POJ1270 following Orders (topological sorting)

Following Orders

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 4059		Accepted: 1623

Description

Order is a important concept in mathematics and in computer. For example, Zorn ' Lemma states: "A partially ordered set in which every chain have an upper bound contains a maximal ele ment. " 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 is to write a program this prints all orderings of the Var Iables that is consistent with the constraints.


For example, given the constraints x < Y and x < Z there is both orderings of the variables x, y, and z that is con Sistent with these constraints:x y Z and x z y.

Input

The input consists of a sequence of constraint specifications. A specification consists of both lines:a list of variables on one lineFollowed bya 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 isSingle character,lower-case Letters. There'll is at least-variables, and no more than-variables in a specification. There'll is at least one constraint, and no more than the constraints in a specification. There'll is at least one, and no more than orderings consistent with the contraints in a specification.


Input is terminated by End-of-file.

Output

For each constraint specification,All orderings consistent and the constraints should be printed. Orderings is printed in lexicographical (alphabetical) order, one per line.


Output for different constraint specifications are 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

Source

Duke Internet Programming Contest 1993,uva 124

Test instructions: Given a string of characters (inter-XOR), then a sequence of characters, indicating a back-and-forth relationship, such as a B E F C D, representing A<b,e<f,c<d.

Sorts the characters that begin to be given so that they conform to the relationship sequence. and output these matching character sequences according to the dictionary order.

#include <stdio.h> #include <vector> #include <string.h>using namespace std;const int N = 30;int In[n],    Exist[n],mapt[n][n],path[n],n;void topesort (int u,int k) {path[k]=u;        if (k==n) {for (int i=1;i<=n;i++) printf ("%c", path[i]+ ' a ');        printf ("\ n");    return;    } in[u]=-1;    for (int i=0;i<26;i++) if (Mapt[u][i]) in[i]-=mapt[u][i];    for (int i=0;i<26;i++) if (Exist[i]&&!in[i]) topesort (i,k+1);    in[u]=0; for (int i=0;i<26;i++) if (Mapt[u][i]) in[i]+=mapt[u][i];}    int main () {int flag=0;    Char str[1000];        while (gets (str)) {if (flag) printf ("\ n"); flag=1;        memset (In,0,sizeof (in));        memset (exist,0,sizeof (exist));        memset (mapt,0,sizeof (MAPT));        n=0;            for (int i=0;str[i]!= ' n '; i++) if (str[i]>= ' a ' &&str[i]<= ' z ') {int ch=str[i]-' a ';            if (exist[ch]==0) n++;        Exist[ch]=1;    }    Gets (str);        int i=0,a,b;            while (str[i]!= ' ") {while (str[i]== ') i++; a=str[i++]-' a '; while (str[i]== ') i++;            b=str[i++]-' a '; mapt[a][b]++;        in[b]++;    } for (int i=0;i<26;i++) if (Exist[i]&&!in[i]) topesort (i,1); }}

POJ1270 following Orders (topological sorting)