Memory pool (fixed-size block allocator) in Embedded C - Time & Space Complexity

Time Complexity: Memory pool (fixed-size block allocator)

O(1)

Understanding Time Complexity

We want to understand how the time to allocate or free memory changes as the number of blocks grows.

How does the allocator's speed behave when managing many fixed-size blocks?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Simple fixed-size block allocator
void* mem_alloc() {
    if (free_list == NULL) return NULL; // no free blocks
    void* block = free_list;           // take first free block
    free_list = *(void**)free_list;   // update free list head
    return block;
}

void mem_free(void* block) {
    *(void**)block = free_list;       // add block back to free list
    free_list = block;
}
    

This code manages a list of free memory blocks. Allocation takes the first free block, and freeing adds a block back to the list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Access and update a pointer to the head of the free list.
• How many times: Each allocation or free does this once, no loops or recursion involved.

How Execution Grows With Input

Each allocation or free operation does a fixed number of steps regardless of how many blocks exist.

Input Size (n)	Approx. Operations
10	2-3 pointer steps
100	2-3 pointer steps
1000	2-3 pointer steps

Pattern observation: The number of steps stays the same no matter how many blocks are managed.

Final Time Complexity

Time Complexity: O(1)

This means allocation and freeing take the same short time no matter how many blocks are in the pool.

Common Mistake

[X] Wrong: "Allocation time grows as more blocks are used because the list gets longer."

[OK] Correct: The allocator always takes the first free block directly, so it does not search through the list.

Interview Connect

Understanding fixed-time memory operations shows you can reason about efficient resource management, a key skill in embedded systems and performance-critical code.

Self-Check

"What if the allocator searched the free list to find a block of a certain size? How would the time complexity change?"

Practice

1.

What is the main advantage of using a memory pool with fixed-size blocks in embedded systems?

easy

A. Unlimited memory usage

B. Automatic garbage collection

C. Faster and predictable memory allocation

D. Dynamic resizing of blocks

Solution

1. Step 1: Understand memory pool purpose

   A memory pool divides memory into fixed-size blocks to allocate memory quickly without fragmentation.

2. Step 2: Identify advantage in embedded systems

   Embedded systems need fast and predictable memory allocation, which memory pools provide.

3. Final Answer:

   Faster and predictable memory allocation -> Option C

4. Quick Check:

   Memory pool advantage = Faster and predictable memory allocation [OK]

Hint: Memory pools speed up allocation by fixed block sizes [OK]

Common Mistakes:

• Confusing memory pools with dynamic resizing
• Thinking memory pools provide garbage collection
• Assuming memory pools allow unlimited memory

2.

Which of the following is the correct way to declare a fixed-size memory pool array for 10 blocks of 32 bytes each in C?

?

easy

A. char pool[10][32];

B. char pool[32][10];

C. char *pool[10];

D. char pool[10*32];

Solution

1. Step 1: Understand array dimensions

   We want 10 blocks, each block is 32 bytes, so array should be 10 rows and 32 columns.

2. Step 2: Match declaration syntax

   char pool[10][32]; declares 10 blocks of 32 bytes each correctly.

3. Final Answer:

   char pool[10][32]; -> Option A

4. Quick Check:

   Array size = 10 blocks x 32 bytes [OK]

Hint: Rows = blocks, columns = block size in bytes [OK]

Common Mistakes:

• Swapping dimensions (32 and 10)
• Using pointer array instead of fixed blocks
• Declaring a single large array without blocks

3.

Given this simplified memory pool allocator code snippet, what will be the output?

char pool[3][16];
int free_blocks = 3;

char* allocate() {
    if (free_blocks > 0) {
        return pool[--free_blocks];
    }
    return NULL;
}

int main() {
    char* p1 = allocate();
    char* p2 = allocate();
    char* p3 = allocate();
    char* p4 = allocate();
    printf("%p %p %p %p\n", p1, p2, p3, p4);
    return 0;
}

medium

A. Three valid pointers and one NULL pointer

B. All pointers are NULL

C. All pointers point to the same block

D. Compilation error due to missing headers

Solution

1. Step 1: Trace allocation calls

   Initially free_blocks=3. Each allocate() call decrements free_blocks and returns pool[free_blocks]. So p1=pool[2], p2=pool[1], p3=pool[0], p4=NULL because free_blocks=0.

