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GATE CSE 2023 Q57: LRU page faults for column-wise access of int D[128][128]

Question

Consider the following two-dimensional array D in the C programming language, which is stored in row-major order:

int D[128][128];

Demand paging is used for allocating memory and each physical page frame holds 512 elements of the array D. The Least Recently Used (LRU) page-replacement policy is used by the operating system. A total of 30 physical page frames are allocated to a process which executes the following code snippet:

for (int i = 0; i < 128; i++)
    for (int j = 0; j < 128; j++)
        D[j][i] *= 10;

The number of page faults generated during the execution of this code snippet is _______.

Try it: numerical answer: type the value

Numerical answer. No negative marking.
Show answer and explanation

Answer: 4096 (official GATE 2023 final answer key)

Concept used: Column-wise traversal of a row-major array touches a new page every few rows; LRU with fewer frames than pages thrashes.

First step: One page holds 4 rows, so the array spans 32 pages; see what LRU with 30 frames does when one column sweeps all 32 pages.

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Source: official GATE 2023 CS question paper and final answer key, organised by IIT Kanpur. Question paper · Answer key

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