树与图的深度优先遍历
AcWing 846. 树的重心

#include <iostream>
#include <cstring>
#include <algorithm>

using namespace std;

const int N = 1e5 + 10, M = N * 2;

int n;
int h[N], e[M], ne[M], idx; //数组开错了，TLE
bool st[N];
int ans = N;

void add(int a, int b)
{
    e[idx] = b, ne[idx] = h[a], h[a] = idx++;
}

int dfs(int u)
{
    st[u] = true;

    int sum = 1, res = 0;
    for (int i = h[u]; i != -1; i = ne[i])
    {
        int j = e[i];
        if (!st[j])
        {
            int s = dfs(j);
            res = max(res, s); //所有子树的最大值
            sum += s;          //累积求这个点的子树大小
        }
    }

    res = max(res, n - sum);   //这个点上面的那个连通块，比一下大小
    ans = min(ans, res);       //题目求的是最大值最小

    return sum;  //返回u点子树的大小
}

int main()
{
    cin >> n;
    memset(h, -1, sizeof h);

    for (int i = 0; i < n - 1; i++)
    {
        int a, b;
        //cin >> a >> b;
        scanf("%d%d", &a, &b);
        add(a, b), add(b, a);
    }

    dfs(1);

    cout << ans << endl;

    return 0;
}


树与图的广度优先遍历
AcWing 847. 图中点的层次

#include <iostream>
#include <cstring>

using namespace std;

const int N = 1e5 + 10;

int n, m;
int h[N], e[N], ne[N], idx;
int d[N], q[N];

void add(int a, int b)
{
    e[idx] = b, ne[idx] = h[a], h[a] = idx++;
}

int bfs()
{
    int hh = 0, tt = 0;
    q[0] = 1;

    memset(d, -1, sizeof d);

    d[1] = 0;
    while (hh <= tt)
    {
        int t = q[hh++];
        for (int i = h[t]; i != -1; i = ne[i])
        {
            int j = e[i];
            if (d[j] == -1)
            {
                d[j] = d[t] + 1;
                q[++tt] = j;
            }
        }

    }

    return d[n];
}

int main()
{
    cin >> n >> m;
    memset(h, -1, sizeof h);

    for (int i = 0; i < m; i++)
    {
        int a, b;
        cin >> a >> b;
        add(a, b);
    }

    cout << bfs() << endl;

    return 0;
}


拓扑排序
AcWing 848. 有向图的拓扑序列

#include <iostream>
#include <cstring>
#include <cstdio>

using namespace std;

const int N = 1e5 + 10;

int n, m;
int h[N], e[N], ne[N], idx;
int d[N], q[N];

void add(int a, int b)
{
    e[idx] = b, ne[idx] = h[a], h[a] = idx++;
}

bool topsort()
{
    int hh = 0, tt = -1;
    for (int i = 1; i <= n; i++)
        if (!d[i]) q[++tt] = i;

    while (hh <= tt)
    {
        int t = q[hh++];
        for (int i = h[t]; i != -1; i = ne[i]) //枚举t的所有出边t -> j
        {
            int j = e[i];  //出边
            d[j] --;       //干掉这条边，就是j的入度-1
            if (d[j] == 0) q[++tt] = j;
        }
    }

    if (tt == n - 1) return true;
    else return false;
}

int main()
{
    scanf("%d%d", &n, &m);
    memset(h, -1, sizeof h);

    for (int i = 0; i < m; i++)
    {
        int a, b;
        scanf("%d%d", &a, &b);

        add(a, b);
        d[b]++;  //b的入度+1
    }

    if (topsort())
    {
        for (int i = 0; i < n; i++)
            printf("%d ", q[i]);
    }
    else
        puts("-1");

    return 0;
}