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:
- 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.
- 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)
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