#include <bits/stdc++.h>
#define pf printf
#define sf(a) scanf("%d",&a)
#define sfl(a) scanf("%lld",&a)
#define sff(a,b) scanf("%d %d",&a,&b)
#define sffl(a,b) scanf("%lld %lld",&a,&b)
#define sfff(a,b,c) scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c) scanf("%lld %lld %lld",&a,&b,&c)
#define sffff(a,b,c,d) scanf("%d %d %d %d",&a,&b,&c,&d)
#define sffffl(a,b,c,d) scanf("%lld %lld %lld %lld",&a,&b,&c,&d)
#define sfffff(a,b,c,d,e) scanf("%d %d %d %d %d",&a,&b,&c,&d,&e)
#define sfffffl(a,b,c,d,e) scanf("%lld %lld %lld %lld %lld",&a,&b,&c,&d,&e)
#define ms(a,b) memset(a,b,sizeof(a))
#define pb(a) push_back(a)
#define db double
#define ft float
#define ll long long
#define ull unsigned long long
#define ff first
#define ss second
#define sz(x) x.size()
#define qu queue
#define pqu priority_queue
#define vc vector
#define vi vector<int>
#define vll vector<long long>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define all(x) x.begin(),x.end()
#define CIN ios_base::sync_with_stdio(0); cin.tie(0)
#define max3(a, b, c) max(a, b) > max(b, c) ? max(a, b) : max(b, c)
#define min3(a, b, c) min(a, b) < min(b, c) ? min(a, b) : min(b, c)
#define loop0(i,n) for(int i=0;i<n;i++)
#define loop1(i,n) for(int i=1;i<=n;i++)
#define loopab(a,b) for(int i=a;i<=b;i++)
#define stlloop(x) for(__typeof(x.begin()) it=x.begin();it!=x.end();it++)
#define gcd(a, b) __gcd(a, b)
#define lcm(a, b) ((a)*((b)/gcd(a,b)))
#define case1(z) cout<<"Case "<<z<<": "
#define case2(z) printf("Case %d: ",z)
#define PI 3.14159265358979323846264338328
#define valid(tx,ty) tx>=0 && tx<r && ty>=0 && ty<c
#define intlim 2147483648
#define MAX 1000000
#define inf 10000000
/*------------------------------Graph Moves----------------------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1}; // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1}; // Kings Move
//const int fx[]={-2, -2, -1, -1, 1, 1, 2, 2}; // Knights Move
//const int fy[]={-1, 1, -2, 2, -2, 2, -1, 1}; // Knights Move
/*---------------------------------------------------------------------*/
using namespace std;
int main()
{
//CIN;
// freopen("in.txt","r",stdin);
// freopen("out.txt","w",stdout);
int t;
sf(t);
loop1(z,t)
{
int q;
sf(q);
int a=q*5;
int b=q/5;
case2(z);
if(b==0) pf("%d\n",a);
else
{
b=b*5;
int c=a-b;
for(int i=c;;i+=5)
{
int k=i;
int sum=0;
while(k!=0)
{
sum+=k/5;
k/=5;
}
if(sum==q)
{
pf("%d\n",i);
break;
}
else if(sum>q)
{
pf("impossible\n");
break;
}
}
}
}
return 0;
}
Category Number Theory
Factorial of big int
#include <bits/stdc++.h>
#define pf printf
#define sf(a) scanf("%d",&a)
#define sfl(a) scanf("%lld",&a)
#define sff(a,b) scanf("%d %d",&a,&b)
#define sffl(a,b) scanf("%lld %lld",&a,&b)
#define sfff(a,b,c) scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c) scanf("%lld %lld %lld",&a,&b,&c)
