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Chapter 10: Problem 4

Assuming that one person can add two numbers in \(t_{e}\) time, how long will it take that person to add all \(n\) numbers of a list considering the operation of addition as the basic operation? Justify your answer.

Short Answer

Expert verified
The time it will take to add all \(n\) numbers of a list is given by \(t_{e} \times (n-1)\).

Step by step solution

01

Define the Basic Operation

Identify the basic operation which is the addition of two numbers, taking a time \(t_{e}\). This is the smallest unit of time we are considering.
02

Calculate Time for All Additions

Perform the addition operation on all numbers in the list. Since every two numbers take \(t_{e}\), adding (n-1) pairs of numbers in the list (as we will need one less operation than the total number of integers to add them all) will take \(t_{e} \times (n-1)\).
03

Result

So to add all \(n\) numbers in the list, it will take \(t_{e} \times (n-1)\)

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Most popular questions from this chapter

Write a PRAM algorithm using \(n^{3}\) processors to multiply two \(n \times n\) matrices. Your algorithm should run in \(\Theta(\lg n)\) time.

Write a CREW PRAM algorithm for determining for each element of an \(n\) -clement linked list if it is the middle \(\left(\int n / 2 \text { th }\right)\) element in \(\Theta(\lg n)\) time.

Write a PRAM algorithm for Quicksort using \(n\) processors to sort a list of \(n\) elements.

Assuming that one person can add two numbers in \(t_{e}\) time, how long will it take that person to add two \(n \times n\) matrices considering the operation of addition as the basic operation? Justify your answer.

Consider the problem of adding two \(n \times n\) matrices. If it takes \(t_{\alpha}\) time for one person to add two numbers, how many people do we need to minimize the total time spent to get the final answer? What will be the minimum amount of time needed to find the answer if we have enough people? Justify your answers.
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