What is the time complexity of Design Memory Allocator?

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

What data structures are used to solve Design Memory Allocator?

This problem uses Array, Hash Table, Design, Simulation. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Design Memory Allocator?

Insight 1: The core idea is to simulate the memory allocation process using an array to represent the memory blocks and their respective IDs. Insight 2: The `allocate` operation requires finding a contiguous block of free memory, which can be done by iterating through the array and keeping track of the current free count.

Which companies ask LeetCode 2502. Design Memory Allocator in interviews?

This problem is frequently asked at ByteDance, OpenAI, Qualcomm, Rubrik, Two Sigma.

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Design Memory Allocator - LeetCode 2502 Solution

Design Memory Allocator - Complete Solution Guide

Design Memory Allocator is LeetCode problem 2502, 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 n representing the size of a 0-indexed memory array. All memory units are initially free. You have a memory allocator with the following functionalities: Allocate a block of size consecutive free memory units and assign it the id mID . Free all memory units with the given id mID . Note that: Multiple blocks can be allocated to the same mID . You should free all the memory units with mID , even if they were allocated in different blocks. Implement the Allocator class: All

Detailed Explanation

The problem asks us to implement a memory allocator that manages a contiguous block of memory. The allocator should support two operations: `allocate` and `freeMemory`. `allocate(size, mID)` finds the leftmost block of `size` consecutive free memory units and assigns the ID `mID` to it, returning the starting index of the allocated block. If no such block exists, it returns -1. `freeMemory(mID)` frees all memory units with the given ID `mID` and returns the number of units freed. The memory is represented as an array, initially all zeros, indicating free memory. We need to design a class with these functionalities, handling constraints on the size of the memory and the number of operations.

Solution Approach

The provided solution uses a simple array-based approach to simulate the memory allocator. The `Allocator` class maintains an integer array `memory` to represent the memory blocks. The `allocate` method iterates through the `memory` array, keeping track of the consecutive free blocks. If it finds a block of sufficient size, it assigns the given `mID` to the block and returns the starting index. The `freeMemory` method iterates through the `memory` array, freeing all blocks with the given `mID` and counting the number of freed blocks.

Step-by-Step Algorithm

Step 1: Initialize the `Allocator` class with the size `n` and create a `memory` array of size `n` filled with zeros.
Step 2: In the `allocate` method, iterate through the `memory` array.
Step 3: Maintain a `free_count` variable to track the number of consecutive free blocks.
Step 4: If `memory[i]` is 0, increment `free_count`. Otherwise, reset `free_count` to 0.
Step 5: If `free_count` equals the requested `size`, calculate the starting index of the block (`start_index = i - size + 1`).
Step 6: Assign the given `mID` to the memory blocks from `start_index` to `start_index + size - 1`.
Step 7: Return `start_index`.
Step 8: If the loop completes without finding a suitable block, return -1.
Step 9: In the `freeMemory` method, iterate through the `memory` array.
Step 10: If `memory[i]` equals the given `mID`, set `memory[i]` to 0 and increment a `freed_count` variable.
Step 11: Return `freed_count`.

Key Insights

Insight 1: The core idea is to simulate the memory allocation process using an array to represent the memory blocks and their respective IDs.
Insight 2: The `allocate` operation requires finding a contiguous block of free memory, which can be done by iterating through the array and keeping track of the current free count.
Insight 3: The `freeMemory` operation requires iterating through the entire array to find and free blocks associated with the specified ID.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Hash Table, Design, Simulation.

Companies

Asked at: ByteDance, OpenAI, Qualcomm, Rubrik, Two Sigma.

Design Memory Allocator | LeetCode 2502

Medium

Array Hash Table Design Simulation

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

Solution Code

Available in:

class Allocator {

    private int n;
    private int[] memory;

    public Allocator(int n) {
        this.n = n;
        this.memory = new int[n];
    }
    
    public int allocate(int size, int mID) {
        int free_count = 0;
        for (int i = 0; i < this.n; i++) {
            if (this.memory[i] == 0) {
                free_count += 1;
            } else {
                free_count = 0;
            }
            
            if (free_count == size) {
                int start_index = i - size + 1;
                for (int j = start_index; j < start_index + size; j++) {
                    this.memory[j] = mID;
                }
                return start_index;
            }
        }
        
        return -1;
    }
    
    public int freeMemory(int mID) {
        int freed_count = 0;
        for (int i = 0; i < this.n; i++) {
            if (this.memory[i] == mID) {
                this.memory[i] = 0;
                freed_count += 1;
            }
        }
        return freed_count;
    }
}

/**
 * Your Allocator object will be instantiated and called as such:
 * Allocator obj = new Allocator(n);
 * int param_1 = obj.allocate(size,mID);
 * int param_2 = obj.freeMemory(mID);
 */

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Problem Info

Description

Problem 2502: Design Memory Allocator - Detailed explanation and solution approaches.

