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hybrid.cpp
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hybrid.cpp
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// hybrid program
#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <algorithm>
#include <map>
#include <vector>
#include <list>
using namespace std;
// map to store prime factors of a number with their powers
map< int, int> factors;
map< int, int> :: iterator itr;
// function to store the factors in the map and their powers
void createMap(int n)
{
if(factors.find(n) == factors.end())
factors[n]=1;
else
factors[n]++;
}
// function to store prime factors of a number in the map
void primeFactors(int n)
{
// divide the number by 2 untill it bcomes the odd number
while (n%2==0)
{
createMap(2);
n = n/2;
}
// find the prime factors of a number which are from 3 onwards
for (int i=3; i*i<=n; i=i+2)
{
while (n%i==0)
{
createMap(i);
n = n/i;
}
}
// number left with no factors
if (n>2)
createMap(n);
}
// function to get sum of divisors of a number
void divisorsSum()
{
int sum=1;
for( itr=factors.begin(); itr!=factors.end(); itr++)
{
sum = sum * ( (pow(itr->first,itr->second+1)-1)/(itr->first-1) );
}
cout<<"sum of divisors : "<<sum<<"\n";
}
// function to get the divisors of a number using prime factors of a number
void getDivisors( int row_size)
{
// dimensions of 2D array
row_size += 1;
int total_row = factors.size();
// 2D array created
int ** a = new int*[total_row];
for ( int i=0; i<total_row; i++)
{
a[i] = new int[row_size];
fill_n(a[i],row_size,0);
}
// to store the powers of prime factors in the 2D array
int row=0;
for( itr=factors.begin(); itr!=factors.end(); itr++)
{
for( int j=0; j<=itr->second; j++)
{
a[row][j] = pow(itr->first,j);
}
row++;
}
// create a temp vector of size = row_size with each element is 1
vector<int> temp(row_size,1);
// final output vector
vector<int> divisors;
vector<int> :: iterator itr1;
// perform operations on the 2D matrix to get all the divisors of the number
for(int i=0; i<total_row; i++)
{
for(int j=0; j<row_size; j++)
{
for(int k=0; k<temp.size(); k++)
{
divisors.push_back(a[i][j]*temp.at(k));
}
}
// sort and remove the duplicates from the vector
sort(divisors.begin(),divisors.end());
divisors.erase( unique( divisors.begin(), divisors.end()), divisors.end());
// clear the previous vector
temp.clear();
// store the resulted vector in temp vector
temp.assign(divisors.begin(),divisors.end());
}
// to remove the 0 form the divisors list if present
if(divisors.at(0) == 0)
divisors.assign(divisors.begin()+1, divisors.end());
// display the divisors of the number
cout<<"divisors are : \n";
for(int i=0;i<divisors.size();i++)
cout<<divisors.at(i)<<" ";
// display count of the divisors of the number
cout<<"\ncount of divisors : "<<divisors.size();
}
// function to get the count of numbers less than n and relative prime to it
void eulersFunction()
{
int count=1;
for( itr=factors.begin(); itr!=factors.end(); itr++)
{
count = count * ( (pow(itr->first,itr->second-1))*(itr->first-1) );
}
cout<<"\ncount of number less than number and relative prime to it : "<<count<<"\n";
}
// function to get the euler set elements
void getEulerElements(int n)
{
// final output list
list<int> reduced_residue_set;
// non relative prime list
list<int> non_relative_prime;
list<int> :: iterator itr2;
// store the numbers from 2 to n-1 in the output list
for(int i=2; i<n; i++)
reduced_residue_set.push_back(i);
// store the number which are multiples of prime factors of n and less than n in the non_relative_prime
for(itr=factors.begin(); itr!=factors.end(); itr++)
{
int temp=itr->first;
while(temp<n)
{
non_relative_prime.push_back(temp);
temp+=itr->first;
}
}
// to remove the duplicates from the non_relative_prime list
non_relative_prime.sort();
non_relative_prime.unique();
// remove the non_relative_prime from the reduced_residue_set
for(itr2=non_relative_prime.begin(); itr2!=non_relative_prime.end(); itr2++)
reduced_residue_set.remove(*itr2);
// insert 1 in the reduced_residue_set
reduced_residue_set.push_front(1);
// display the elements of the reduced_residue_set
for(itr2=reduced_residue_set.begin(); itr2!=reduced_residue_set.end(); itr2++)
cout<<*itr2<<" ";
// display size of reduced_residue_set
cout<<"\ncount (for verification) : "<<reduced_residue_set.size();
}
int main()
{
int n,max_power=0;
cin>>n;
// get the prime factors of a number
primeFactors(n);
// print the prime factors of a number and get the maximum power
cout<<"Prime factors are : \n";
for( itr=factors.begin(); itr!=factors.end(); itr++)
{
if(itr->second > max_power)
max_power = itr->second;
cout<<itr->first<<" : "<<itr->second<<"\n";
}
// for sum of divisors of a number
divisorsSum();
// get the divisors of a number using prime factors of a number
getDivisors(max_power);
// get the count of numbers less than n and relative prime to it
eulersFunction();
// get euler set elements
getEulerElements(n);
return 0;
}