10394 - Twin Primes

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hager
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Post by hager » Tue Jun 17, 2003 12:11 pm

The problem is that the contents of your array table is undefined. You could initialize it with either:
[c]memset(table, 1, 18409201);[/c]
or by just looping over all elements and setting them to some nonzero value. Otherwise it seems to work fine. I notice that you call the isPrime in the sieve loop, why not look it up in table instead? It would save you some time when running the program.

Best regards

Max108
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Post by Max108 » Wed Jun 18, 2003 12:27 am

Thank you!!

That was the problem, I got AC now! :P

Park, Kwang-Kyu
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10394

Post by Park, Kwang-Kyu » Sat Jul 19, 2003 11:03 am

I think my source makes output in time, but I got TLE. ㅜ_ㅜ

plz check this.
[cpp]#include <iostream>
#include <cmath>

using namespace std;

int prime1[10000];
bool prime2[20000000];

void main(void)
{
int c1, c2;
int input=0;
bool p;

for(c1=2; c1<=4473; c1++)
{
p=true;
for(c2=2; c2<sqrt(c1); c2++)
{
if(c1%c2==0)
{
p=false;
break;
}
}
if(p)
{
prime1[input++]=c1;
}
}
for(c1=0; c1<20000000; c1++)
{
prime2[c1]=true;
}
for(c1=0; c1<input; c1++)
{
for(c2=2; c2<=10000000; c2++)
{
if(c2*prime1[c1]>=20000000) break;
prime2[c2*prime1[c1]]=false;
}
}
int t1=0;
while(1)
{
cin >> input;
t1++;
if(cin.eof()) break;
if(input<0) break;
c2=0;
for(c1=2; c1<20000000; c1++)
{
if(prime2[c1+2] && prime2[c1])
{
c2++;
}
if(c2==input)
{
cout << "(" << c1 << ", " << c1+2 << ")" << endl;
break;
}
}
if(t1==10000) break;
}
}[/cpp]

SilVer DirectXer
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Post by SilVer DirectXer » Fri Aug 01, 2003 3:06 pm

Jalal wrote:Thanx Michniewski!
u r right......... :P
eric!
try with the following one :wink:

for(m= 6 ; m < x; m+=6)
if(prime(m-1) && prime(m+1))
printf("%ld %ld\n", m-1, m+1);
the algorithm is great.
but..how do u guys discover that all twins prime are subset of (6*k-1,6*k+1), for k is integers?

however, i am still TLE using this algorithm, why?
[cpp]
#include <iostream>
using namespace std;
int i,j,k,n;
int prime[100005];
int counter;
int isprime(int);
void main(void)
{
prime[1]=3;
prime[2]=5;


counter=3;
for (i=12;counter<=100002;i+=6)
{
if (isprime(i-1) && isprime(i+1))
{
prime[counter++]=i-1;
}

}
while (1)
{
cin>>n;
if (cin.eof())
break;
cout<<"("<<prime[n]<<", "<<prime[n]+2<<")"<<endl;
}
}

int isprime(int get)
{
int k;
for (k=3;k*k<=get;k+=2)
{
if (get % k ==0)
return 0;
}
return 1;
}
[/cpp]

Larry
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Post by Larry » Fri Aug 01, 2003 5:03 pm

Use sieve for your prime checker..

SilVer DirectXer
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Post by SilVer DirectXer » Sat Aug 02, 2003 7:28 pm

Larry wrote:Use sieve for your prime checker..
thanks....
but, could you explain more details?
how to use a sieve for the prime checker?

pavelph
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HOW DO IT FASTER?

Post by pavelph » Fri Jan 02, 2004 1:10 am

I read all posts about this problem but can`t uderstand how I can optimize my program. It`s work very slow...
[pascal]
program acm10394; {Twince Prime Numbers}
{type integer = longint;}
const maxn = 4500;
koltw = 100000;
var ck : array[1 .. maxn] of boolean;
list : array[1 .. 700] of integer;
tw : array[1 .. koltw] of integer;
n, l : integer;

procedure get_primes; {Eratosphen}
var i, j: integer;
begin
fillchar(ck, sizeof(ck), true);
for i := 3 to 67 do
if ck then begin
j := i * i;
while j <= maxn do begin
ck[j] := false;
j := j + i;
end;
end;

list[1]:=2; l:=1;
i:=1;
while i<=maxn do begin
inc(i, 2);
if ck then begin
inc(l);
list[l] := i;
end;
end; {number of prime numbers - l}
end;

function be_prime( x : integer) : boolean; {prime or not}
var i,j : integer;
begin
j := trunc(sqrt(x));
be_prime := false;
i:=2;
while list <= j do begin
if x mod list = 0 then exit;
inc(i);
end;
be_prime := true;
end;

procedure twins;
var i, k: integer;
begin
tw[1]:=3; i:=1; k:=0;
while i<koltw do begin
inc(k, 6);
if be_prime(k-1) then
if be_prime(k+1) then begin
inc(i);
tw:=k-1;
end;
end;
end;

begin
{ assign(input, 'input.txt');
reset(input);}
get_primes;
twins;
while not eof do begin
readln(n);
writeln('(', tw[n], ', ', tw[n]+2, ')');
end;
end.
[/pascal][/pascal]

rjhadley
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Location: United States