#define sffff(a,b,c,d) scanf("%d %d %d %d",&a,&b,&c,&d)
#define sffffl(a,b,c,d) scanf("%lld %lld %lld %lld",&a,&b,&c,&d)
#define sfffff(a,b,c,d,e) scanf("%d %d %d %d %d",&a,&b,&c,&d,&e)
#define sfffffl(a,b,c,d,e) scanf("%lld %lld %lld %lld %lld",&a,&b,&c,&d,&e)
#define sfc(a) scanf("%c",&a)
#define ms(a,b) memset(a,b,sizeof(a))
#define pb(a) push_back(a)
#define pbp(a,b) push_back({a,b})
#define db double
#define ft float
#define ll long long
#define ull unsigned long long
#define ff first
#define ss second
#define sz(x) x.size()
#define qu queue
#define pqu priority_queue
#define vc vector
#define vi vector<int>
#define vll vector<long long>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define all(x) x.begin(),x.end()
#define CIN ios_base::sync_with_stdio(0); cin.tie(0)
#define max3(a, b, c) max(a, b) > max(b, c) ? max(a, b) : max(b, c)
#define min3(a, b, c) min(a, b) < min(b, c) ? min(a, b) : min(b, c)
#define loop0(i,n) for(int i=0;i<n;i++)
#define loop1(i,n) for(int i=1;i<=n;i++)
#define loopab(i,a,b) for(int i=a;i<=b;i++)
#define REV(i,n) for(i=n; i>=0; i--)
#define stlloop(x) for(__typeof(x.begin()) it=x.begin();it!=x.end();it++)
#define gcd(a, b) __gcd(a, b)
#define lcm(a, b) ((a)*((b)/gcd(a,b)))
#define case1(z) cout<<"Case "<<z<<": "
#define case2(z) printf("Case %d: ",z)
#define PI 3.14159265358979323846264338328
#define valid(tx,ty) tx>=0 && tx<r && ty>=0 && ty<c
#define intlim 2147483648
#define MAX 1000000
#define inf 10000000
/*------------------------------Graph Moves----------------------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1}; // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1}; // Kings Move
//const int fx[]={-2, -2, -1, -1, 1, 1, 2, 2}; // Knights Move
//const int fy[]={-1, 1, -2, 2, -2, 2, -1, 1}; // Knights Move
/*---------------------------------------------------------------------*/
using namespace std;
#include <bits/stdc++.h>
#define pf printf
#define sf(a) scanf("%d",&a)
#define sfl(a) scanf("%lld",&a)
#define sff(a,b) scanf("%d %d",&a,&b)
#define sffl(a,b) scanf("%lld %lld",&a,&b)
#define sfff(a,b,c) scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c) scanf("%lld %lld %lld",&a,&b,&c)
#define sffff(a,b,c,d) scanf("%d %d %d %d",&a,&b,&c,&d)
#define sffffl(a,b,c,d) scanf("%lld %lld %lld %lld",&a,&b,&c,&d)
#define sfffff(a,b,c,d,e) scanf("%d %d %d %d %d",&a,&b,&c,&d,&e)
#define sfffffl(a,b,c,d,e) scanf("%lld %lld %lld %lld %lld",&a,&b,&c,&d,&e)
#define sfc(a) scanf("%c",&a)
#define ms(a,b) memset(a,b,sizeof(a))
#define pb(a) push_back(a)
#define pbp(a,b) push_back({a,b})
#define db double
#define ft float
#define ll long long
#define ull unsigned long long
#define ff first
#define ss second
#define sz(x) x.size()
#define qu queue
#define pqu priority_queue
#define vc vector
#define vi vector<int>
