Math Problem Statement

You said: To calculate the memory requirements for a HybridDeque object storing 9 items, we can break the memory consumption into smaller parts based on the assumptions provided. Here's a step-by-step approach:

  1. Memory for Object Overheads Each block and supporting structure consumes memory in the following ways:

12-byte header: Each object has a 12-byte header. 7 references, each 4 bytes: There are 7 references used in the object (for leftCursor, rightCursor, block, block, prev, elements, next). 3 integers, each 4 bytes: Three integers (size, index, index) are used in the structure. So, the memory required for this part is the same as for an empty HybridDeque:

48 + 28 + 12

88  bytes 48+28+12=88 bytes 2. Memory for the Elements Array We know that each block has space for 8 items, and arrays have 16 bytes of overhead. Each reference in the array occupies 4 bytes. So, for an 8-item block, the memory required is:

16 + 8 × 4

48  bytes 16+8×4=48 bytes Since the HybridDeque is storing 9 items, and each block can hold 8 items, we need two blocks (one full block for 8 items and another block for 1 item). For each block, we add 48 bytes for the elements array.

The memory for two blocks is:

2 × 48

96  bytes 2×48=96 bytes 3. Total Memory Calculation Finally, to calculate the total memory required for the HybridDeque storing 9 items:

88  bytes (object overhead) + 96  bytes (two blocks)

184  bytes 88 bytes (object overhead)+96 bytes (two blocks)=184 bytes This isn't over 200 bytes, but we missed considering the headers and some potential additional overheads for managing multiple blocks.

  1. Adding Headers for Each Block Each block has its own 12-byte header. Since there are two blocks, the memory for the block headers is:

2 × 12

24  bytes 2×12=24 bytes 5. Final Total Memory Now, adding the memory for the block headers:

88  bytes + 96  bytes + 24  bytes

208  bytes 88 bytes+96 bytes+24 bytes=208 bytes Thus, a HybridDeque object storing 9 items requires 208 bytes.

This is a correct solution to another problem. Use the exact same steps to answer this

Assuming a block size of 64 How many bytes are required for a HybridDeque object that stores 10,000 items. Assume that at most one block is partially filled.

Solution

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Math Problem Analysis

Mathematical Concepts

Memory calculation
Block data structures

Formulas

Memory overhead formula: 12 + 7 * 4 + 3 * 4 = 88 bytes
Block memory formula: 16 + block_size * 4
Number of blocks required: ceil(total_items / block_size)

Theorems

Memory allocation for data structures
Block management

Suitable Grade Level

Undergraduate (Computer Science)