Post by rjhadley » Fri Jan 02, 2004 7:20 pm

SilVer DirectXer:
but..how do u guys discover that all twins prime are subset of (6*k-1,6*k+1), for k is integers?
Let q and q + 2 be twin primes. The number between them is (clearly) q + 1.
Aside from 2, every prime number is odd. So q and q + 2 must both be odd, as both are prime. Hence, q + 1 is even. i.e. q + 1 is divisible by 2.
For any three consecutive integers, exactly one of them is divisible by 3. So either q = 3 and q + 2 = 5 [as 3 | q, q prime => q = 3] or q + 1 is divisible by 3. [And 3 | q + 2 is extraneous since, as before, it would require q + 2 = 3 => q = 1, which isn't prime].
Hence, the twin primes are (3, 5) or (q, q + 2) where q + 1 is divisible by 2 * 3 = 6. The result now follows.

As for the sieve method for generating primes, see an article about Eratosthenes' Sieve, e.g. http://mathworld.wolfram.com/EratosthenesSieve.html

pavelph:
I'm sorry, but I don't know Pascal very well. But, I think that calling be_prime() in twins() is the cause of the slowness since you'll end up calling it so many times.

Subeen
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Post by Subeen » Sat Jan 10, 2004 7:24 am

I am getting RTE in my program. Please help me to find my bug. Here is my code:
[c]#include <stdio.h>
#include <math.h>

const int max = 20000000;
char p[2500100];

#define isprime(n) (p[n/8] & (1<<(7-n % 8 )))

void seive()
{
int i,j;

for(i=3; i<=max; i+=2)
p[i/8] = p[i/8]|(1<<7-i % 8 );

int lim = sqrt(max);

for(i=3; i<=lim; i+=2)
if((p[i/8] & (1<<(7-i % 8 ))))
for(j=i; i*j<=max; j+=2)
p[i*j/8] = p[i*j/8] & ~(1<<7-(i*j) % 8 );
}

void main()
{
seive();
long s[100100];
long i, j;

for(i=3, j=1; j<100010; i+=2)
if(isprime(i) && isprime(i+2))
s[j++] = i;

while(1==scanf("%ld", &i))
printf("(%ld, %ld)\n", s, s+2);
}
[/c]

Ferdous
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10394

Post by Ferdous » Sun Mar 07, 2004 8:29 am

This problem seemed to me easy. But very often a simple looking problem makes us crazy by fooling. I have received Run Time Error but don't know why. Please help me.

Here's my code:

..........deleted later
Last edited by Ferdous on Sun Mar 07, 2004 12:11 pm, edited 1 time in total.
I am destined to live on this cruel world........

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sohel
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Location: New York

right

Post by sohel » Sun Mar 07, 2004 8:39 am

Hi Ferdous,

Try to make the twin and prime array global.

that is;


[c]
char prime[MAX+1];
long twin[100005];

int main()
{

}
[/c]

Declaring huge arrays in the main function is the cause of RTE.

Hope it helps.
:wink:

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shamim
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Post by shamim » Sun Mar 07, 2004 8:41 am

[cpp]
#define MAX 20000000

int main(void)
{
char prime[MAX+1];
[/cpp]

You are trying to declare a very large array inside the main function, which causes overflow and hence the run time error.

Just declare large arrays as global. :wink:

Ferdous
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Post by Ferdous » Sun Mar 07, 2004 12:18 pm

Thanks a lot for your help. I declared those two large arrays as global variables according to your suggession and got AC. But I can't understand why do the program crash if I declare so large array in the main function? Would you please explain it?
I am destined to live on this cruel world........

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shamim
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Post by shamim » Sun Mar 07, 2004 1:09 pm

As far I know, the main function is a procedure which has a limited amount of data area.

So if you declare a large array inside main, it tries to use the limited data area of main, which of course is smaller than the array size, hence the program crashes.

But if you declare it global, it is located in a seperate memory area, which can handle such big array.

Ferdous
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Post by Ferdous » Mon Mar 08, 2004 10:25 am

Thanks a lot , Shamim vai. You are a great helper !!
I am destined to live on this cruel world........

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