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Semmy [17]
3 years ago
14

Suppose that a computer can run an algorithm on a problem of size 1,024 in time t. We do not know the complexity of the algorith

m. We note that when we run the same algorithm on a computer 8 times faster, in the same time t, we can solve a problem of size 8,192. We also note that when we run the same algorithm on a computer 8 times slower, in the same time t, we can solve a problem of size 128.
Computers and Technology
1 answer:
Setler79 [48]3 years ago
5 0

Answer:

Time Complexity of Problem - O(n)

Explanation:

When n= 1024 time taken is t. on a particular computer.

When computer is 8 times faster in same time t , n can be equal to 8192. It means on increasing processing speed input grows linearly.

When computer is 8 times slow then with same time t , n will be 128 which is (1/8)th time 1024.

It means with increase in processing speed by x factor time taken will decrease by (1/x) factor. Or input size can be increased by x times. This signifies that time taken by program grows linearly with input size n. Therefore time complexity of problem will be O(n).

If we double the speed of original machine then we can solve problems of size 2n in time t.

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Write a program that grades arithmetic quizzes as follows: Ask the user how many questions are in the quiz. Ask the user to ente
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Answer:

The program in C++ is as follows:

#include <iostream>

using namespace std;

int main(){

   int questions, answer;

   cout<<"Questions: ";

   cin>>questions;

   int answerkey[questions];

   cout<<"Enter answer keys: ";

   for(int i = 0; i< questions; i++){

       cin>>answerkey[i];    }

   int correct = 0;

   cout<<"Enter answers: ";

   for(int i = 0; i< questions; i++){

       cin>>answer;

       if(answer == answerkey[i]){

           correct++;        }    }

   cout<<"Correct answers: "<<correct<<endl;

   cout<<"Percentage correct : "<<(100 * correct)/questions<<"%";

   return 0;

}

Explanation:

This declares the number of questions and the answers submitted to each equation

   int questions, answer;

Prompt to get the number of questions

   cout<<"Questions: ";

This gets input for the number of questions

   cin>>questions;

This declares the answerkey as an array

   int answerkey[questions];

Prompt to get the answer key

   cout<<"Enter answer keys: ";

This iteration gets the answer key for each question

<em>    for(int i = 0; i< questions; i++){</em>

<em>        cin>>answerkey[i];    }</em>

This initializes the number of correct answers to 0

   int correct = 0;

Prompt to get the enter the answers

   cout<<"Enter answers: ";

This iterates through the answer keys

   for(int i = 0; i< questions; i++){

This gets the answer to each question

       cin>>answer;

This compares the answer to the answer key of the question

       if(answer == answerkey[i]){

If they are the same, correct is incremented by 1

           correct++;        }    }

Print the number of correct answers

   cout<<"Correct answers: "<<correct<<endl;

Print the percentage of correct answers

   cout<<"Percentage correct : "<<(100 * correct)/questions<<"%";

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