hdu1863 畅通工程 Kruskal/Prim

题目链接:

http://acm.hdu.edu.cn/showproblem.php?pid=1863

题意:

题解:

Kruskal是按照边权排序，每次选择一条最小的边，判断这条边的两个端点是否在同一个集合，用并查集维护
Prim是随便选择一个点作为当前集合，找到与这个集合相连的边中最短的那条，用优先队列取出最短的，如果另一个端点不在当前集合，就加进来，并且把与这个点相连的所有边加到优先队列里

代码:

Kruskal：

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define MS(a) memset(a,0,sizeof(a))
#define MP make_pair
#define PB push_back
const int INF = 0x3f3f3f3f;
const ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
inline ll read(){
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
//////////////////////////////////////////////////////////////////////////
const int maxn = 100+10;

int N,M,fa[maxn];
ll ans;

struct node{
    int u,v,w;
    bool operator<(const node& rhs)const{
        return w < rhs.w;
    }
}E[maxn];

int find(int x){
    return fa[x]==x ? x : fa[x]=find(fa[x]);
}

void Union(int x,int y){
    int p1 = find(x), p2 = find(y);
    if(p1 == p2) return;
    fa[p1] = p2;
}

bool same(int x,int y){
    return find(x)==find(y);
}

void kruskal(){
    sort(E,E+M);
    for(int i=0; i<M; i++){
        int u = E[i].u, v = E[i].v, w = E[i].w;
        if(same(u,v)) continue;
        Union(u,v);
        ans += w;
    }
}

int main(){
    while(scanf("%d%d",&M,&N)==2){
        if(M==0) break;
        ans = 0;
        for(int i=0; i<maxn; i++) fa[i] = i;
        for(int i=0; i<M; i++){
            int u,v,w; scanf("%d%d%d",&u,&v,&w);
            E[i].u = u, E[i].v = v, E[i].w = w;
        }

        kruskal();

        for(int i=1; i<=N; i++)
            if(same(1,i) == 0)
                ans = -1;
        if(ans == -1)
            cout << "?
";
        else
            cout << ans << endl;
    }   

    return 0;
}

Prim：

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define MS(a) memset(a,0,sizeof(a))
#define MP make_pair
#define PB push_back
const int INF = 0x3f3f3f3f;
const ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
inline ll read(){
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
//////////////////////////////////////////////////////////////////////////
const int maxn = 100+10;

struct node{
    int to,cost;
    node(int to=0,int cost=0) : to(to),cost(cost) {}
    bool operator<(const node& rhs)const{
        return cost > rhs.cost;
    }
};

priority_queue<node> que;
std::vector<node> G[maxn];

int N,M;
bool vis[maxn];

ll prim(){
    ll res = 0;
    vis[1] = 1;
    for(int i=0; i<(int)G[1].size(); i++)
        que.push(node(G[1][i]));
    while(!que.empty()){
        node e = que.top(); que.pop();
        if(vis[e.to]) continue;
        vis[e.to] = 1;
        res += e.cost;
        for(int i=0; i<(int)G[e.to].size(); i++)
            que.push(G[e.to][i]);
    }
    return res;
}

int main(){
    while(scanf("%d%d",&M,&N) == 2){
        if(M == 0) break;
        for(int i=0; i<=N; i++) G[i].clear();
        while(que.size()) que.pop();
        MS(vis);
        for(int i=1; i<=M; i++){
            int u,v,w;scanf("%d%d%d",&u,&v,&w);
            G[u].push_back(node(v,w));
            G[v].push_back(node(u,w));
        }

        ll res = prim();

        for(int i=1; i<=N; i++)
            if(vis[i] == 0)
                res = -1;
        if(res == -1)
            printf("?
");
        else
            printf("%I64d
",res);

    }

    return 0;
}