拓扑排序

拓扑排序队列实现:

1、将所有入度为0的节点加入队列，如果不存在入度为0的节点，则图中有环，如果有多个入度为0的节点，则拓扑排序不唯一

2、弹出队首元素u,并且将与u相关联的顶点v的入度减1，如果v的入度为0，则将v加入队列

3、重复第二步，如果所有的顶点都被访问到，则输出序列就是一个拓扑排序，否则该有向图中有环。

poj1094很经典的拓扑排序题；

#include<cstdio>#include<cstring>#include<cmath>#include<cstdlib>#include<climits>#include<cctype>#include<iostream>#include<algorithm>#include<queue>#include<vector>#include<string>#include<set>#include<stack>#include<map>#define ll long long#define MAX 110#define INF INT_MAX#define eps 1e-6#define REP(i,n) for (int i=0; i<(n); i++)#define FOR(i,s,t) for (int i=(s); i<=(t); i++)using namespace std;vector<int>G[MAX];int n,m,in[MAX],res[MAX],map[MAX][MAX];int topo(){int t[MAX];memcpy(t,in,sizeof(in));queue<int>q;for (int i=0; i<n; i++) if (!t[i]) q.push(i);int flag = 0,cnt = 0;while (!q.empty()){if (q.size() > 1) flag  = 1;   //如果队列中有两个元素时，说明拓扑排序并不唯一int u = q.front();res[cnt++] = u;q.pop();for (int i=0; i<G[u].size(); i++){int v = G[u][i];if (--t[v] == 0) q.push(v);}}if (cnt != n) return 0;       //如果存在元素未被访问到时，说明图中有环if (flag) return 1;return 2;}char s[10];int main(){while (scanf("%d%d",&n,&m) && n != 0){int i,ok1 = 0,ok2 = 0;for (i=0; i<30; i++) G[i].clear();memset(in,0,sizeof(in));for (i=0; i<m; i++){scanf("%s",s);G[s[0]-'A'].push_back(s[2]-'A');in[s[2] - 'A']++;int ans = topo();if (ans == 0){printf("Inconsistency found after %d relations.\n",i+1);ok1 = 1;break;} if (ans == 1){continue;}if (ans == 2){printf("Sorted sequence determined after %d relations: ",i+1);for (int j=0; j<n; j++) printf("%c",res[j]+'A');  printf(".\n");ok2 = 1;break;}}for (int j=i+1; j<m; j++) scanf("%s",s);if (!ok1 && !ok2) printf("Sorted sequence cannot be determined.\n");}return 0;}

poj3687很好的拓扑排序题；

这个题目要注意逆序建图，并且要去除重边。

#include<cstdio>#include<cstring>#include<cmath>#include<cstdlib>#include<climits>#include<cctype>#include<iostream>#include<algorithm>#include<queue>#include<vector>#include<map>#include<set>#include<string>#include<stack>#define ll long long#define MAX 210#define INF INT_MAX#define eps 1e-8using namespace std;int a[MAX][MAX],in[MAX],c[MAX],n;int topo(){             priority_queue<int>q;       //用优先队列在所有入度为0的点中选一个最大出来，则其对应的重量就应该为当前最大的重量。这个也是逆序建图的好处for (int i=1; i<=n; i++){if (!in[i]){q.push(i);}}int cnt = n;while (!q.empty()){int u = q.top();q.pop();c[u] = cnt--;for (int i=1; i <= n; i++){if (a[u][i]){in[i]--;if (!in[i]) q.push(i);}}}for (int i=1; i<=n; i++) if (in[i]) return -1;return 1;}int main(){int T,m;scanf("%d",&T);while (T--){scanf("%d%d",&n,&m);int u,v;memset(a,0,sizeof(a));memset(in,0,sizeof(in));for (int i=0; i<m; i++){scanf("%d%d",&u,&v);if (a[v][u]) continue;  //去除重边a[v][u] = 1;in[u]++;}int sign = topo();if (sign < 0) printf("-1\n");else {printf("%d",c[1]);for (int i=2; i<=n; i++) printf(" %d",c[i]); printf("\n");}}return 0;}

附:有关优先队列使用的优先级，以及vector中sort函数使用时的比较级的使用；

/*struct cmp  {        bool operator ()(int &a,int &b)      {            return a>b;//最小值优先         }    };struct cmp  {        bool operator ()(int &a,int &b)      {            return a<b;//最大值优先         }    }; priority_queue<int,vector<int>,cmp> 优先队列存放int类型时默认的是降序排序，如果要想升序输出，需要重新定义优先级；在结构体里的优先级可以通过重载小于号实现 *//*vector中的sort函数用法,当vector中存的是int类型时，即vector<int>G;可以用sort(G.begin(),G.end(),lexx<int>())升序排列，sort<G.begin(), G.end(),greater<int>()>降序排列 */