2. Step 2: Understand output

   First three pointers are valid addresses, last pointer is NULL.

3. Final Answer:

   Three valid pointers and one NULL pointer -> Option A

4. Quick Check:

   3 blocks allocated, 4th returns NULL [OK]

Hint: Allocation decreases free_blocks; NULL when none left [OK]

Common Mistakes:

• Assuming pointers are all NULL
• Thinking pointers point to same block
• Forgetting to decrement free_blocks

4.

Identify the bug in this memory pool free function and select the correct fix.

void free_block(char* block) {
    if (free_blocks < MAX_BLOCKS) {
        pool[free_blocks++] = block;
    }
}

medium

A. No bug; function works correctly

B. Incrementing free_blocks before storing pointer causes overwrite

C. Should check if block is NULL before freeing

D. Store pointer in pool array is wrong; should mark block as free differently

Solution

1. Step 1: Analyze free_block logic

   The pool array holds actual memory blocks, not pointers. Storing a pointer in pool overwrites data.

2. Step 2: Correct way to free block

   Freeing should mark the block as available in a separate structure or use a free list, not overwrite pool data.

3. Final Answer:

   Store pointer in pool array is wrong; should mark block as free differently -> Option D

4. Quick Check:

   Freeing must not overwrite pool memory [OK]

Hint: Freeing must not overwrite pool data blocks [OK]

Common Mistakes:

• Overwriting pool memory with pointers
• Not checking block validity
• Assuming pool holds pointers, not blocks

5.

You want to implement a memory pool that supports 5 blocks of 64 bytes each. You also want to track which blocks are free using a bitmap (an integer where each bit represents a block's status: 0 = free, 1 = used). Which of the following code snippets correctly initializes the bitmap and allocates a block?

?

hard

A. int bitmap = 0xFF; // all used
char pool[5][64];
char* allocate() {
for (int i = 0; i < 5; i++) {
if ((bitmap & (1 << i)) == 0) {
bitmap &= ~(1 << i);
return pool[i];
}
}
return NULL;
}

B. int bitmap = 0; // all free
char pool[5][64];
char* allocate() {
for (int i = 0; i < 5; i++) {
if ((bitmap & (1 << i)) == 0) {
bitmap |= (1 << i);
return pool[i];
}
}
return NULL;
}

C. int bitmap = 0; // all used
char pool[5][64];
char* allocate() {
for (int i = 0; i < 5; i++) {
if ((bitmap & (1 << i)) != 0) {
bitmap |= (1 << i);
return pool[i];
}
}
return NULL;
}

D. int bitmap = 0xFF; // all free
char pool[5][64];
char* allocate() {
for (int i = 0; i < 5; i++) {
if ((bitmap & (1 << i)) != 0) {
bitmap &= ~(1 << i);
return pool[i];
}
}
return NULL;
}

Solution

1. Step 1: Understand bitmap meaning

   Bitmap bit 0 means free, 1 means used. So initializing bitmap=0 means all blocks free.

2. Step 2: Check allocation logic

   Allocation finds first free bit (0), sets it to 1 (used), and returns that block.

3. Final Answer:

   Bitmap initialized to 0; allocate sets bit to 1 on allocation -> Option B

4. Quick Check:

   0 = free, set bit to 1 when used [OK]

Hint: 0 bits free, set bit to 1 when allocated [OK]

Common Mistakes:

• Initializing bitmap with all bits set (all used)
• Checking wrong bit condition for free blocks
• Setting bits incorrectly on allocation