Anti-prime sequences

anti-prime Sequences

Time Limit: 3000MS		Memory Limit: 30000K
Total Submissions: 3355		Accepted: 1531

Description

Given a sequence of consecutive integers n,n+1,n+2,..., m, an anti-prime sequence are a rearrangement of these integers so t Hat each adjacent pair of integers sums to a composite (non-prime) number. For example, if n = 1 and M = ten, 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 are 1,3,5,4,6,2,10,8,7,9.

Input

Input would consist of multiple input sets. Each set would consist of three integers, N, m, and D on a. The values of N, M and D would satisfy 1 <= n < m <=, and 2 <= D <= 10. The line 0 0 0 would 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 seq Uence (do not inserts any spaces and does 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 WI Th 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 21 10 31 10 540 60 70 0 0

Sample Output

1,3,5,4,2,6,9,7,8,101,3,5,4,6,2,10,8,7,9no 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
Test instructions: The "2,d" length of the continuous sequence of the and are to be composite.
Idea: DFS.

1#include <stdio.h>2#include <algorithm>3#include <iostream>4#include <stdlib.h>5#include <string.h>6#include <queue>7#include <stack>8#include <math.h>9 using namespacestd;TentypedefLong LongLL; One BOOLprime[20000]= {0}; A inttt[10000]; - BOOLcm[1005]; - intts=0; the BOOLCheckintNintm); - intDfsintNintMintDintKkintpp); - intMainvoid) - { +     inti,j,k; -      for(i=2; i<= +; i++) +     { A         if(!Prime[i]) at         { -              for(J=i; (I*J) <=20000; J + +) -             { -prime[i*j]=true; -             } -         } in     } -     intn,m; to      while(SCANF (" %d%d%d", &n,&m,&k), n!=0&&m!=0&&k!=0) +     { -memset (CM,0,sizeof(cm)); thets=0; *         intUu=dfs (0, m-n+1, k,n,m); $         if(UU)Panax Notoginseng         { -printf"%d", tt[0]); the              for(i=1; i< (m-n+1); i++) +             { Aprintf",%d", Tt[i]); the             } +printf"\ n"); -         } $         Elseprintf"No anti-prime sequence exists.\n"); $     } - } - BOOLCheckintNintm) the { -     inti,j;Wuyi  the  -LL sum=Tt[m]; Wu          for(i=m-1; I>=max (N,0); i--) -         { Aboutsum+=Tt[i]; $             if(!Prime[sum]) -                 return false; -         } -         return true; A } + intDfsintNintMintDintKkintpp) the { -     inti; $     if(TS)return 1; the     if(n==m) the     { the  the             BOOLCc=check (n-d,m-1); -             if(!cc) in             { the                 return 0; the             } Aboutts=1; the         return 1; the     } the     Else +     { -         BOOLCc=check (n-d,n-1); the         if(CC)Bayi         { the              for(I=KK; i<=pp; i++) the             { -                 if(TS)return 1; -                 if(!Cm[i]) the                 { thett[n]=i; thecm[i]=true; the                     intUu=dfs (n+1, m,d,kk,pp); -cm[i]=false; the                     if(UU)return 1; the                 } the             }94         } the         Else return 0; the     } the     return 0;98}

Anti-prime sequences