POJ 1270 Following Orders(拓扑排序:输出所有可能)

题意：给出一串字母和关系，问输出所有可能满足拓扑排序的排列组合

思路：由于要输出所有的组合并且题目保证一定有输出，那么可以用dfs来构造组合。需要满足两个条件

           1.当前被选的字母必须有效(即mark[i]==true)且当前被选的字母vis=false(即还没被选)。

          2.当我们从前到后依次选择一个字母x放进topo数组的时候，我们要保证在topo数组的当前位置cnt的前面那些位置中不会出现y这种字母。其中y<x，即y被要求出现在x后面。

#include <cstdio>#include <queue>#include <cstring>#include <iostream>#include <cstdlib>#include <algorithm>#include <vector>#include <map>#include <string>#include <set>#include <ctime>#include <cmath>#include <cctype>using namespace std;#define maxn 30#define LL long longint cas=1,T;int G[maxn][maxn];int vis[maxn];int ans[maxn];int n,cnt;int mark[maxn];bool ok(int i,int cnt){for (int j = 0;j<cnt;j++)if (G[i][ans[j]])return false;return true;}void dfs(int cnt){if (cnt==n){for (int i = 0;i<n;i++)   printf("%c",ans[i]+'a');printf("\n");}else{for (int i = 0;i<26;i++)if (mark[i] && !vis[i] && ok(i,cnt)){vis[i]=1;ans[cnt]=i;dfs(cnt+1);vis[i]=0;}}}int main(){char str[1000];while (gets(str)){n=0;memset(mark,0,sizeof(mark));memset(G,0,sizeof(G));memset(vis,0,sizeof(vis));for (int i = 0;str[i];i++)if(str[i]!=' '){mark[str[i]-'a']=1;n++;}gets(str);for (int i = 0;str[i];i++)if (str[i]!=' '){int a,b;a=str[i++]-'a';while (str[i]==' ')i++;b=str[i]-'a';G[a][b]=1;}dfs(0);printf("\n");}//freopen("in","r",stdin);//scanf("%d",&T);//printf("time=%.3lf",(double)clock()/CLOCKS_PER_SEC);return 0;}

题目

Description

Order is an important concept in mathematics and in computer science. For example, Zorn's Lemma states: ``a partially ordered set in which every chain has an upper bound contains a maximal element.'' Order is also important in reasoning about the fix-point semantics of programs. 


This problem involves neither Zorn's Lemma nor fix-point semantics, but does involve order. 
Given a list of variable constraints of the form x < y, you are to write a program that prints all orderings of the variables that are consistent with the constraints. 


For example, given the constraints x < y and x < z there are two orderings of the variables x, y, and z that are consistent with these constraints: x y z and x z y. 

Input

The input consists of a sequence of constraint specifications. A specification consists of two lines: a list of variables on one line followed by a list of contraints on the next line. A constraint is given by a pair of variables, where x y indicates that x < y. 


All variables are single character, lower-case letters. There will be at least two variables, and no more than 20 variables in a specification. There will be at least one constraint, and no more than 50 constraints in a specification. There will be at least one, and no more than 300 orderings consistent with the contraints in a specification. 


Input is terminated by end-of-file. 

Output

For each constraint specification, all orderings consistent with the constraints should be printed. Orderings are printed in lexicographical (alphabetical) order, one per line. 


Output for different constraint specifications is separated by a blank line. 

Sample Input

a b f ga b b fv w x y zv y x v z v w v

Sample Output

abfgabgfagbfgabfwxzvywzxvyxwzvyxzwvyzwxvyzxwvy