates.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to maintain original indices. Simply sorting the array and taking the first `k` elements will not work because it disregards the order of elements in the original array.

✗Common mistake 2: Incorrect handling of duplicate elements. The solution must ensure that if multiple elements have the same value, the correct order (based on the original array) is preserved.

✅

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: Selecting the top `k` performing employees from a company database based on their performance scores (where order of employment might be important).

🏦Real-world scenario 2: In finance, selecting the top `k` performing stocks from a portfolio based on their returns. Maintaining the order of investment could be crucial for analysis.

💡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

Don't rush. Explain your thought process clearly. Easy problems are often about communication.

⚠️ 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: September 28, 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.

How do I choose between a hash map and a hash set?

Use a hash set when you only need to track presence/absence of elements (like detecting duplicates). Use a hash map when you need to associate values with keys (like counting frequencies or storing indices). Hash sets use less memory since they only store keys.

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 "Find Subsequence of Length K With the Largest Sum"?

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 hash table techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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