What is the time complexity of Minimize Maximum Pair Sum in Array?

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

What data structures are used to solve Minimize Maximum Pair Sum in Array?

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

What are the key insights for solving Minimize Maximum Pair Sum in Array?

Insight 1: Sorting the array is crucial. Pairing the smallest element with the largest, the second smallest with the second largest, and so on, will minimize the maximum pair sum. Insight 2: The 'two pointers' technique is effective after sorting to efficiently iterate from both ends of the sorted array.

Which companies ask LeetCode 1877. Minimize Maximum Pair Sum in Array in interviews?

This problem is frequently asked at eBay.

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Minimize Maximum Pair Sum in Array - LeetCode 1877 Solution

Minimize Maximum Pair Sum in Array - Complete Solution Guide

Minimize Maximum Pair Sum in Array is LeetCode problem 1877, 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

The pair sum of a pair (a,b) is equal to a + b . The maximum pair sum is the largest pair sum in a list of pairs. For example, if we have pairs (1,5) , (2,3) , and (4,4) , the maximum pair sum would be max(1+5, 2+3, 4+4) = max(6, 5, 8) = 8 . Given an array nums of even length n , pair up the elements of nums into n / 2 pairs such that: Each element of nums is in exactly one pair, and The maximum pair sum is minimized . Return the minimized maximum pair sum after optimally pairing up the elements

Detailed Explanation

The problem requires us to pair elements of an array (of even length) such that the sum of each pair is calculated, and the maximum of all these pair sums is minimized. In essence, we want to find the best pairing to make the largest pair sum as small as possible. For instance, given `[3, 5, 2, 3]`, pairing `3` with `3` and `5` with `2` results in pair sums of `6` and `7` respectively. The maximum of these is `7`, which is the desired output. The constraints state that the array's length is even and between 2 and 10^5, and each element is between 1 and 10^5.

Solution Approach

The solution involves sorting the input array first. Once sorted, we use two pointers, `left` and `right`, initialized to the start and end of the array respectively. We iterate while `left < right`, calculating the sum of the elements at these two pointers. We update the `max_pair_sum` if the current sum is greater. Then, we move `left` one step to the right and `right` one step to the left. This pairing strategy (smallest with largest, second smallest with second largest, and so on) guarantees that the maximum pair sum will be minimized.

Step-by-Step Algorithm

Step 1: Sort the input array `nums` in ascending order using an efficient sorting algorithm (e.g., merge sort or quicksort).
Step 2: Initialize two pointers, `left` to 0 and `right` to `len(nums) - 1`.
Step 3: Initialize `max_pair_sum` to 0.
Step 4: Iterate while `left < right`:
Step 5: Calculate the current pair sum: `current_sum = nums[left] + nums[right]`.
Step 6: Update `max_pair_sum` if `current_sum > max_pair_sum`.
Step 7: Increment `left` and decrement `right`.
Step 8: Return `max_pair_sum`.

Key Insights

Insight 1: Sorting the array is crucial. Pairing the smallest element with the largest, the second smallest with the second largest, and so on, will minimize the maximum pair sum.
Insight 2: The 'two pointers' technique is effective after sorting to efficiently iterate from both ends of the sorted array.
Insight 3: We only need to keep track of the maximum pair sum encountered so far. No need to store all the pair sums.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(1)

Topics

This problem involves: Array, Two Pointers, Greedy, Sorting.

Companies

Asked at: eBay.

Minimize Maximum Pair Sum in Array | LeetCode 1877

Medium

Array Two Pointers Greedy Sorting

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

Solution Code

Available in:

import java.util.Arrays;

class Solution {
    public int minPairSum(int[] nums) {
        Arrays.sort(nums);
        int max_pair_sum = 0;
        int left = 0;
        int right = nums.length - 1;
        
        while (left < right) {
            int current_sum = nums[left] + nums[right];
            if (current_sum > max_pair_sum) {
                max_pair_sum = current_sum;
            }
            left += 1;
            right -= 1;
        }
        
        return max_pair_sum;
    }
}

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Problem Info

Description

Problem 1877: Minimize Maximum Pair Sum in Array - Detailed explanation and solution approaches.

