BZOJ 1196 公路修建问题(二分+最小生成树)

题目要求求出图中的一颗生成树，使得最大的边权最小，且满足一级公路的个数>=k。

考虑二分最大边，问题就变为给出的图的生成树中，是否满足所有的边<=val,且一级公路的个数>=k。

所以我们把边按一级公路权值排序，优先选择能构成生成树的一级公路。这样贪心的构造。

# include <cstdio>

# include <cstring>

# include <cstdlib>

# include <iostream>

# include <vector>

# include <queue>

# include <stack>

# include <map>

# include <set>

# include <cmath>

# include <algorithm>

using namespace std;

# define lowbit(x) ((x)&(-x))

# define pi acos(-1.0)

# define eps 1e-

# define MOD

# define INF

# define mem(a,b) memset(a,b,sizeof(a))

# define FOR(i,a,n) for(int i=a; i<=n; ++i)

# define FO(i,a,n) for(int i=a; i<n; ++i)

# define bug puts("H");

# define lch p<<,l,mid

# define rch p<<|,mid+,r

# define mp make_pair

# define pb push_back

typedef pair<int,int> PII;

typedef vector<int> VI;

# pragma comment(linker, "/STACK:1024000000,1024000000")

typedef long long LL;

int Scan() {

    int res=, flag=;

    char ch;

    if((ch=getchar())=='-') flag=;

    else if(ch>=''&&ch<='') res=ch-'';

    while((ch=getchar())>=''&&ch<='')  res=res*+(ch-'');

    return flag?-res:res;

}

void Out(int a) {

    if(a<) {putchar('-'); a=-a;}

    if(a>=) Out(a/);

    putchar(a%+'');

}

const int N=;

//Code begin...

struct Edge{int u, v, w1, w2;}edge[N<<];

int n, m, k, fa[N];

int find(int x)

{

    int s, temp;

    for (s=x; fa[s]>=; s=fa[s]) ;

    while (s!=x) temp=fa[x], fa[x]=s, x=temp;

    return s;

}

void union_set(int x, int y)

{

    int temp=fa[x]+fa[y];

    if (fa[x]>fa[y]) fa[x]=y, fa[y]=temp;

    else fa[y]=x, fa[x]=temp;

}

bool check(int x)

{

    int num=;

    mem(fa,-);

    FO(i,,m) {

        int u=find(edge[i].u), v=find(edge[i].v);

        if (edge[i].w2>x||u==v) continue;

        if (edge[i].w1<=x) ++num;

        union_set(u,v);

    }

    return num>=k&&fa[find()]==-n;

}

bool comp(Edge a, Edge b){return a.w1<b.w1;}

int main ()

{

    int u, v, w1, w2;

    n=Scan(); k=Scan(); m=Scan();

    FO(i,,m) edge[i].u=Scan(), edge[i].v=Scan(), edge[i].w1=Scan(), edge[i].w2=Scan();

    sort(edge+,edge+m,comp);

    int l=, r=, mid;

    while (l<r) {

        mid=(l+r)>>;

        if (check(mid)) r=mid;

        else l=mid+;

    }

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

    return ;

}