#define vll vector<long long>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define all(x) x.begin(),x.end()
#define CIN ios_base::sync_with_stdio(0); cin.tie(0)
#define max3(a, b, c) max(a, b) > max(b, c) ? max(a, b) : max(b, c)
#define min3(a, b, c) min(a, b) < min(b, c) ? min(a, b) : min(b, c)
#define loop0(i,n) for(int i=0;i<n;i++)
#define loop1(i,n) for(int i=1;i<=n;i++)
#define loopab(i,a,b) for(int i=a;i<=b;i++)
#define REV(i,n) for(i=n; i>=0; i--)
#define stlloop(x) for(__typeof(x.begin()) it=x.begin();it!=x.end();it++)
#define gcd(a, b) __gcd(a, b)
#define lcm(a, b) ((a)*((b)/gcd(a,b)))
#define case1(z) cout<<"Case "<<z<<": "
#define case2(z) printf("Case %d: ",z)
#define PI 3.14159265358979323846264338328
#define valid(tx,ty) tx>=0 && tx<r && ty>=0 && ty<c
#define intlim 2147483648
#define MAX 1000000
#define inf 10000000
/*------------------------------Graph Moves----------------------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1}; // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1}; // Kings Move
//const int fx[]={-2, -2, -1, -1, 1, 1, 2, 2}; // Knights Move
//const int fy[]={-1, 1, -2, 2, -2, 2, -1, 1}; // Knights Move
/*---------------------------------------------------------------------*/
using namespace std;
string cut_leading_zero(string a)
{
string s;
int i;
if( a[0]!='0' ) return a;
loop0(i,sz(a)-1) if( a[i]!='0' ) break;
for(i=i;i<sz(a);i++) s+=a[i];
return s;
}
int compare(string a,string b)
{
int i;
a = cut_leading_zero(a);
b = cut_leading_zero(b);
if( sz(a)>sz(b) ) return 1;
if( sz(a)<sz(b) ) return -1;
loop0(i,sz(a))
{
if( a[i]>b[i] ) return 1;
else if( a[i]<b[i] ) return -1;
}
return 0;
}
string Addition(string a,string b)
{
int carry=0, i;
string ans;
if( sz(a)>sz(b) ) b = string(sz(a)-sz(b),'0')+b;
if( sz(b)>sz(a) ) a = string(sz(b)-sz(a),'0')+a;
ans.resize(sz(a));
REV(i,sz(a)-1)
{
int sum = carry+a[i]+b[i]-96;
ans[i] = (char)(sum%10+'0');
carry = sum/10;
}
if( carry ) ans.insert(0,string(1,carry+'0'));
ans = cut_leading_zero(ans);
return ans;
}
string Multiplication(string a,string b)
{
int i, j, multi, carry;
string ans, temp;
ans = "0";
REV(j,sz(b)-1)
{
temp = "";
carry = 0;
REV(i,sz(a)-1)
{
multi = (a[i]-'0')*(b[j]-'0')+carry;
temp += (multi%10+'0');
carry = multi/10;
}
if( carry ) temp += (carry+'0');
reverse(all(temp));
temp += string(sz(b)-j-1,'0');
ans = Addition(ans,temp);
}
ans = cut_leading_zero(ans);
return ans;
}
string Multiplication(string a,int k)
{
string ans;
int i, sum, carry=0;
REV(i,sz(a)-1)
{
sum = (a[i]-'0')*k+carry;
carry = sum/10;
ans+=(sum%10)+'0';
}
while(carry)
{
ans += (carry%10)+'0';
carry/=10;
}
reverse(all(ans));
ans = cut_leading_zero(ans);
return ans;
}
string Subtraction(string a,string b)
{
int borrow = 0, i, sub;
string ans;
if( sz(b)<sz(a) ) b = string(sz(a)-sz(b),'0')+b;
REV(i,sz(a)-1)
{
sub = a[i]-b[i]-borrow;
