<poj,sicily>Anti-prime Sequences (DFS)
1002. Anti-prime Sequences
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Description
Given a sequence of consecutive integers n,n+1,n+2,...,m, an anti-prime sequence is a rearrangement of these integers so that each adjacent pair of integers sums to a composite (non-prime) number. For example, if n = 1 and m = 10, one such anti-prime sequence is 1,3,5,4,2,6,9,7,8,10. This is also the lexicographically first such sequence. We can extend the definition by defining a degree danti-prime sequence as one where all consecutive subsequences of length 2,3,...,d sum to a composite number. The sequence above is a degree 2 anti-prime sequence, but not a degree 3, since the subsequence 5, 4, 2 sums to 11. The lexicographically .rst degree 3 anti-prime sequence for these numbers is 1,3,5,4,6,2,10,8,7,9. Input
Input will consist of multiple input sets. Each set will consist of three integers, n, m, and d on a single line. The values of n, m and d will satisfy 1 <= n < m <= 1000, and 2 <= d <= 10. The line 0 0 0 will indicate end of input and should not be processed. Output
For each input set, output a single line consisting of a comma-separated list of integers forming a degree danti-prime sequence (do not insert any spaces and do not split the output over multiple lines). In the case where more than one anti-prime sequence exists, print the lexicographically first one (i.e., output the one with the lowest first value; in case of a tie, the lowest second value, etc.). In the case where no anti-prime sequence exists, output No anti-prime sequence exists. Sample Input
1 10 2 1 10 3 1 10 5 40 60 7 0 0 0 Sample Output
1,3,5,4,2,6,9,7,8,10 1,3,5,4,6,2,10,8,7,9 No anti-prime sequence exists. 40,41,43,42,44,46,45,47,48,50,55,53,52,60,56,49,51,59,58,57,54 |
AC code
#include <iostream> #include <cstdio> #include <memory.h> using namespace std; int ans[1000],m,n,d,len;//len为sequence的长度,就是m-n+1 bool flag,vis[1001],composite[10000]={1,1};//flag用于判断是否生成anti-prime sequence //筛选素数,composite[i]=1当且仅当i不是素数 void InitComposite() { for(int i=2;i<1001;i++) { if(!composite[i]) { for(int j=2;j*i<10000;j++) composite[i*j]=1; } } //for(int i=0;i<100;i++) cout<<i<<":"<<composite[i]<<" "; } //检查sum是否是composite number bool CheckSum(int idx) { int sum=ans[idx]; for(int i=idx-1;i>-1&&i>idx-d;i--) { sum+=ans[i]; if(!composite[sum]) return 0; } return 1; } //depth记录当前有多少个数成功加入sequence void DFS(int depth) { //当depth大于len时,代表找到anti-prime sequence if(depth==len) { flag=1; return ; } else { for(int i=n;i<=m;i++) { if(!vis[i]) { ans[depth]=i; if(CheckSum(depth)) { vis[i]=1; //ans中第depth个数已经确定,往depth+1处搜索 DFS(depth+1); vis[i]=0;//不要漏了这个!!! if(flag) return ; } } } } return ; } int main() { InitComposite(); while(scanf("%d%d%d",&n,&m,&d) && m) { memset(vis,0,sizeof(vis)); len=m-n+1; flag=0; DFS(0); if(flag) { for(int i=0;i<len-1;i++) printf("%d,",ans[i]); printf("%d\n",ans[len-1]); } else puts("No anti-prime sequence exists."); } return 0; }