【解题报告】【图论专题】

/*
转化为图论模型
求一个图的最大联通分量
用并查集，每个联通分量用一个集合维护，最后求集合元素个数的最大值 
*/
#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;

const int maxn = 10000010;
int fa[maxn];
int ans[maxn];
void init(){
    for(int i=0;i<maxn;++i){
        fa[i] = i;
    }
    memset(ans , 0, sizeof(ans));
}

int find(int u){
    return u==fa[u] ? u : fa[u] = find(fa[u]);
}
void un(int u, int v){
    int fu = find(u);
    int fv = find(v);
    fa[fv] = fu; 
}

int main(){
    int n;
    while(scanf("%d", &n)==1){
        if(n==0){
            printf("1\n");
            continue;    
        } 
        init();
        int u, v;
        int maxnum = -1;
        for(int i=0;i<n;++i){
            scanf("%d%d", &u, &v);
            if(u>maxnum) maxnum = u;
            if(v>maxnum) maxnum = v;
            if(find(u)!=find(v)) un(u, v);
        }
        
//        ///test 
//        for(int i=1;i<=maxnum;++i){
//            cout << fa[i] << " ";
//        }
//        cout << endl;
        
        
        for(int i=1;i<=maxnum;++i){
            ans[find(i)]++;
        }
        int maxans = -1;
        for(int i=1;i<=maxn;++i){
            if(ans[i] > maxans) maxans = ans[i];
        }
        printf("%d\n", maxans);
    }
    
    return 0;
}

/*
克鲁斯卡尔算法
将边从小到大排序 
*/
#include<iostream>
#include<cstdio>
#include<algorithm>
using namespace std;

const int maxn = 10010;
    
struct node{
    int u;
    int v; 
    int weight;
} ;
node edges[maxn];
bool cmp(const node & e1, const node & e2){
    return e1.weight <= e2.weight;
}

int d[105];        //并查集
int find(int u){
    return u==d[u] ? u : d[u] = find(d[u]);
} 
void init(){
    for(int i=0;i<105;++i){
        d[i] = i;
    }
}
void un(int u, int v){
    int fu = find(u);
    int fv = find(v);
    d[fv] = fu;
}

int main(){
    int n;
    int en = 0;
    int w; 
    init();
    scanf("%d", &n);
    for(int i=1;i<=n;++i){
        for(int j=1;j<=n;++j){
            scanf("%d", &w);    
            if(j>i){
                edges[en].weight = w;
                edges[en].u = i;
                edges[en].v = j;
                en++;
            }
        }
    }
    
    int q;
    int u, v;
    scanf("%d", &q);
    for(int i=0;i<q;++i){
        scanf("%d%d", &u, &v);
        if(find(u)!=find(v)) un(u, v);
    }

    int ans = 0;
    sort(edges, edges+en, cmp);
    for(int i=0;i<en;++i){
        if(find(edges[i].u) != find(edges[i].v)){
            ans+=edges[i].weight;
            un(edges[i].u, edges[i].v);
        }
    }
    
    printf("%d\n", ans);
    return 0;
}