if( sub<0 )
{
sub += 10;
borrow = 1;
}
else borrow = 0;
ans += sub+'0';
}
reverse(all(ans));
ans = cut_leading_zero(ans);
return ans;
}
string Division(string a,string b)
{
string mod, temp, ans="0";
int i, j;
loop0(i,sz(a))
{
mod += a[i];
mod = cut_leading_zero(mod);
loop0(j,10)
{
temp = Multiplication(b,j);
if( compare(temp,mod)==1 )
break;
}
temp = Multiplication(b,j-1);
mod = Subtraction(mod,temp);
ans += (j-1)+'0';
}
mod = cut_leading_zero(mod);
ans = cut_leading_zero(ans);
return ans;
}
string Division(string a,int k)
{
int i, sum=0;
string ans = "0";
loop0(i,sz(a))
{
sum = (sum*10+(a[i]-'0'));
ans += (sum/k)+'0';
sum = sum%k;
}
ans = cut_leading_zero(ans);
return ans;
}
string Div_mod(string a,string b)
{
string mod, temp, ans="0";
int i, j;
loop0(i,sz(a))
{
mod += a[i];
mod = cut_leading_zero(mod);
for(int j=1;j<10;j++)
{
temp = Multiplication(b,j);
if( compare(temp,mod)>0 )
break;
}
temp = Multiplication(b,j-1);
mod = Subtraction(mod,temp);
ans += (j-1)+'0';
}
mod = cut_leading_zero(mod);
ans = cut_leading_zero(ans);
return mod;
}
int Div_mod(string a,int k)
{
int i, sum=0;
loop0(i,sz(a))
sum = (sum*10+(a[i]-'0'))%k;
return sum;
}
string dp[1005];
void fact()
{
string ans="1";
dp[0]=ans;
for(int i=1; i<=1000; i++)
{
ans=Multiplication(ans,i);
dp[i]=ans;
}
}
int main()
{
CIN;
// freopen("in.txt","r",stdin);
// freopen("out.txt","w",stdout);
fact();
int n;
while(cin>>n)
{
cout<<n<<"!"<<endl;
cout<<dp[n]<<endl;
}
return 0;
}
Factorial counting
Solution:
#include <iostream>
using namespace std;
////////// Recursive function/////////
long long rec_factorial(int n)
{
if(n==0)
{
return 1;
}
return n*rec_factorial(n-1);
}
/////////////Iterative function///////
int fact(int n)
{
int ans=1;
for(int i=1;i<=n;i++)
{
ans*=i;
}
return ans;
}
int main()
{
cout<<rec_factorial(6)<<endl;
cout<<fact(9)<<endl;
return 0;
}
4. No. of common divisors betwn 2 numbers
Problem Link:
Solution:
#include <bits/stdc++.h>
#define pf printf
#define sf(a) scanf("%d",&a)
#define sfl(a) scanf("%lld",&a)
#define sff(a,b) scanf("%d %d",&a,&b)
#define sffl(a,b) scanf("%lld %lld",&a,&b)
#define sfff(a,b,c) scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c) scanf("%lld %lld %lld",&a,&b,&c)
#define ms(a,b) memset(a,b,sizeof(a))
#define pb(a) push_back(a)
#define db double
#define ft float
#define ll long long
#define ull unsigned long long
#define ff first
#define ss second
#define sz(x) x.size()
#define qu queue
#define pqu priority_queue
#define vc vector
#define vi vector<int>
#define vll vector<long long>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define all(x) x.begin(),x.end()
#define CIN ios_base::sync_with_stdio(0); cin.tie(0)
#define loop0(i,n) for(int i=0;i<n;i++)
#define loop1(i,n) for(int i=1;i<=n;i++)
#define stlloop(x) for(__typeof(x.begin()) it=x.begin();it!=x.end();it++)
