What is the time complexity of Sort Array by Increasing Frequency?

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

What data structures are used to solve Sort Array by Increasing Frequency?

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

What are the key insights for solving Sort Array by Increasing Frequency?

Insight 1: Using a hash map (or dictionary in Python) to efficiently count the frequency of each number is crucial for achieving an optimal time complexity. Insight 2: The sorting process requires a custom comparison function (or lambda in Python) that prioritizes frequency first (ascending) and then value (descending) when frequencies are equal.

Which companies ask LeetCode 1636. Sort Array by Increasing Frequency in interviews?

This problem is frequently asked at Accenture, Agoda, Akuna Capital, SAP, tcs.

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Sort Array by Increasing Frequency - LeetCode 1636 Solution

Sort Array by Increasing Frequency - Complete Solution Guide

Sort Array by Increasing Frequency is LeetCode problem 1636, 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

Given an array of integers nums , sort the array in increasing order based on the frequency of the values. If multiple values have the same frequency, sort them in decreasing order. Return the sorted array . Example 1: Input: nums = [1,1,2,2,2,3] Output: [3,1,1,2,2,2] Explanation: '3' has a frequency of 1, '1' has a frequency of 2, and '2' has a frequency of 3. Example 2: Input: nums = [2,3,1,3,2] Output: [1,3,3,2,2] Explanation: '2' and '3' both have a frequency of 2, so they are sorted in decr

Detailed Explanation

The problem asks you to sort an array of integers based on the frequency of each number. The sorting should prioritize numbers with lower frequency first. If two numbers have the same frequency, the number with the larger value should come first. The input is an array of integers, and the output is a new array sorted according to these rules. Constraints limit the array size and the range of integer values.

Solution Approach

The provided solutions generally follow a two-step approach: First, they count the frequency of each number using a hash map (or equivalent). Second, they sort the array based on the frequency and value using a custom comparator or a key function in the sorting algorithm. The Python solution elegantly uses a lambda function within the `sort()` method for conciseness. The Java solution employs a custom comparator for the `Collections.sort()` method, explicitly handling the frequency and value comparisons. The C++ solution uses `map` and then sorts based on frequency, followed by reverse sorting within each frequency group. The C solution uses a struct to store frequency and values, and `qsort` to sort this array.

Step-by-Step Algorithm

Step 1: Count the frequency of each number using a hash map (or equivalent). For each number in the input array, increment its count in the hash map.
Step 2: Sort the input array based on a custom comparison criteria. The comparison should first check the frequencies of the numbers being compared. The number with the lower frequency comes first. If frequencies are equal, the number with the higher value comes first.
Step 3: Return the sorted array.

Key Insights

Insight 1: Using a hash map (or dictionary in Python) to efficiently count the frequency of each number is crucial for achieving an optimal time complexity.
Insight 2: The sorting process requires a custom comparison function (or lambda in Python) that prioritizes frequency first (ascending) and then value (descending) when frequencies are equal.
Insight 3: Handling negative numbers correctly is important, as the example includes negative integers. The sorting criteria must work correctly regardless of sign.

Complexity Analysis

Time Complexity: O(nlogn)

Space Complexity: O(n)

Topics

This problem involves: Array, Hash Table, Sorting.

Companies

Asked at: Accenture, Agoda, Akuna Capital, SAP, tcs.

Sort Array by Increasing Frequency | LeetCode 1636

Easy

Array Hash Table Sorting

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

Solution Code

Available in:

import java.util.HashMap;
import java.util.Map;
import java.util.ArrayList;
import java.util.Collections;

class Solution {
    public int[] frequencySort(int[] nums) {
        Map<Integer, Integer> frequencyMap = new HashMap<>();
        for (int num : nums) {
            frequencyMap.put(num, frequencyMap.getOrDefault(num, 0) + 1);
        }

        ArrayList<Integer> list = new ArrayList<>();
        for (int num : nums) {
            list.add(num);
        }

        Collections.sort(list, (a, b) -> {
            int frequencyA = frequencyMap.get(a);
            int frequencyB = frequencyMap.get(b);
            if (frequencyA != frequencyB) {
                return frequencyA - frequencyB;
            } else {
                return b - a;
            }
        });

        int[] result = new int[nums.length];
        for (int i = 0; i < nums.length; i++) {
            result[i] = list.get(i);
        }

        return result;
    }
}

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Problem Info

Description

Problem 1636: Sort Array by Increasing Frequency - Detailed explanation and solution approaches.

Topics

Array Hash Table Sorting

Companies

AccentureAgodaAkuna CapitalSAPtcs

Stats

Difficulty:Easy

Languages:4

Companies:5

Problem #:1636

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

3 steps

1
Step 1: Count the frequency of each number using a hash map (or equivalent). For each number in the input array, increment its count in the hash map.
2
Step 2: Sort the input array based on a custom comparison criteria. The comparison should first check the frequencies of the numbers being compared. The number with the lower frequency comes first. If frequencies are equal, the number with the higher value comes first.
3
Step 3: Return the sorted 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(nlogn)

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is dominated by the sorting step, which takes O(n log n) time in the average and worst cases for most comparison-based sorting algorithms. The space complexity is O(n) because the hash map to store frequencies can, in the worst case, store all unique numbers from the input array.

📖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 priority queue (heap)

Maintain a min-heap where each element is a pair (frequency, value). Iterate through the frequency map. For each number and its frequency, push the pair onto the heap. Then pop elements one by one to reconstruct the sorted array.

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

Trade-offs: This approach might offer slightly different constant factors in time complexity compared to direct sorting, but the overall asymptotic complexity remains the same.

✨

Key Insights

1Insight 1: Using a hash map (or dictionary in Python) to efficiently count the frequency of each number is crucial for achieving an optimal time complexity.
2Insight 2: The sorting process requires a custom comparison function (or lambda in Python) that prioritizes frequency first (ascending) and then value (descending) when frequencies are equal.
3Insight 3: Handling negative numbers correctly is important, as the example includes negative integers. The sorting criteria must work correctly regardless of sign.

📚

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: Empty input array. The solutions should gracefully handle this case; most of them implicitly do so by using the length of the input array.
Edge case 2: All numbers are the same. The solution should return the same array as the input because the frequency is the same for all numbers. The sorting by decreasing value then keeps the order intact.
Edge case 3: Presence of negative numbers and zero. The solutions must handle negative numbers correctly and distinguish between them based on both frequency and magnitude.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly implementing the comparison function during sorting. Failing to prioritize frequency correctly or mishandling the tie-breaker based on decreasing value can lead to an incorrect output.

✗Common mistake 2: Not handling edge cases, particularly an empty input array. This can result in runtime errors or unexpected behavior.

✗Common mistake 3: Inefficient frequency counting. Using nested loops or other inefficient methods for frequency counting will lead to a higher than optimal time complexity.

✅

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: Log analysis. Sorting log entries based on the frequency of different events can help identify the most frequent occurrences and pinpoint potential issues.

🏦Real-world scenario 2: Data visualization. When presenting data, it is often useful to order items by frequency to emphasize the most common occurrences. This is commonly used to generate bar charts.

💡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 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

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

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

What are the trade-offs of using a hash table?

Hash tables provide O(1) average-case lookup, insertion, and deletion, making them ideal for frequency counting and duplicate detection. However, they use O(n) extra space and may degrade to O(n) time in worst-case scenarios with hash collisions. Always consider if the space trade-off is acceptable.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Sort Array by Increasing Frequency"?

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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