Problem I
23 Out of 5
Input: standard input
Output: standard output
Time Limit: 1 second
Memory Limit: 32 MB
Your task is to write a program that can decide whether you can find an arithmetic expression consisting of five given numbers 
(1<=i<=5) that will yield the value 23.
For this problem we will only consider arithmetic expressions of the following from:
(1<=i<=5) that will yield the value 23.For this problem we will only consider arithmetic expressions of the following from:
where 
: {1,2,3,4,5} -> {1,2,3,4,5} is a bijective function
and 
{+,-,*} (1<=i<=4)
Input
The Input consists of 5-Tupels of positive Integers, each between 1 and 50.
Input is terminated by a line containing five zero's. This line should not be processed.
Input is terminated by a line containing five zero's. This line should not be processed.
Output
For each 5-Tupel print "Possible" (without quotes) if their exists an arithmetic expression (as described above) that yields 23. Otherwise print "Impossible".
Sample Input
1 1 1 1 1
1 2 3 4 5
2 3 5 7 11
0 0 0 0 0
Sample Output
Impossible
Possible
Possible
Thomas Strohmann
DFS +backtracking
#include<stdio.h>
#include<cstring>
#include<string>
#include<vector>
#define REP(i, b, n) for (int i = b; i < n; i++)
#define rep(i, n) REP(i, 0, n)
#define DBG 0
using namespace std;
int data[5];
bool used[5];
bool DFS(int ind,int num,int len,int left){
if(DBG)printf("dfs: ind num %d %d\n",ind,num);
int b;
if(len==5)return num==23;
if(num-23>left){if(DBG)printf("len num left %d %d %d\n",len,num,left);return 0;}
used[ind]=1;
rep(i,5){
if(!used[i]){
b=left-data[i];
if(DFS(i,num+data[i],len+1,b))return 1;
if(DFS(i,num-data[i],len+1,b))return 1;
if(DFS(i,num*data[i],len+1,b))return 1;
}
}
used[ind]=0;
return 0;
}
void ans(){
int tot=0;
rep(i,5)tot+=data[i];
memset(used,0,sizeof(used));
rep(i,5)if(DFS(i,data[i],1,tot-data[i])){printf("Possible\n");return;}
printf("Impossible\n");
}
int main(){
int a,i;
while(scanf("%d%d%d%d%d",&data[0],&data[1],&data[2],&data[3],&data[4])==5){
for(i=0;i<5;i++)if(data[i]>0)break;
if(i==5)break;
ans();
}
}
) and the number of edges m (
). The next m lines describe the m edges. Each edge is given by the numbers of the two nodes connected by it. Nodes are numbered from 0 to n-1. Edges are undirected. Nodes have degrees of three or less. The network is not neccessarily connected.
with the following four properties:
) there exist two (not neccessarily different) integers i and j ( 
) with ak=ai +aj
into each circle separately, and the sum of numbers in two adjacent circles should be a prime.