#define gcd(a, b) __gcd(a, b)
#define lcm(a, b) ((a)*((b)/gcd(a,b)))
#define case(z,x) cout<<"Case "<<i<<": "<<x<<endl
#define case(z) cout<<"Case "<<z<<": "
#define PI 3.14159265358979323846264338328
#define valid(tx,ty) tx>=0 && tx<r && ty>=0 && ty<c
#define MAX 1000000
#define inf 10000000
/*------------------------------Graph Moves----------------------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1}; // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1}; // Kings Move
//const int fx[]={-2, -2, -1, -1, 1, 1, 2, 2}; // Knights Move
//const int fy[]={-1, 1, -2, 2, -2, 2, -1, 1}; // Knights Move
/*---------------------------------------------------------------------*/
using namespace std;
int n,m;
//int prime[]= {2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 , 127 , 131 , 137 , 139 , 149 , 151 , 157 , 163 , 167 , 173 , 179 , 181 , 191 , 193 , 197 , 199 , 211 , 223 , 227 , 229 , 233 , 239 , 241 , 251 , 257 , 263 , 269 , 271 , 277 , 281 , 283 , 293 , 307 , 311 , 313 , 317 , 331 , 337 , 347 , 349 , 353 , 359 , 367 , 373 , 379 , 383 , 389 , 397 , 401 , 409 , 419 , 421 , 431 , 433 , 439 , 443 , 449 , 457 , 461 , 463 , 467 , 479 , 487 , 491 , 499 , 503 , 509 , 521 , 523 , 541 , 547 , 557 , 563 , 569 , 571 , 577 , 587 , 593 , 599 , 601 , 607 , 613 , 617 , 619 , 631 , 641 , 643 , 647 , 653 , 659 , 661 , 673 , 677 , 683 , 691 , 701 , 709 , 719 , 727 , 733 , 739 , 743 , 751 , 757 , 761 , 769 , 773 , 787 , 797 , 809 , 811 , 821 , 823 , 827 , 829 , 839 , 853 , 857 , 859 , 863 , 877 , 881 , 883 , 887 , 907 , 911 , 919 , 929 , 937 , 941 , 947 , 953 , 967 , 971 , 977 , 983 , 991 , 997 , 1009 , 1013 , 1019 , 1021 , 1031 , 1033 , 1039 , 1049 , 1051 , 1061 , 1063 , 1069 , 1087 , 1091 , 1093 , 1097 , 1103 , 1109 , 1117 , 1123 , 1129 , 1151 , 1153 , 1163 , 1171 , 1181 , 1187 , 1193 , 1201 , 1213 , 1217 , 1223 , 1229 , 1231 , 1237 , 1249 , 1259 , 1277 , 1279 , 1283 , 1289 , 1291 , 1297 , 1301 , 1303 , 1307 , 1319 , 1321 , 1327 , 1361 , 1367 , 1373 , 1381 , 1399 , 1409 , 1423 , 1427 , 1429 , 1433 , 1439 , 1447 , 1451 , 1453 , 1459 , 1471 , 1481 , 1483 , 1487 , 1489 , 1493 , 1499 , 1511 , 1523 , 1531 , 1543 , 1549 , 1553 , 1559 , 1567 , 1571 , 1579 , 1583 , 1597 , 1601 , 1607 , 1609 , 1613 , 1619 , 1621 , 1627 , 1637 , 1657 , 1663 , 1667 , 1669 , 1693 , 1697 , 1699 , 1709 , 1721 , 1723 , 1733 , 1741 , 1747 , 1753 , 1759 , 1777 , 1783 , 1787 , 1789 , 1801 , 1811 , 1823 , 1831 , 1847 , 1861 , 1867 , 1871 , 1873 , 1877 , 1879 , 1889 , 1901 , 1907 , 1913 , 1931 , 1933 , 1949 , 1951 , 1973 , 1979 , 1987 , 1993 , 1997 , 1999};
bool p[MAX+2];
vector<int>prime;
void sieve()
{
p[0]=p[1]=1;
int root=sqrt(MAX);
for(int i=2; i<=root; i++)
{
if(p[i]==0)
{
prime.pb(i);
for(int j=i*i; j<=MAX; j+=i)
{
p[j]=1;
if(i%2==1) j+=i;
}
}
}
}
int divisor_count(int n)
{
