What is the time complexity of Max Number of K-Sum Pairs?

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

What data structures are used to solve Max Number of K-Sum Pairs?

This problem uses Array, Hash Table, Two Pointers, Sorting. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Max Number of K-Sum Pairs?

Insight 1: The core idea is to find pairs of numbers that sum to `k`. This immediately suggests using a hash table (or counter) to efficiently keep track of the frequency of each number in the array. Insight 2: For each number `num` in the array, we need to check if its complement `k - num` exists in the array and has a frequency greater than 0. If it does, we can form a pair and decrement the frequency of both `num` and `k - num`.

Which companies ask LeetCode 1679. Max Number of K-Sum Pairs in interviews?

This problem is frequently asked at DE Shaw.

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Max Number of K-Sum Pairs - LeetCode 1679 Solution

Max Number of K-Sum Pairs - Complete Solution Guide

Max Number of K-Sum Pairs is LeetCode problem 1679, a Medium 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 . In one operation, you can pick two numbers from the array whose sum equals k and remove them from the array. Return the maximum number of operations you can perform on the array . Example 1: Input: nums = [1,2,3,4], k = 5 Output: 2 Explanation: Starting with nums = [1,2,3,4]: - Remove numbers 1 and 4, then nums = [2,3] - Remove numbers 2 and 3, then nums = [] There are no more pairs that sum up to 5, hence a total of 2 operations. Example 2:

Detailed Explanation

The problem asks us to find the maximum number of pairs in a given array `nums` that sum up to a target value `k`. In each operation, we can select two numbers from the array that add up to `k` and remove them. The goal is to maximize the number of such operations we can perform.

Solution Approach

The provided solutions all use a hash table (or counter) to store the frequency of each number in the input array `nums`. The algorithm iterates through the array, and for each number `num`, it calculates the `complement` needed to reach the target sum `k`. It then checks if the `complement` exists in the hash table and has a frequency greater than 0. If it does, a pair is found, the operation count is incremented, and the frequency of the `complement` is decremented in the hash table. If the `complement` is not found or its frequency is 0, the frequency of the current number `num` is incremented in the hash table.

Step-by-Step Algorithm

Step 1: Initialize a hash table (or counter) called `counts` to store the frequency of each number in the array.
Step 2: Initialize a variable `operations` to 0. This variable will keep track of the number of successful operations.
Step 3: Iterate through the input array `nums`.
Step 4: For each number `num` in `nums`, calculate its complement: `complement = k - num`.
Step 5: Check if the `complement` exists in the `counts` hash table and if its frequency is greater than 0.
Step 6: If the `complement` exists and its frequency is greater than 0:
a. Increment `operations` by 1.
b. Decrement the frequency of the `complement` in the `counts` hash table.
Step 7: Otherwise (if the `complement` doesn't exist or its frequency is 0):
a. Increment the frequency of the current number `num` in the `counts` hash table.
Step 8: After iterating through the entire array, return the value of `operations`.

Key Insights

Insight 1: The core idea is to find pairs of numbers that sum to `k`. This immediately suggests using a hash table (or counter) to efficiently keep track of the frequency of each number in the array.
Insight 2: For each number `num` in the array, we need to check if its complement `k - num` exists in the array and has a frequency greater than 0. If it does, we can form a pair and decrement the frequency of both `num` and `k - num`.
Insight 3: Careful handling of duplicate numbers is crucial. The counter data structure helps ensure that we only remove pairs when both numbers are available in sufficient quantities.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Hash Table, Two Pointers, Sorting.

Companies

Asked at: DE Shaw.

Max Number of K-Sum Pairs | LeetCode 1679

Medium

Array Hash Table Two Pointers Sorting

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

Solution Code

Available in:

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

class Solution {
    public int maxOperations(int[] nums, int k) {
        Map<Integer, Integer> counts = new HashMap<>();
        int operations = 0;
        for (int num : nums) {
            int complement = k - num;
            if (counts.containsKey(complement) && counts.get(complement) > 0) {
                operations++;
                counts.put(complement, counts.get(complement) - 1);
            } else {
                counts.put(num, counts.getOrDefault(num, 0) + 1);
            }
        }
        return operations;
    }
}

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Problem Info

Description

Problem 1679: Max Number of K-Sum Pairs - Detailed explanation and solution approaches.