Topics

Array Hash Table Design Simulation

Companies

ByteDanceOpenAIQualcommRubrikTwo Sigma

Stats

Difficulty:Medium

Languages:4

Companies:5

Problem #:2502

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 the `Allocator` class with the size `n` and create a `memory` array of size `n` filled with zeros.
2
Step 2: In the `allocate` method, iterate through the `memory` array.
3
Step 3: Maintain a `free_count` variable to track the number of consecutive free blocks.
4
Step 4: If `memory[i]` is 0, increment `free_count`. Otherwise, reset `free_count` to 0.
5
Step 5: If `free_count` equals the requested `size`, calculate the starting index of the block (`start_index = i - size + 1`).
6
Step 6: Assign the given `mID` to the memory blocks from `start_index` to `start_index + size - 1`.
7
Step 7: Return `start_index`.
8
Step 8: If the loop completes without finding a suitable block, return -1.
9
Step 9: In the `freeMemory` method, iterate through the `memory` array.
10
Step 10: If `memory[i]` equals the given `mID`, set `memory[i]` to 0 and increment a `freed_count` variable.
11
Step 11: Return `freed_count`.

💡

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 `allocate` method has to potentially scan the entire array to find a contiguous free block. The `freeMemory` method has to scan the entire array to release all blocks with a certain `mID`. Hence O(n) time complexity for both. The space complexity is determined by the size of the memory array, which is proportional to the input `n`.

📖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

Linked List

Represent the memory as a linked list of free and allocated blocks. This can allow for faster allocation and freeing in some cases, especially when there are many small allocations and deallocations interspersed.

Time: Allocate: O(n) in worst case (need to traverse the list), Free: O(n) to traverse list but O(1) if you use a hashmap that maps mID to a list of blocksSpace: O(n), where n is the size of the memory.

Trade-offs: Using a linked list can improve performance if allocations and deallocations are frequent and scattered, but it adds the overhead of managing the linked list structure. The array based solution is simpler to implement.

Segment Tree

A segment tree can be used to efficiently find the leftmost available block of a certain size. Each node in the segment tree would store the maximum contiguous free space in the corresponding range.

Time: Allocate: O(log n), Free: O(log n)Space: O(n)

Trade-offs: A segment tree provides logarithmic time complexity for both allocation and freeing, making it significantly faster for large memory sizes and frequent operations. However, it's a more complex data structure to implement and has a higher constant overhead.

✨

Key Insights

1Insight 1: The core idea is to simulate the memory allocation process using an array to represent the memory blocks and their respective IDs.
2Insight 2: The `allocate` operation requires finding a contiguous block of free memory, which can be done by iterating through the array and keeping track of the current free count.
3Insight 3: The `freeMemory` operation requires iterating through the entire array to find and free blocks associated with the specified ID.

📚

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: `allocate` called with a `size` larger than `n`. The method correctly iterates through the loop, never finding a suitable block and returns -1.
Edge case 2: `freeMemory` called with an `mID` that does not exist. The method iterates through the loop, `freed_count` remains 0, and 0 is returned.
Edge case 3: Allocating immediately after freeing. The allocate method should correctly find the newly freed block if it fits the required size.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Failing to reset `free_count` when a non-free block is encountered in the `allocate` method, leading to incorrect allocation.

✗Common mistake 2: Not handling the edge case where no free block of the required `size` exists, causing incorrect return values or errors.

✗Common mistake 3: Forgetting to iterate through the entire memory array in `freeMemory`, leading to only partially freeing the memory associated with a given `mID`.

✅

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: Operating systems use memory allocation algorithms to manage system memory for running processes. The problem mimics a simplified version of such a system.

🏦Real-world scenario 2: Game development utilizes memory allocators to efficiently allocate and deallocate memory for game objects, textures, and other resources.

💡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

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ 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: November 10, 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

❓

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.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

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 "Design Memory Allocator"?

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.

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