Sorting It All Out 【拓扑】

学习了，
第一道 拓扑
求拓扑的 算法思路
拓扑排序。拓扑排序：若G包含有向边(U,V)，则在序列中U出现在V之前，即该序列使得图中所有有向边均从左指向右。如果图是有回路的，就不存在这样的序列。首先选择一个无前驱的顶点(即入度为0的顶点，图中至少应该有一个这样的顶点，否则肯定存在回路)，然后从图中移去该顶点以及由其发出的所有有向边，如果图中还存在无前驱的顶点，则重复上述操作，直到操作无法进行。如果图不为空，说明图中存在回路，无法进行拓扑排序；否则移出的顶点的顺序就是对该图的一个拓扑排序。

此题 的还有一个 坑点就是，对于每种情况的输出是有优先级的，只要成环一定输出，所以当当前的 序列为无序的时候，也不能输出，因为之后可能导致成环 ，。。逻辑
代码
Sorting It All Out
An ascending sorted sequence of distinct values is one in which some form of a less-than operator is used to order the elements from smallest to largest. For example, the sorted sequence A, B, C, D implies that A < B, B < C and C < D. in this problem, we will give you a set of relations of the form A < B and ask you to determine whether a sorted order has been specified or not.
Input
Input consists of multiple problem instances. Each instance starts with a line containing two positive integers n and m. the first value indicated the number of objects to sort, where 2 <= n <= 26. The objects to be sorted will be the first n characters of the uppercase alphabet. The second value m indicates the number of relations of the form A < B which will be given in this problem instance. Next will be m lines, each containing one such relation consisting of three characters: an uppercase letter, the character “<” and a second uppercase letter. No letter will be outside the range of the first n letters of the alphabet. Values of n = m = 0 indicate end of input.
Output
For each problem instance, output consists of one line. This line should be one of the following three:

Sorted sequence determined after xxx relations: yyy…y.
Sorted sequence cannot be determined.
Inconsistency found after xxx relations.

where xxx is the number of relations processed at the time either a sorted sequence is determined or an inconsistency is found, whichever comes first, and yyy…y is the sorted, ascending sequence.
Sample Input

4 6A < BA < CB<CC<DB<DA<B3 2A<BB<A26 1A<Z0 0

Sample Output
Sorted sequence determined after 4 relations: ABCD.
Inconsistency found after 2 relations.
Sorted sequence cannot be determined..

代码

#include<cstdio>#include<cstring>#include<algorithm>#include<iostream>#include<cmath>#include<queue>#include<stack>#include<map>#include<vector>#include<set>#define CLR(a,b) memset((a),(b),sizeof(a))#define inf 0x3f3f3f3f#define mod 100009#define LL long long#define M  50#define ll o<<1#define rr o<<1|1#define lson o<<1,l,mid#define rson o<<1|1,mid+1,rusing namespace std;int n,m; int mp[M][M];  //  建图 int in[M];  //  入度情况 int mark[M]; //  每个条件之后，的入度情况 int topo[M];  //存储着topo序列 void init()  // 初始化  {    CLR(in,0);    CLR(mp,0);}void trans()   //  赋值给 标记数组 {    int i,j;    for(i=1;i<=n;i++)    mark[i]=in[i];}int toposort(){    int num;   // 记录 每一次 找的时候有几个 入度为0 的个数     int t=0;   // 标记 topo 的数组     int i,j;    int flag=1; // 记录 是无序还是 有序     int next;  // 记录下一个将要并入 topo的序号     trans();  // 获取一次当前 的入度情况     for(i=1;i<=n;i++)    {        num=0;        for(j=1;j<=n;j++)        {            if(!mark[j])             {                num++;                next=j;            }        }        if(!num) return 0;  // 成环了          if(num>1)  flag=-1; // 这里可以判定 一定是无序的，但是 之后还可能是成环的情况 所以这里只能标记         topo[t++]=next;  //  并入数组         mark[next]=-1;  //  将next 这个顶点删除掉         for(j=1;j<=n;j++)        {            if(mp[next][j])  //以next为起点的有向边都删除掉             mark[j]--;            }      }      return flag;}int main(){    int i,j;    while(~scanf("%d%d",&n,&m)&&(n||m))    {        init();        char c[5];int a,b;        int exist;int flag=0;        for(  i=0;i<m;i++)        {           scanf("%s",c);        if(flag)  continue; //虽然已经 得出结果，但是 输入还没有完，要把输入输完         a=c[0]-'A'+1;        b=c[2]-'A'+1;        mp[a][b]=1;        in[b]++;        exist=toposort();        if(!exist)         printf("Inconsistency found after %d relations.\n",i+1),flag=1;         else  if(exist==1)  //          {            printf("Sorted sequence determined after %d relations: ",i+1);            for(  j=0;j<n;j++)            printf("%c",topo[j]+'A'-1);            printf(".\n");            flag=1;          }         }        if(!flag)   // 既没有 成环，也没有排序成功         printf("Sorted sequence cannot be determined.\n");    }    return 0;}