luogu P2619 [国家集训队2]Tree I

题目链接

luogu P2619 [国家集训队2]Tree I

题解

普通思路就不说了二分增量，生成树check

说一下坑点

二分时，若黑白边权有相同，因为权值相同优先选白边，若在最有增量时出现黑白等权边则更新出 > 和 = 最小值等价，那么不会更新到 = 情况，

因为等价，那么处理时只需看做把等价的黑白两边交换即可

需要每次直接减去 增量 * need 的价值

代码

#include<cstdio>
#include<algorithm>
const int maxn = 100007; 
int E,V,need;
struct node {
    int u,v,w,col;
    bool operator < (const node & a) const {
        if(a.w == w) return col < a.col;
        else return w < a.w;
    }
}edge[maxn],e[maxn];
int ans = 0;
int fa[maxn];
int find(int x) {
    if(fa[x] != x) fa[x] = find(fa[x]);
    return fa[x];
}
bool check(int x) {
    int tmp = 0;
    for(int i = 1;i <= V;++ i) {
        e[i] = edge[i];
    if(e[i].col == 0) e[i].w = edge[i].w + x;
    }
    for(int i = 0;i <= E + 1;++ i) fa[i] = i;
    std::sort(e + 1,e + V + 1);int bs = 0;
    for(int num = 0,i = 1;i <= V;++ i) {
        int X = e[i].u,y = e[i].v;
        int fx = find(X),fy = find(y);
        if(fx != fy) {
            tmp += e[i].w;
            num ++;
            fa[fx] = fy;
            if(e[i].col == 0) bs ++;
        }
        if(num == E - 1) break;
    }
    if(bs >= need) {
        ans = tmp - (x * need);
        return true;
    }
    return false;
}
int main() {
    scanf("%d%d%d",&E,&V,&need);
    for(int i = 1;i <= V;++ i) {
        scanf("%d%d%d%d",&edge[i].u,&edge[i].v,&edge[i].w,&edge[i].col);
    }
    int l = -107,r = 107;
    while(l <= r) {
        int mid = (l + r) >> 1;
        if(check(mid)) l = mid + 1;
        else r = mid - 1;
    }
    printf("%d\n",ans);
    return 0;
}