Topics

Array Hash Table Two Pointers Sorting

Companies

DE Shaw

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:1679

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

11 steps

1
Step 1: Initialize a hash table (or counter) called `counts` to store the frequency of each number in the array.
2
Step 2: Initialize a variable `operations` to 0. This variable will keep track of the number of successful operations.
3
Step 3: Iterate through the input array `nums`.
4
Step 4: For each number `num` in `nums`, calculate its complement: `complement = k - num`.
5
Step 5: Check if the `complement` exists in the `counts` hash table and if its frequency is greater than 0.
6
Step 6: If the `complement` exists and its frequency is greater than 0:
7
a. Increment `operations` by 1.
8
b. Decrement the frequency of the `complement` in the `counts` hash table.
9
Step 7: Otherwise (if the `complement` doesn't exist or its frequency is 0):
10
a. Increment the frequency of the current number `num` in the `counts` hash table.
11
Step 8: After iterating through the entire array, return the value of `operations`.

💡

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(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is linear because we iterate through the array once. Hash table operations (insertion, retrieval, and deletion) have an average time complexity of O(1). The space complexity is linear because, in the worst-case scenario, we might need to store all unique elements of the array in the hash table. The C implementation includes a hash table with collision handling, so the insert/get/decrement operations still have O(1) average complexity.

📖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

Two Pointers (Sorting)

Sort the array first. Then, use two pointers, one at the beginning and one at the end of the array. If the sum of the numbers pointed to by the pointers is equal to `k`, increment the operation count and move both pointers. If the sum is less than `k`, move the left pointer. If the sum is greater than `k`, move the right pointer.

Time: O(n log n) for sorting + O(n) for two pointers = O(n log n)Space: O(1) if sorting in place; O(n) otherwise (depending on the sorting algorithm used)

Trade-offs: This approach has a slightly worse time complexity due to the sorting step (O(n log n) vs. O(n) for the hash table approach). However, it uses less space if the sorting can be done in place. This method is efficient when modification of the input array is acceptable and space is a major concern.

✨

Key Insights

1Insight 1: The core idea is to find pairs of numbers that sum to `k`. This immediately suggests using a hash table (or counter) to efficiently keep track of the frequency of each number in the array.
2Insight 2: For each number `num` in the array, we need to check if its complement `k - num` exists in the array and has a frequency greater than 0. If it does, we can form a pair and decrement the frequency of both `num` and `k - num`.
3Insight 3: Careful handling of duplicate numbers is crucial. The counter data structure helps ensure that we only remove pairs when both numbers are available in sufficient quantities.

📚

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!

Two Pointers

Using two indices to traverse data from different positions simultaneously.

Sorting

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

Edge Cases

Edge case 1: Empty input array `nums`. The code handles this correctly because the loop won't execute, and `operations` will remain 0, which is the correct answer.
Edge case 2: `k` is smaller than any number in the array. In this case, no pairs will be found, and `operations` will remain 0, which is correct.
Edge case 3: The same number appears multiple times, and two of the same number adds up to `k`. For example, `nums = [3, 3, 3, 3], k = 6`. The hash table correctly tracks the frequencies, and the code finds the correct number of operations.
Edge case 4: Negative numbers in the array. The given solutions all handle negative numbers correctly, as the hash table can store negative keys and perform the necessary subtractions.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not handling duplicate numbers correctly. If the same number appears multiple times in the array and contributes to multiple pairs, it's essential to use a counter (hash table with frequency tracking) to ensure that each number is only used as many times as it appears in the array.

✗Common mistake 2: Not considering the case where the complement might be the same as the number itself (e.g., when k = 6 and num = 3). The hash table correctly accounts for this.

✗Common mistake 3: Assuming that the input array is sorted. The problem does not guarantee this, so sorting it unconditionally would increase the time complexity unnecessarily if using the hashmap approach.

✅

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: Finding pairs of items in an inventory that can be combined to fulfill an order with a specific value (e.g., combining ingredients to make a recipe).

🏦Real-world scenario 2: Identifying matching transactions in a financial system where debits and credits should balance to zero. (In this case, 'k' would be zero, and the numbers would represent positive and negative transaction amounts.)

💡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

Consider multiple approaches before coding. Mentioning alternatives shows breadth of knowledge.

⚠️ 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: July 30, 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.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

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 "Max Number of K-Sum Pairs"?

For this medium-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.

🤖 Need help with this problem?