[IOI 2008] Island

[题目链接]

         https://www.lydsy.com/JudgeOnline/problem.php?id=1791

[算法]

        不难看出，要求的是这个基环树森林中每棵基环树的直径之和

[代码]

          

#include<bits/stdc++.h>
using namespace std;
const int MAXN = 1e6 + 10;

struct edge
{
        int to,w,nxt;
} e[MAXN << 1];

int i,v,w,tot,n,u,cnt;
int degree[MAXN],belong[MAXN],head[MAXN];
long long d[MAXN],f[MAXN],a[MAXN << 1],sum[MAXN << 1];
long long ans;
bool cal[MAXN];

inline void addedge(int u,int v,int w)
{
        tot++;
        e[tot] = (edge){v,w,head[u]};
        head[u] = tot;
}
inline void bfs(int u,int t)
{
        int i,cur,v,w;
        queue< int > q;
        belong[u] = t;
        q.push(u);
        while (!q.empty())
        {
                cur = q.front();
                q.pop();
                for (i = head[cur]; i; i = e[i].nxt)
                {
                        v = e[i].to;
                        w = e[i].w;
                        if (!belong[v])
                        {
                                belong[v] = t;
                                q.push(v);
                        } 
                }
        }
}
inline void topsort()
{
        int i,u,v,w;
        queue< int > q;
        for (i = 1; i <= n; i++)
        {
                if (degree[i] == 1)
                        q.push(i);        
        } 
        while (!q.empty())
        {
                u = q.front();
                q.pop();
                for (i = head[u]; i; i = e[i].nxt)
                {
                        v = e[i].to;
                        w = e[i].w;
                        if (degree[v] > 1)
                        {
                                d[belong[u]] = max(d[belong[u]],f[u] + f[v] + w);
                                f[v] = max(f[v],f[u] + w);
                                if ((--degree[v]) == 1) q.push(v);
                        }
                }
        }
} 
inline void dp(int t,int x)
{
        long long i,l,r,y = x,m = 0,v,w;
        static int q[MAXN << 1];
        do
        {
                a[++m] = f[y];
                degree[y] = 1;
                for (i = head[y]; i; i = e[i].nxt)
                {
                        v = e[i].to;
                        w = e[i].w;
                        if (degree[v] > 1)
                        {
                                y = v;
                                sum[m + 1] = sum[m] + w;
                                break;
                        }
                }
        } while(i);
        if (m == 2)
        {
                l = 0;
                for (i = head[y]; i; i = e[i].nxt)
                {
                        v = e[i].to;
                        w = e[i].w;
                        if (v == x) l = max(l,w);
                }
                d[t] = max(d[t],f[x] + f[y] + l);
                return;
        }
        for (i = head[y]; i; i = e[i].nxt)
        {
                v = e[i].to;
                w = e[i].w;
                if (v == x) 
                {
                        sum[m + 1] = sum[m] + w;        
                        break;
                }
        } 
        for (i = 1; i < m; i++) 
        {
                a[m + i] = a[i];
                sum[m + i] = sum[m + 1] + sum[i];
        }
        q[l = r = 1] = 1;
        for (i = 2; i <= 2 * m - 1; i++)
        {
                while (l <= r && i - q[l] >= m) l++;
                d[t] = max(d[t],a[q[l]] + a[i] + sum[i] - sum[q[l]]);
                while (l <= r && a[q[r]] - sum[q[r]] <= a[i] - sum[i]) r--;
                q[++r] = i;
        }
}
int main() 
{
        
        scanf("%d",&n);
        for (u = 1; u <= n; u++)
        {
                scanf("%d%d",&v,&w);
                addedge(u,v,w);
                addedge(v,u,w);
                degree[u]++; degree[v]++;
        }
        for (i = 1; i <= n; i++)
        {
                if (!belong[i])    
                        bfs(i,++cnt);
        }    
        topsort();
        for (i = 1; i <= n; i++)
        {
                if (degree[i] > 1 && !cal[belong[i]])
                {
                        cal[belong[i]] = true;
                        dp(belong[i],i);
                      ans += d[belong[i]]; 
                }
        }
        printf("%lld
",ans);
        
        return 0;
    
}