Topics

Array Two Pointers Greedy Sorting

Companies

eBay

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:1877

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

8 steps

1
Step 1: Sort the input array `nums` in ascending order using an efficient sorting algorithm (e.g., merge sort or quicksort).
2
Step 2: Initialize two pointers, `left` to 0 and `right` to `len(nums) - 1`.
3
Step 3: Initialize `max_pair_sum` to 0.
4
Step 4: Iterate while `left < right`:
5
Step 5: Calculate the current pair sum: `current_sum = nums[left] + nums[right]`.
6
Step 6: Update `max_pair_sum` if `current_sum > max_pair_sum`.
7
Step 7: Increment `left` and decrement `right`.
8
Step 8: Return `max_pair_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 log n)

✨ Log-linear - Great for sorting algorithms!

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is dominated by the sorting step, which typically takes O(n log n) time using algorithms like merge sort or quicksort. The two-pointer iteration takes O(n) time, but this is subsumed by the sorting time. The space complexity is O(1) because we are sorting the array in-place (depending on the sorting algorithm implementation) and using only a few extra variables to store pointers and the maximum sum.

📖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

Counting Sort

If the range of numbers in the array is relatively small (e.g., up to 10^5 as in the constraints), counting sort can be used for sorting. This would reduce the time complexity to O(n + k), where k is the range of the numbers.

Time: O(n + k), where k is the range of input values.Space: O(k)

Trade-offs: Counting sort is faster when k is significantly smaller than n log n, but it requires extra space O(k). It's useful if the range of numbers is known to be limited and considerably smaller than n.

✨

Key Insights

1Insight 1: Sorting the array is crucial. Pairing the smallest element with the largest, the second smallest with the second largest, and so on, will minimize the maximum pair sum.
2Insight 2: The 'two pointers' technique is effective after sorting to efficiently iterate from both ends of the sorted array.
3Insight 3: We only need to keep track of the maximum pair sum encountered so far. No need to store all the pair sums.

📚

Key Terms Explained

For Students

Array

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

Two Pointers

Using two indices to traverse data from different positions simultaneously.

Greedy Algorithm

Making the best choice at each step without looking ahead.

Sorting

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

Edge Cases

Edge case 1: Array with only two elements: The algorithm works correctly in this case as well, since it sorts the array and directly calculates the sum of the two elements.
Edge case 2: Array with duplicate elements: The algorithm handles duplicate elements effectively because the sorting process groups similar elements together, ensuring that the pairing strategy (smallest with largest, etc.) is still optimal.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not sorting the array: Without sorting, there is no guarantee of finding the optimal pairing strategy. The pairing may lead to a larger maximum pair sum.

✗Common mistake 2: Incorrectly initializing pointers: Failing to initialize the pointers correctly or incorrectly incrementing/decrementing them in the loop can lead to out-of-bounds errors or incorrect results.

✅

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: Resource allocation: Allocating resources of varying capacities to tasks, such that the 'bottleneck' (maximum resource required) is minimized. For example, assigning servers with different processing power to tasks with different computational demands.

🏦Real-world scenario 2: Load Balancing: In a distributed system, pairing servers with high load and low load to distribute the load evenly, minimizing the maximum load on any single server.

💡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: August 17, 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

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

@InterviewProJul 13

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

@CodeNinjaJul 6

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

@TechLeadJun 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 avoid infinite loops with two pointers?

Always ensure your loop condition guarantees termination (typically left < right or slow != fast). Move at least one pointer in each iteration, and handle edge cases where pointers might not move (like skipping duplicates). Draw out pointer movement on paper first.

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 "Minimize Maximum Pair Sum in Array"?

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

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