What is the time complexity of Maximum Number of Pairs in Array?

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

What data structures are used to solve Maximum Number of Pairs in Array?

This problem uses Array, Hash Table, Counting. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Maximum Number of Pairs in Array?

Insight 1: Using a hash map (or frequency array) to efficiently count the occurrences of each integer is crucial for determining the number of pairs that can be formed. This allows for a linear time solution. Insight 2: Integer division (`//` in Python, `/` in Java, C++, C) and modulo operation (`%` in all languages) are used to calculate the number of pairs and leftovers respectively for each integer.

Which companies ask LeetCode 2341. Maximum Number of Pairs in Array in interviews?

This problem is frequently asked at Altimetrik.

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Maximum Number of Pairs in Array - LeetCode 2341 Solution

Maximum Number of Pairs in Array - Complete Solution Guide

Maximum Number of Pairs in Array is LeetCode problem 2341, 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 . In one operation, you may do the following: Choose two integers in nums that are equal . Remove both integers from nums , forming a pair . The operation is done on nums as many times as possible. Return a 0-indexed integer array answer of size 2 where answer[0] is the number of pairs that are formed and answer[1] is the number of leftover integers in nums after doing the operation as many times as possible . Example 1: Input: nums = [1,3,2,1,3,2,2]

Detailed Explanation

The problem asks you to find the maximum number of pairs that can be formed from identical integers in an array and the number of integers left over after forming all possible pairs. The input is a 0-indexed integer array `nums`. In each operation, you can select two identical integers and remove them, creating a pair. You repeat this until no more pairs can be formed. The output is a 0-indexed array `answer` of size 2, where `answer[0]` is the number of pairs and `answer[1]` is the count of remaining single integers.

Solution Approach

The solution uses a frequency counting approach. It first counts the occurrences of each integer in the input array using a hash map (or frequency array). Then, for each integer, it calculates the number of pairs that can be formed by integer division (number of occurrences divided by 2). The remainder from this division represents the leftover integers. Finally, it sums up the total number of pairs and leftovers across all integers to produce the final result.

Step-by-Step Algorithm

Step 1: Create a hash map (or array) to store the frequency of each integer in the input array `nums`. Iterate through `nums`, incrementing the count for each integer encountered.
Step 2: Initialize variables `pairs` and `leftovers` to 0. These will store the total number of pairs and leftovers, respectively.
Step 3: Iterate through the frequency counts (values of the hash map or array). For each count:
Step 4: Calculate the number of pairs formed using integer division (`count // 2` or `count / 2`). Add this to the `pairs` variable.
Step 5: Calculate the number of leftovers using the modulo operator (`count % 2`). Add this to the `leftovers` variable.
Step 6: After iterating through all counts, return an array containing `pairs` and `leftovers`.

Key Insights

Insight 1: Using a hash map (or frequency array) to efficiently count the occurrences of each integer is crucial for determining the number of pairs that can be formed. This allows for a linear time solution.
Insight 2: Integer division (`//` in Python, `/` in Java, C++, C) and modulo operation (`%` in all languages) are used to calculate the number of pairs and leftovers respectively for each integer.
Insight 3: The problem's constraints (array size <= 100, integer values <= 100) allow for a simple frequency array to be used in C and C++, improving space efficiency compared to HashMaps in Python and Java, although the space difference is negligible for this problem size.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Hash Table, Counting.

Companies

Asked at: Altimetrik.

Maximum Number of Pairs in Array | LeetCode 2341

Easy

Array Hash Table Counting

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

Solution Code

Available in:

import java.util.HashMap;

class Solution {
    public int[] numberOfPairs(int[] nums) {
        HashMap<Integer, Integer> counts = new HashMap<>();
        for (int num : nums) {
            counts.put(num, counts.getOrDefault(num, 0) + 1);
        }
        int pairs = 0;
        int leftovers = 0;
        for (int count : counts.values()) {
            pairs += count / 2;
            leftovers += count % 2;
        }
        return new int[]{pairs, leftovers};
    }
}

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Problem Info

Description

Problem 2341: Maximum Number of Pairs in Array - Detailed explanation and solution approaches.

Topics

Array Hash Table Counting

Companies

Altimetrik

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:2341

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

6 steps

1
Step 1: Create a hash map (or array) to store the frequency of each integer in the input array `nums`. Iterate through `nums`, incrementing the count for each integer encountered.
2
Step 2: Initialize variables `pairs` and `leftovers` to 0. These will store the total number of pairs and leftovers, respectively.
3
Step 3: Iterate through the frequency counts (values of the hash map or array). For each count:
4
Step 4: Calculate the number of pairs formed using integer division (`count // 2` or `count / 2`). Add this to the `pairs` variable.
5
Step 5: Calculate the number of leftovers using the modulo operator (`count % 2`). Add this to the `leftovers` variable.
6
Step 6: After iterating through all counts, return an array containing `pairs` and `leftovers`.

💡

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 dominant factor in time complexity is the single pass through the input array and the frequency array/hashmap. Space complexity is determined by the size of the data structure used to store the frequency of each element which is proportional to the number of unique elements in the array (in worst case, all are unique).

📖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

Sorting-based approach

Sort the array first. Then, iterate through the sorted array, counting consecutive identical elements to form pairs.

Time: O(n log n) due to sortingSpace: O(1) or O(n) depending on the sorting algorithm used (in-place or not)

Trade-offs: Less efficient than the hash map/frequency array approach for larger inputs because of the O(n log n) sorting time. Might be preferred if you need the array sorted for other purposes.

✨

Key Insights

1Insight 1: Using a hash map (or frequency array) to efficiently count the occurrences of each integer is crucial for determining the number of pairs that can be formed. This allows for a linear time solution.
2Insight 2: Integer division (`//` in Python, `/` in Java, C++, C) and modulo operation (`%` in all languages) are used to calculate the number of pairs and leftovers respectively for each integer.
3Insight 3: The problem's constraints (array size <= 100, integer values <= 100) allow for a simple frequency array to be used in C and C++, improving space efficiency compared to HashMaps in Python and Java, although the space difference is negligible for this problem size.

📚

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!

Edge Cases

Edge case 1: Empty input array. The solution handles this correctly by returning [0, 0].
Edge case 2: An array with only one element. The solution correctly returns [0, 1] as there are no pairs and one leftover element.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to handle the case where the input array is empty or contains only one element.

✗Common mistake 2: Incorrectly calculating the number of pairs and leftovers. The integer division and modulo operations must be applied correctly for each frequency count.

✅

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: Inventory management. Determining how many complete sets of items can be assembled from available parts and how many individual parts will remain.

🏦Real-world scenario 2: Data analysis. Counting the frequency of occurrences of different values in a dataset and identifying patterns.

💡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

Use this problem to demonstrate clean code practices. Variable naming and code organization matter.

⚠️ 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: June 2, 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

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

@AlgoMasterJul 13

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 6

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJun 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 "Maximum Number of Pairs in Array"?

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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