374  Big Mod
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 New poster
 Posts: 4
 Joined: Thu Jul 08, 2004 12:53 pm
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374  error
It is the 'Big Mod' (374) problem, i use Java Programming.
everything seems to be normal ...but my code is getting rejected. what cud b the problem.
code removed (frustrated, there are lot other problems to b solved...hence moving forward).
everything seems to be normal ...but my code is getting rejected. what cud b the problem.
code removed (frustrated, there are lot other problems to b solved...hence moving forward).
 newton
 Experienced poster
 Posts: 162
 Joined: Thu Jul 13, 2006 7:07 am
 Location: Campus Area. Dhaka.Bangladesh
 Contact:
i also got AC in 00.002 sec. but is there any algorithm that we can get the mod without recursiving.
Mr Olongbin
After AC you should remove your code from the forum.
always try to represent your code using code tag[/code]
then the program will be more reliable to check for other.
best of luck
newton........................................... simply the best!
Mr Olongbin
After AC you should remove your code from the forum.
always try to represent your code using code tag
Code: Select all
[code]...thank you very much!
i got AC now ! ...
then the program will be more reliable to check for other.
best of luck
newton........................................... simply the best!
 newton
 Experienced poster
 Posts: 162
 Joined: Thu Jul 13, 2006 7:07 am
 Location: Campus Area. Dhaka.Bangladesh
 Contact:
as for macro declaration
the compiler has to compile the code (n) and (n) twice
in the code
bigmod function is called twice more.
so if we chang the code into:
it will reduce time limit twice more.
is there any wrong with me?
is not this more sufficient algorithm?
best of luck
newton.............................. simply the best
Code: Select all
#define square(n) (n)*(n)
in the code
Code: Select all
long bigmod(long b,long p,long m) {
if (p == 0)
return 1;
else if (p%2 == 0)
return square(bigmod(b,p/2,m)) % m; // square(x) = x * x
else
return ((b % m) * bigmod(b,p1,m)) % m;
}
so if we chang the code into:
Code: Select all
long bigmod(long b,long p,long m) {
if (p == 0)
return 1;
else if (p%2 == 0)
{
long temp=bigmod(b,p/2,m)%m;
return square(temp) % m; // square(x) = x * x
}
else
return ((b % m) * bigmod(b,p1,m)) % m;
}
is there any wrong with me?
is not this more sufficient algorithm?
best of luck
newton.............................. simply the best
Yes, there is one, but it requires a bit more thought.
Consider
Consider
Code: Select all
/* calculates a^b mod m */
integer modpow(integer a, integer b, integer m) {
integer p = 1; // such that a0^b0 is always p*a^b
while (b != 0) {
if (b%2 == 0) b/= 2;
else {
b = (b1)/2;
p = (p*a)%m;
}
a = (a*a)%m;
}
return p%m;
}
I can't figure out which algorithm are you talking about. This is the algorithm I used to solve the problem using simple bitwise operations. Is this the one you are talking about? If it is, I can't see why would it run in O(1) time. It depends of the number of digits of the binary representation of P; meaning it takes O(log P) time.Per wrote:Well, yeah sure, but if you see it that way, almost any algorithm is O(1), even if it takes O(2^P), so it's not very informative .
I'm guessing you're talking about the same algorithm as me, the standard squareandmultiplythingy. This algorithm uses O(#bits in P) multiplications and modular reductions. So if you consider the number of bits constant (which as I said maybe is not so informative), this is O(1), but if you consider the asymptotic case with unbounded P, it is O(log P).
Code: Select all
long f(long b, long p, long m){
long mask = 1;
long pow2 = b % m;
long r = 1;
while (mask){
if (p & mask)
r = (r * pow2) % m;
pow2 = (pow2*pow2) % m;
mask <<= 1;
}
return r;
}
Runtime errors in Pascal are reported as Wrong Answers by the online judge. Be careful.
Are you dreaming right now?
http://www.dreamviews.com
Are you dreaming right now?
http://www.dreamviews.com
374, Time limit exceeded
Hi, all.
I tried the problem 374,
but I got the "Time limit exceeded".
How can I improve my code?
Also, if I create a array with size 46340,
it become "Runtime error".
