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拓扑排序

复习一下拓扑排序

参考:hihocoder-1174

方法

  1. 每次删除一个入度为0的点,直到没有入度为0的点为止。
  2. 维护每个点的入度值,也就是在删除点的同时更新受影响的点的入度值,用容器记录入度为0的点,依次pop出来。

复杂度

O(N + M) 顶点数 + 边数

代码

#include <iostream>
#include <vector>
#include <queue>
#include <cstdio>
#include <cstring>
using namespace std;
const int MAXN = 100000;
const int MAXM = 5000000;

int head[MAXN + 1] = { 0 }; // 表示头指针,初始化为0
int p[MAXM + 1];        // 表示指向的节点
int nexte[MAXM + 1] = { 0 };    // 模拟指针,初始化为0
int edgecnt;            // 记录边的数量

void addedge(int u, int v) {    // 添加边(u,v)
    ++edgecnt;
    p[edgecnt] = v;
    nexte[edgecnt] = head[u];
    head[u] = edgecnt;
}

// 枚举边的过程,u为起始点
/*for (int i = head[u]; i; i = next[i]) {
    v = p[i];
    ...
}*/
int N, M;
void calcin(int degin[])
{
    for (int k = 1; k <= N; k++)
    {
        for (int i = head[k]; i; i = nexte[i]) {
            int v = p[i];
            degin[v]++;
        }
    }
}

void checkring(queue<int> Q, int degin[])
{
    while (!Q.empty())
    {
        int s = Q.front();
        Q.pop();
        N--;
        for (int i = head[s]; i; i = nexte[i]) {
            int v = p[i];
            degin[v]--;
            if (degin[v] == 0)
                Q.push(v);
        }
    }
}

int main()
{
    //freopen("t.txt","r", stdin);
    int T;
    cin >> T;
    for (int ti = 0; ti < T; ti++)
    {

        memset(head, 0, sizeof(head));
        memset(p, 0, sizeof(p));
        memset(nexte, 0, sizeof(nexte));
        edgecnt = 0;

        cin >> N >> M;
        for (int i = 0; i < M; i++)
        {
            int u, v;
            scanf("%d %d", &u, &v);
            addedge(u, v);
        }

        int degin[MAXN + 1] = { 0 };
        calcin(degin);

        queue<int> Q;
        for (int i = 1; i <= N; i++)
        {
            if (degin[i] == 0)
                Q.push(i);
        }

        if (Q.empty())
            cout << "Wrong" << endl;
        else
        {
            checkring(Q, degin);
            cout << (N > 0 ? "Wrong" : "Correct") << endl;
        }

    }

    return 0;
}

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