Counting

Accept:100??	??Submit:807
Time Limit:2000MS??	??Memory Limit:65536KB

Description

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We are familiar with the game called “Counting 24”. Now it comes a problem that we want to know whether we can figure out the exact answer with given 4 numbers only using +,-,*,/ and (,).

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Input

There are several cases in a test. Each case contains only 5 integers, a1, a2, a3, a4 and required answer. All integers are positive and no more than 100.

Output

If it is possible to figure out the required answer, output “Possible”; otherwise output “Impossible”.

Sample Input

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5 5 1 5 24

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Sample Output

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Impossible

#include<cstdio> #include<cstdlib> #include<cstring> #include<algorithm> #include<set> using namespace std; int a[4],ans; set<int>s[16]; set<int>::iterator it1,it2; inline void deal(int x,int tmp){s[x].insert(tmp);} void cal(int x){if(!s[x].empty())return;for(int i=1;i<16;i++)if((x&i)==i)for(it1=s[i].begin();it1!=s[i].end();it1++)for(it2=s[x-i].begin();it2!=s[x-i].end();it2++){deal(x,(*it1)+(*it2));deal(x,(*it1)*(*it2));deal(x,(*it1)-(*it2));if((*it2)&&(*it1)%(*it2)==0)deal(x,(*it1)/(*it2));} } bool can(){int i;for(i=0;i<16;i++)s[i].clear();for(i=0;i<4;i++)s[1<<i].insert(a[i]);for(i=1;i<16;i++)cal(i);return s[15].find(ans)==s[15].end()?false:true; } int main(){while(~scanf("%d%d%d%d%d",&a[0],&a[1],&a[2],&a[3],&ans))printf("%s\n",can()?"Possible":"Impossible");return 0; }

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