int divisor=1;
int k=n;
int root=sqrt(n);
for(int i=0;prime[i]<=root;i++)
{
if(k%prime[i]==0)
{
int c=1;
while(k%prime[i]==0) // searching prime factorization
{
k/=prime[i];
c++;
}
root=sqrt(k); //Important optimization point,eta na dileo ans aki asbe,but eta dile time complexity kombe
divisor*=c;
}
}
if(k>1)
{
divisor*=2; // let n=28, then 2^2 * 7^1 . Here, k=7 which is > 1 . so for 7^1 this condition
}
return divisor;
}
int gcd(int a,int b)
{
return b==0 ? a : gcd(b,a%b);
}
int main()
{
//freopen("in.txt","r",stdin);
//freopen("out.txt","w",stdout);
sieve();
int t;
sf(t);
loop1(z,t)
{
sff(n,m);
int x;
if(n==m) pf("%d\n",divisor_count(n));
else if(n>m)
{
x=gcd(n,m);
pf("%d\n",divisor_count(x));
}
else
{
x=gcd(m,n);
pf("%d\n",divisor_count(x));
}
}
return 0;
}
3. Sum of divisors of n
Solution:
#include <bits/stdc++.h>
#define pf printf
#define sf(a) scanf("%d",&a)
#define sfl(a) scanf("%lld",&a)
#define sff(a,b) scanf("%d %d",&a,&b)
#define sffl(a,b) scanf("%lld %lld",&a,&b)
#define sfff(a,b,c) scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c) scanf("%lld %lld %lld",&a,&b,&c)
#define sffff(a,b,c,d) scanf("%d %d %d %d",&a,&b,&c,&d)
#define sffffl(a,b,c,d) scanf("%lld %lld %lld %lld",&a,&b,&c,&d)
#define sfffff(a,b,c,d,e) scanf("%d %d %d %d %d",&a,&b,&c,&d,&e)
#define sfffffl(a,b,c,d,e) scanf("%lld %lld %lld %lld %lld",&a,&b,&c,&d,&e)
#define ms(a,b) memset(a,b,sizeof(a))
#define pb(a) push_back(a)
#define db double
#define ft float
#define ll long long
#define ull unsigned long long
#define ff first
#define ss second
#define sz(x) x.size()
#define qu queue
#define pqu priority_queue
#define vc vector
#define vi vector<int>
#define vll vector<long long>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define all(x) x.begin(),x.end()
#define CIN ios_base::sync_with_stdio(0); cin.tie(0)
#define max3(a, b, c) max(a, b) > max(b, c) ? max(a, b) : max(b, c)
#define min3(a, b, c) min(a, b) < min(b, c) ? min(a, b) : min(b, c)
#define loop0(i,n) for(int i=0;i<n;i++)
#define loop1(i,n) for(int i=1;i<=n;i++)
#define loopab(a,b) for(int i=a;i<=b;i++)
#define stlloop(x) for(__typeof(x.begin()) it=x.begin();it!=x.end();it++)
#define gcd(a, b) __gcd(a, b)
#define lcm(a, b) ((a)*((b)/gcd(a,b)))
#define case1(z) cout<<"Case "<<z<<": "
#define case2(z) printf("Case %d: ",z)
#define PI 3.14159265358979323846264338328
#define valid(tx,ty) tx>=0 && tx<r && ty>=0 && ty<c
#define intlim 2147483648
#define MAX 1000000
#define inf 10000000
/*------------------------------Graph Moves----------------------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1}; // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1}; // Kings Move
//const int fx[]={-2, -2, -1, -1, 1, 1, 2, 2}; // Knights Move
//const int fy[]={-1, 1, -2, 2, -2, 2, -1, 1}; // Knights Move
