1.合并集合

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#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 10;
int arr[N];

int find(int x)
{
    if (arr[x] != x)
    {
        arr[x] = find(arr[x]);
    }
    return arr[x];
}
int main()
{
    int n, m;
    cin >> n >> m;
    for (int i = 1; i <= n; i++)
    {
        arr[i] = i;
    }

    while (m--)
    {

        
        char c1;
        int a, b;
        cin >> c1 >> a >> b;
        if (c1 == 'M')
        {
            
            // a的祖先节点的下标
            arr[find(a)] = find(b);
        }
        else if (c1 == 'Q')
        {
           
            if (find(a) == find(b))
            {
                cout << "Yes" << endl;
            }
            else
            {
                cout << "No" << endl;
            }
        }
    }
    return 0;
}

2.连通块中点的数量

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#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 10;
int arr[N];
int size_q[N];

// 递归查找 + 路径压缩
int find(int x)
{
    if (arr[x] != x)
        arr[x] = find(arr[x]);
    return arr[x];
}
int main()
{
    ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
    int n, m;
    cin >> n >> m;
    for (int i = 1; i <= n; i++)
    {
        arr[i] = i;
        size_q[i] = 1;
    }

    while (m--)
    {
        string s1;
        cin >> s1;
        int a, b;
        if (s1 == "C")
        {
            cin >> a >> b;
            if (find(a) == find(b))
                continue;
            else
                size_q[find(b)] += size_q[find(a)];
                arr[find(a)] = find(b);
        } else if(s1 == "Q1")
        {
            cin >> a >> b;
            if(find(a) == find(b)) 
            {
                cout << "Yes" << endl;
            } else {
                cout << "No" << endl;
            }
        } else {
            cin >> a;
            cout << size_q[find(a)] << endl;

        }
    }
    return 0;
}

3.（难）食物链

240. 食物链 - AcWing题库

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#include <iostream>

using namespace std;

const int N = 50010;

int n, m;
int p[N], d[N];

int find(int x)
{
    if (p[x] != x)
    {
        int t = find(p[x]);
        d[x] += d[p[x]];
        p[x] = t;
    }
    return p[x];
}

int main()
{
    scanf("%d%d", &n, &m);

    for (int i = 1; i <= n; i ++ ) p[i] = i;

    int res = 0;
    while (m -- )
    {
        int t, x, y;
        scanf("%d%d%d", &t, &x, &y);

        if (x > n || y > n) res ++ ;
        else
        {
            int px = find(x), py = find(y);
            if (t == 1)
            {
                if (px == py && (d[x] - d[y]) % 3) res ++ ;
                else if (px != py)
                {
                    p[px] = py;
                    d[px] = d[y] - d[x];
                }
            }
            else
            {
                if (px == py && (d[x] - d[y] - 1) % 3) res ++ ;
                else if (px != py)
                {
                    p[px] = py;
                    d[px] = d[y] + 1 - d[x];
                }
            }
        }
    }

    printf("%d\n", res);

    return 0;
}