In operating systems that use paging for memory management, page replacement algorithm is needed to decide which page needs to be replaced when the new page comes in. Whenever a new page is referred and is not present in memory, the page fault occurs and Operating System replaces one of the existing pages with a newly needed page.
Given a sequence of pages in an array pages[] of length N and memory capacity C, find the number of page faults using Least Recently Used (LRU) Algorithm.
Note:- Before solving this example revising the OS LRU cache mechanism is recommended.
Example 1:
Input: N = 9, C = 4
pages = {5, 0, 1, 3, 2, 4, 1, 0, 5}
Output: 8
Explaination: memory allocated with 4 pages 5, 0, 1,
3: page fault = 4
page number 2 is required, replaces LRU 5:
page fault = 4+1 = 5
page number 4 is required, replaces LRU 0:
page fault = 5 + 1 = 6
page number 1 is required which is already present:
page fault = 6 + 0 = 6
page number 0 is required which replaces LRU 3:
page fault = 6 + 1 = 7
page number 5 is required which replaces LRU 2:
page fault = 7 + 1 = 8.
Your Task:
You do not need to read input or print anything. Your task is to complete the function pageFaults() which takes N, C and pages[] as input parameters and returns the number of page faults.
Expected Time Complexity: O(N*C)
Expected Auxiliary Space: O(N)
Constraints:
1 ≤ N ≤ 1000
1 ≤ C ≤ 100
1 ≤ pages[i] ≤ 1000

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