**Fundamental Theorem of Arithmetic:**Every positive integer greater than 1 can be written uniquely as a prime or as the product of two or more primes, where the prime factors are written in order of nondecreasing size. The task is to use a stack to read a number and print all of its prime divisors in descending order. For example, with the integer 2100, the output should be:\[ 7 \quad 5 \quad 5 \quad 3 \quad 2 \quad 2 \]**Tasks:**1. **Prime_Factorization Algorithm:** - Develop an algorithm named `Prime_Factorization`, which takes a positive integer greater than 1 and generates its prime factorization according to the theorem. - *Hint:* The smallest divisor greater than 1 of any integer is guaranteed to be a prime.2. **Stack-Based Algorithm Proposal:** - Design a stack structure-based algorithm to handle this prime decomposition. - First, compute the prime factorization of an integer. - Second, print all corresponding prime divisors in descending order.

According to the information given:- We have to 1. First declare the variable - iterate = 2 and enter the variable number (to find out its prime factors.) 2. Launch while loop-1 to check that the number is not equal to 1 3. Inside the loop is a conditional statement if (number% iterate == 0) 4. If the condition satisfies the flexible printer, which are the prime factors 5. Then another while loop-2 is run with status (number% iterate == 0). Inside this while loop - update number = number / iterate, until the situation satisfies 6. When loop-2 fails we multiply the recurring variable by 1 = iterate ++ 7. Line number 2 follows again, While loop -1 checks the status Pseudo-Code number , iterate=2 ; Input (number) while (number!=1) { if (number % iterate==0) { Print (Iterate) } while (number % iterate==0) { number = number / iterate; } Iterate ++; } Now to print the prime factors of a number in descending order we can introduce a stack,where the smallest prime number will be in filled first in the stack by the Push method Later we can Pop from the stack which will automatically print the prime factors in descending order as the stack follows LAST IN FIRST OUT PRINCIPLE 2. Stack Based Algorithm 1. First declare the variable - iterate = 2 and enter the variable number (to find out its Prime factors.) Also start stacking -prime_factor 2. Use while loop-1 temporarily to check that the number is not equal to 1 3. Inside the loop is a conditional statement if (number% iterate == 0) 4. If the condition is satisfactory than doing the push function to push the value - it is repeated in the stack. 5. Then another while loop-2 is run with status (number% iterate == 0) Inside this while loop update number = number / iterate, until the situation is satisfied 6. When loop-2 fails we increase the iterate variable by 1 = iterate ++ 7. Number 2 follows again, While loop -1 checks status. 8. If the Angmos loop-1 condition fails, in order to print the main features we need to check whether the stack is empty or not. If the stack is empty than the perform pop function - We will print all the key elements stored in the stack using the LAST IN FINAL OUT PRINCIPLE. Stack Based Algorithm C++ IMPLEMENTATION #include <bits/stdc++.h>using namespace std;void PrimeFactors(int number){ //Initialize the stack stack<int>prime_factor; int iterate = 2; while (number != 1) { if (number % iterate == 0) { // Insert iterate into stack prime_factor.push(iterate); while (number % iterate == 0) { // Update number number = number / iterate; } } // increment iterate iterate++; } // Print value of stack prime_factor using pop operation while (!prime_factor.empty()) { printf("%d ", prime_factor.top()); prime_factor.pop(); }} int main(){ int number=1001; PrimeFactors(number); return 0;} From the above program say number =1001 So in the stack, 7 will be pushed, then 11 will be pushed and then 13 will be pushed When we pop the values from the stack to display it , 13 will be removed first from the stack, then 11 will be removed from the stack, and then 7 will be removed from the stack. So we can print the prime factors of the number 1001 in descending order using pop operation. Output:- 13 11 7

Engineering

Computer Science

P follows: Every positive integer greater than 1 can be written uniquely as a prime or as the product of two or more primes, where the prime factors are written in order of nondecreasing size. We want to use a stack to read a number and print all of its prime divisors in descending order. For example, with the integer 2100, the output should be: 1: Consider the fundamental theorem of arithmetic, which is stated as 7 5 5 3 2 2 1. Write an algorithm, called Prime_Factorization, which accepts a positive integer greater than 1, and generates its prime factorization according to the above-mentioned theorem. [Hint: The smallest divisor greater than 1 of any integer is guaranteed to be a prime.] 2. Propose a stack structure based algorithm to accommodate this prime decomposition. First, you should compute the prime factorization of an integer. Second, you need to print all corresponding prime divisors in descending order.

P follows: Every positive integer greater than 1 can be written uniquely as a prime or as the product of two or more primes, where the prime factors are written in order of nondecreasing size. We want to use a stack to read a number and print all of its prime divisors in descending order. For example, with the integer 2100, the output should be: 1: Consider the fundamental theorem of arithmetic, which is stated as 7 5 5 3 2 2 1. Write an algorithm, called Prime_Factorization, which accepts a positive integer greater than 1, and generates its prime factorization according to the above-mentioned theorem. [Hint: The smallest divisor greater than 1 of any integer is guaranteed to be a prime.] 2. Propose a stack structure based algorithm to accommodate this prime decomposition. First, you should compute the prime factorization of an integer. Second, you need to print all corresponding prime divisors in descending order.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

**Fundamental Theorem of Arithmetic:**
Every positive integer greater than 1 can be written uniquely as a prime or as the product of two or more primes, where the prime factors are written in order of nondecreasing size. The task is to use a stack to read a number and print all of its prime divisors in descending order. For example, with the integer 2100, the output should be:

\[ 7 \quad 5 \quad 5 \quad 3 \quad 2 \quad 2 \]

**Tasks:**

1. **Prime_Factorization Algorithm:**
- Develop an algorithm named `Prime_Factorization`, which takes a positive integer greater than 1 and generates its prime factorization according to the theorem.
- *Hint:* The smallest divisor greater than 1 of any integer is guaranteed to be a prime.

2. **Stack-Based Algorithm Proposal:**
- Design a stack structure-based algorithm to handle this prime decomposition.
- First, compute the prime factorization of an integer.
- Second, print all corresponding prime divisors in descending order.

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