WHU 2013 Summer Contest #8 B Dividing a Chocolate

http://acm.hust.edu.cn/vjudge/contest/view.action?cid=26275#problem/B

B - Dividing a Chocolate

Crawling in process...Crawling failedTime Limit:2000MS    Memory Limit:65536KB     64bit IO Format:%lld & %llu

Submit Status Practice ZOJ 2705

 

Description

The boy and Karlsson are dividing a chocolate that the boy's parents have presented him for his birthday. A chocolate is a rectangle that consists ofm × n chocolate squares, separated from each other by cutlines. 

Of course, Karlsson does the dividing.  First Karlsson divides the chocolate into two rectangular pieces,  breaking it along some cutline. Since Karlsson wants to  divide chocolate fairly, he would not be satisfied if the two pieces have different sizes. In this case he  cuts away the piece equal to the smaller piece out of the larger  piece, and eats it. If the pieces are still not equal, he does so again, and so on. After the pieces are finally equal,  Karlsson eats one of the pieces, and the boy eats another.

Karlsson wants to make an initial cut in such a way that he would eat as much chocolate as possible. However, the boy  knows that Karlsson likes chocolate very much, and  he watches for the process closely. Karlsson must be very  careful not to offend the boy. So he must not successively  cut away and eat chocolate from the same piece --- this would seem too suspicious to the boy. 

Help Karlsson to find out how much chocolate he can eat.

Input

There are mutiple cases in the input file.

Each case contains m and n (1 <= m, n <= 10⁹ ).

There is an empty line after each case.

Output

Output one integer number --- how many chocolate squares Karlsson can eat. If Karlsson cannot divide chocolate using his method, output0 instead.

There should be am empty line after each case.

Sample Input

6 5

Sample Output

24

In the example Karlsson must initially break a chocolate into  pieces of sizes 3 × 6 and 2 × 6 . After that he can eat all chocolate but the boy's piece that would finally be 1 × 6 . Karlsson cannot, for example, cut a chocolate initially into pieces of sizes 5 × 5 and 1 × 5 --- after doing so, he would have to successively cut a piece away from the first one several times, that  would offend the boy.

思路就是从斐波那契数列出发，推理的过程如图：

最后 a*b a*b
2*a*b a*b
3*a*b 2*a*b
5*a*b 3*a*b....依次类推，要使得a*b最小必须使所取的斐波那契数最大，long long 以内的斐波那契数总共有91个，因此可以使用91以内的斐波那契数来进行计算。

 

 

#include<iostream>
#include<stdio.h>
using namespace std;
long long fib[92];
int main()
{
    fib[0]=1;fib[1]=1;
    for(int i=2;i<92;i++)
    {
        fib[i]=fib[i-1]+fib[i-2];
        cout<<fib[i]<<endl;
    }
    long long m,n;
    while(cin>>m>>n)
    {
        long long maxf=0;
        for(int i=59;i>=0;i--)
        {
            if(m%fib[i]==0||n%fib[i]==0)
            {
                maxf=fib[i];break;
            }
        }
        cout<<n*m-n*m/maxf<<endl;
        cout<<endl;
    }
    return 0;
}