/*---------------------------------------------------------------------*/
using namespace std;
///It's for SPOJ only/// :p
//int prime[]={2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 , 127 , 131 , 137 , 139 , 149 , 151 , 157 , 163 , 167 , 173 , 179 , 181 , 191 , 193 , 197 , 199 , 211 , 223 , 227 , 229 , 233 , 239 , 241 , 251 , 257 , 263 , 269 , 271 , 277 , 281 , 283 , 293 , 307 , 311 , 313 , 317 , 331 , 337 , 347 , 349 , 353 , 359 , 367 , 373 , 379 , 383 , 389 , 397 , 401 , 409 , 419 , 421 , 431 , 433 , 439 , 443 , 449 , 457 , 461 , 463 , 467 , 479 , 487 , 491 , 499 , 503 , 509 , 521 , 523 , 541 , 547 , 557 , 563 , 569 , 571 , 577 , 587 , 593 , 599 , 601 , 607 , 613 , 617 , 619 , 631 , 641 , 643 , 647 , 653 , 659 , 661 , 673 , 677 , 683 , 691 , 701 , 709 , 719 , 727 , 733 , 739 , 743 , 751 , 757 , 761 , 769 , 773 , 787 , 797 , 809 , 811 , 821 , 823 , 827 , 829 , 839 , 853 , 857 , 859 , 863 , 877 , 881 , 883 , 887 , 907 , 911 , 919 , 929 , 937 , 941 , 947 , 953 , 967 , 971 , 977 , 983 , 991 , 997 , 1009 , 1013 , 1019 , 1021 , 1031 , 1033 , 1039 , 1049 , 1051 , 1061 , 1063 , 1069 , 1087 , 1091 , 1093 , 1097 , 1103 , 1109 , 1117 , 1123 , 1129 , 1151 , 1153 , 1163 , 1171 , 1181 , 1187 , 1193 , 1201 , 1213 , 1217 , 1223 , 1229 , 1231 , 1237 , 1249 , 1259 , 1277 , 1279 , 1283 , 1289 , 1291 , 1297 , 1301 , 1303 , 1307 , 1319 , 1321 , 1327 , 1361 , 1367 , 1373 , 1381 , 1399 , 1409 , 1423 , 1427 , 1429 , 1433 , 1439 , 1447 , 1451 , 1453 , 1459 , 1471 , 1481 , 1483 , 1487 , 1489 , 1493 , 1499 , 1511 , 1523 , 1531 , 1543 , 1549 , 1553 , 1559 , 1567 , 1571 , 1579 , 1583 , 1597 , 1601 , 1607 , 1609 , 1613 , 1619 , 1621 , 1627 , 1637 , 1657 , 1663 , 1667 , 1669 , 1693 , 1697 , 1699 , 1709 , 1721 , 1723 , 1733 , 1741 , 1747 , 1753 , 1759 , 1777 , 1783 , 1787 , 1789 , 1801 , 1811 , 1823 , 1831 , 1847 , 1861 , 1867 , 1871 , 1873 , 1877 , 1879 , 1889 , 1901 , 1907 , 1913 , 1931 , 1933 , 1949 , 1951 , 1973 , 1979 , 1987 , 1993 , 1997 , 1999};
bool p[MAX+2];
vector<int>prime;
void sieve()
{
p[0]=p[1]=1;
int root=sqrt(MAX);
for(int i=2; i<=root; i++)
{
if(p[i]==0)
{
prime.pb(i);
for(int j=i*i; j<=MAX; j+=i)
{
p[j]=1;
if(i%2==1) j+=i;
}
}
}
}
int sum_of_divisor(int n)
{
int sum=1,p,s;
int k=n;
int root=sqrt(n);
for(int i=0;prime[i]<=root;i++)
{
if(k%prime[i]==0)
{
p=1;
while(k%prime[i]==0) // searching prime factorization
{
k/=prime[i];
p=p*prime[i];
}
p=p*prime[i];
root=sqrt(k); //Important optimization point,eta na dileo ans aki asbe,but eta dile time complexity kombe
s=(p-1)/(prime[i]-1);
sum*=s;
}
}
if(k>1)
{
p=k*k; // let n=28, then 2^2 * 7^1 . Here, k=7 which is > 1 . so for 7^1 this condition
s=(p-1)/(k-1);
sum*=s;
}
return sum;
}
int main()
{
sieve();
int n;
cout<<"Enter a number whose sum of divisors has to be determined: "<<endl;
cin>>n;
cout<<sum_of_divisor(n)<<endl;
return 0;
}
Fall out, Codes! 