#include <stdio.h>
int main()
{
long long int basis=0, p_num=0, m_num=0;
long long int tmp=1;
int i=0, n=0;
while(scanf("%lld %lld %lld", &basis, &p_num, &m_num) == 3) {
tmp = 1;
n = 0;
i = 0;
if(basis%m_num == 0) {
printf("0\n");
continue;
}
do {
tmp *= basis;
tmp %= m_num;
n++;
} while(tmp != 1);
i = (p_num%n);
while(i) {
tmp *= basis;
tmp %= m_num;
}
printf("%d\n", tmp);
}
return 0;
}
I tried the problem 374,
but I got the "Time limit exceeded".
How can I improve my code?
Also, if I create a array with size 46340,
it become "Runtime error".
#include <stdio.h>
int main()
{
long long int basis=0, p_num=0, m_num=0;
long long int tmp=1;
int i=0, n=0;
while(scanf("%lld %lld %lld", &basis, &p_num, &m_num) == 3) {
tmp = 1;
n = 0;
i = 0;
if(basis%m_num == 0) {
printf("0\n");
continue;
}
do {
tmp *= basis;
tmp %= m_num;
n++;
} while(tmp != 1);
i = (p_num%n);
while(i) {
tmp *= basis;
tmp %= m_num;
}
printf("%d\n", tmp);
}
return 0;
}
Re: 374, Time limit exceeded
Looks like you're trying here to find n>0, such that B^n = 1 (mod M).dadai wrote: do {
tmp *= basis;
tmp %= m_num;
n++;
} while(tmp != 1);
Well, such n doesn't always exist, and your program enters infinite loop. Try B=4, M=6.
Use a better algorithm.How can I improve my code?
http://en.wikipedia.org/wiki/Exponentiation_by_squaring
Thanks for your advice,
I follow the page and change my code.
Now I follow the algorithm,
and work well in my computer.
But I get "Runtime error" when I update.
Is there anything wrong with my code?
#include <stdio.h>
long long int basis, p_num, m_num;
long long int sqrt_alg(long long int tmp)
{
long long int a=0, b=0;
if(tmp == 2) {
b = (basis*basis)%m_num;
return b;
}
else if(tmp&1) {
tmp;
a = tmp>>1;
b = sqrt_alg(a);
return ((basis%m_num)*b*b)%m_num;
}
else {
a = tmp>>1;
b = sqrt_alg(a);
return (b*b)%m_num;
}
}
int main()
{
long long int tmp=1;
int i=0, n=0;
while(scanf("%lld %lld %lld", &basis, &p_num, &m_num) == 3) {
if(p_num == 0)
printf("1\n");
else if(p_num == 1)
printf("%lld\n", basis%m_num);
else {
tmp = sqrt_alg(p_num);
printf("%lld\n", tmp);
}
}
return 0;
}
I follow the page and change my code.
Now I follow the algorithm,
and work well in my computer.
But I get "Runtime error" when I update.
Is there anything wrong with my code?
#include <stdio.h>
long long int basis, p_num, m_num;
long long int sqrt_alg(long long int tmp)
{
long long int a=0, b=0;
if(tmp == 2) {
b = (basis*basis)%m_num;
return b;
}
else if(tmp&1) {
tmp;
a = tmp>>1;
b = sqrt_alg(a);
return ((basis%m_num)*b*b)%m_num;
}
else {
a = tmp>>1;
b = sqrt_alg(a);
return (b*b)%m_num;
}
}
int main()
{
long long int tmp=1;
int i=0, n=0;
while(scanf("%lld %lld %lld", &basis, &p_num, &m_num) == 3) {
if(p_num == 0)
printf("1\n");
else if(p_num == 1)
printf("%lld\n", basis%m_num);
else {
tmp = sqrt_alg(p_num);
printf("%lld\n", tmp);
}
}
return 0;
}
Well, apparently you haven't put much effort into testing it. It should crash due to stack overflow whenever the two leading bits of P are 11.  in this case at some point there's a call to sqrt_alg(3), followed by sqrt_alg(1), followed by infinitely recursive sqrt_alg(0)...
And by theory of probability it should've taken you just around 2 random tests to discover this on your own.
The proper base case for recursion is: x^0 = 1 % M. Everything boils down to it.
And by theory of probability it should've taken you just around 2 random tests to discover this on your own.
The proper base case for recursion is: x^0 = 1 % M. Everything boils down to it.
Last edited by mf on Fri Feb 22, 2008 5:21 pm, edited 1 time in total.