(a)
Describe thenumber of disk accesses and CPU time for n stack operations in worse-case by using the simple implementation.
(a)
Explanation of Solution
In worse case for every stack operation it requires disk access for implementation sothe number of disk accesses for n stack operations using this simple implementation is asymptotically equals to
The CPU time in worse case for n -stack operations is
(b)
Describethe number of diskaccesses and the CPU time required for n -PUSH operations in worse-case.
(b)
Explanation of Solution
The new page starts only when everymthpushes therefore the number of disk operations is n/m. The diskaccess requires time of asymptotically
Hence,the number of disk accesses and CPU time for n - PUSH operations in worse-case is
(c)
Describe the disk accesses and the CPU time required for n -stack operations in worse-case.
(c)
Explanation of Solution
Stack operations include PUSH and POP. The PUSH and POP operations requires alternate disk accesses that means mdisk accesses for performing stack operation so the number of disk accesses asymptotically is
The CPU time for performing stack operations is equal to
(d)
Describe that the amortized number of disk accesses is O (1 /m ) and the amortized CPU time is O (1) for any stack operation .
(d)
Explanation of Solution
At the initial function called as Potential Function of stack defined by difference of size of stack and recent pass which is multiple of m. The value of potential function is 0 at initial state.
When any stack operation is performed the value is decreased and increased according to the operation by one.Loading new pages requires the position which is at leastm position away from recent position to cross the page boundary therefore loading and storing of new stack page requires CPU time of O ( m ).
By dropping appropriate Potential function of order O ( m ) and selecting the suitable value for potential value results to managed the stack pages so that the amortized number of disk accesses for any stack operation is O (1 /m ) and the amortized CPU time for any stack operation is O (1).
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