1040: Alex and Asd fight for two pieces of cake
Time Limit: 1 Sec Memory Limit: 128 MBSubmit: 27 Solved: 12
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Description
Alex and Asd have found two pieces of cake on table of weight a and b grams.They are so greedy that they all want the larger piece. A fight may happenes.
Now the smart person-Radical comes in and starts the dialog: "Stupid people, wait a little, I will make your pieces equal"
"Wow,you are so amazing, how are you going to do that?", Alex and Asd ask. Radical says"Ok,listen to me,If the mass of a certain piece is divisible by two, then I can eat exactly a half of the piece.
If the mass of a certain piece is divisible by three, then I can eat exactly two-thirds, and if the mass is divisible by five,
then I can eat four-fifths. I'll eat a little here and there and make the pieces equal".
Alougth they are not som smart , they got it.So they agrees to his proposal, but on one condition: Radical should make the pieces equal as quickly as possible.
Find the minimum number of operations Radical needs to make pieces equal.
Input
The first line contains two space-separated integers a and b (1 ≤ a, b ≤ 109).
Output
If it is impossible to make the pieces equal, print -1. Otherwise, print the required minimum number of operations. If the pieces of the cake are initially equal, the required number is 0.
Sample Input
36 30
7 8
11 11
Sample Output
3
-1
0
题意：两个人的一定要分到相等的蛋糕，否则输出-1，若初始值就相等， 输出0。跟狐狸给两只熊分饼一个道理，每次吃掉1/2或2/3或4/5。
那么此题就可以理解为每次将初始值乘以1/2或1/3或1/5，Alex和Asd乘以这几个数的次数可以不一样，每次乘的值也可以不一样，求最少的次数让这两个人相等。
首先感觉是贪心，但是后来感觉2、3、5都是质数，2^a和3^b和5^c次的公因数都是1，应该不是贪心。
比如例一、36与30，gcd为6，6/36=1/6，6/30=1/5。
再进一步，题意就成了用1/2，1/3，1/5来凑gcd(Alex,Asd)/Alex（或Asd，可行状态下这两个假分数肯定相等且最简式分子为1）且项数最少。
再进一步，就是求上述分母分解为2、3、5的个数（感觉由于三个数互质，只有唯一解，不存在最大最小的问题。）
代码：
#include<iostream>
#include<algorithm>
#include<cstdlib>
#include<sstream>
#include<cstring>
#include<cstdio>
#include<string>
#include<deque>
#include<cmath>
#include<queue>
#include<set>
#include<map>
using namespace std;
typedef long long LL;
LL list[3]={5,3,2};//为了循环方便用个数组
LL gcd(LL a,LL b)
{
return b?gcd(b,a%b):a;
}
int main (void)
{
LL a,b;
while (cin>>a>>b)
{
LL g=gcd(a,b);
LL ca,cb,ag,bg,fenzia,fenzib,fenmua,fenmub;
if(a==b)
{
cout<<0<<endl;
continue;
}
else
{
map<LL,LL>lista;//记录Alex分母的分解情况
map<LL,LL>listb;//记录Asd分母的分解情况
ag=gcd(a,g);
bg=gcd(b,g);
fenmua=a/ag;//得到Alex最简分式的分母
fenmub=b/bg;//得到Asd最简分式的分母
for (int i=0; i<3; i++)//Alex分解
{
while (fenmua>=list[i])
{
if(fenmua%list[i]==0)
{
fenmua/=list[i];
lista[list[i]]++;
}
else
break;
}
}
for (int i=0; i<3; i++)//Asd分解
{
while (fenmub>=list[i])
{
if(fenmub%list[i]==0)
{
fenmub/=list[i];
listb[list[i]]++;
}
else
break;
}
}
if(fenmua==1&&fenmub==1)
cout<<lista[2]+lista[3]+lista[5]+listb[2]+listb[3]+listb[5]<<endl;//输出操作次数(Alex+Asd)
else
cout<<-1<<endl;
}
}
return 0;
}