URAL 1079. Maximum

problem url: http://acm.timus.ru/problem.aspx?space=1&num=1079

this should be a mathematics question. So far I got two answers. MY own is using static array to cache all the sequence elements while there is another mathematic way which dosn't require Array or cache(of each sequence element):

#simple approach(not good at scalability):


#include <cstdio>


#include <iostream>






#define MAXNUM 100000




using namespace std;




//GLOBAL VARIABLES


int NUMS[MAXNUM/2+2]; //each item of the sequence




int curmax = 0;




int inputs[10];


int maxs[10];


int inputcnt = 0;


int maxinput = 0;




void main()




...{


int i =0,j=0;


int curinput=0;




do




...{


scanf("%d", &curinput);


inputs[inputcnt++] = curinput;




if(curinput > maxinput) maxinput = curinput;




}while(curinput != 0);




curmax =0;


int curitem = 0;




for(i=0;i<= maxinput;++i)




...{


if(i==0) curitem = 0;


else if(i == 1) curitem = 1;


else




...{


if(i%2)




...{


curitem = NUMS[i/2] + NUMS[i/2 +1];


}else




...{


curitem = NUMS[i/2];


}


}




if(curmax < curitem) curmax = curitem;




if(i<(MAXNUM/2+2)) NUMS[i] = curitem;




for(j=0;j<inputcnt-1;++j)




...{


if(inputs[j] == i) maxs[j] = curmax;


}




}




for(i=0;i<inputcnt-1;++i) printf("%d ", maxs[i]);


}





#pure mathematics approach(can not understand yet :( ):

/*

Assume g(n,i,j)=i*f(n)+j*f(n+1).
Then
g(2n,i,j)=g(n,i+j,j)
g(2n+1,i,j)=g(n,i,i+j)
We must find f(n)=g(n,1,0), so...

*/

#include <iostream>
int n,x;
int a[10];m
int i,t;

int _max(int s1,int s2,int x)
{
if (x==n)
return s1+s2;
else {
int t1,t2;
if (x*2-1<=n)
t1 = _max(s1,s2+s1,x*2-1);
else
t1 = 0;
if (x*2+1<=n)
t2 = _max(s1+s2,s2,x*2+1);
else
t2 = 0;
if ((t1==t2)&&(t2==0))
return s1+s2;
else
return t1>t2?t1:t2;
}
}

int main()
{
std::cin >> n;
i = 0;
while (n){
if (n==2)
a[i] = 1;
else
if (n==1)
a[i] = 1;
else
if (n==0)
a[i] = 0;
else
a[i] = _max(1,1,3);
std::cin >> n;
i++;
}
for (n = 0;n<i;n++)
std::cout << a
<< " ";

return 0;
}