BZOJ 3246 IOI 2013 Dreaming 树形DP

题目大意

给出一个缺若干条边的树，现在让你填一些长度为定值的边，使得整个树的直径最小。

思路

给一个详细的网址，讲的非常明白。

http://www.ccf.org.cn/resources/1190201776262/fujian/xuhaoran2013-07-25-03_33_55.pdf

还有数据范围是50w。

CODE

#define _CRT_SECURE_NO_WARNINGS

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define MAX 500010
using namespace std;

int points,edges,cost;
int head[MAX],total;
int _next[MAX << 1],aim[MAX << 1],length[MAX << 1];
int father[MAX],dis[MAX];
int f[MAX];

int Find(int x)
{
    if(f[x] == x)   return x;
    return f[x] = Find(f[x]);
}

inline void Add(int x,int y,int len)
{
    _next[++total] = head[x];
    aim[total] = y;
    length[total] = len;
    head[x] = total;
}

int max_length[MAX],next_length[MAX];
int max_son[MAX];

void DFS(int x,int last)
{
    father[x] = last;
    for(int i = head[x]; i; i = _next[i]) {
        if(aim[i] == last)  continue;
        DFS(aim[i],x);
        if(max_length[aim[i]] + length[i] > max_length[x]) {
            max_length[x] = max_length[aim[i]] + length[i];
            max_son[x] = aim[i];
        }
    }
    for(int i = head[x]; i; i = _next[i]) {
        if(aim[i] != last && aim[i] != max_son[x])
            next_length[x] = max(next_length[x],max_length[aim[i]] + length[i]);
    }
}

int g[MAX];
int cnt,now_tree;

int __max[MAX],__min[MAX];

void Calc(int x,int last)
{
    for(int i = head[x]; i; i = _next[i]) {
        if(aim[i] == last)  continue;
        g[aim[i]] = max(g[x],max_son[x] == aim[i] ? next_length[x]:max_length[x]) + length[i];
        int now = max(g[aim[i]],max_length[aim[i]]);
        __max[now_tree] = max(__max[now_tree],now);
        __min[now_tree] = min(__min[now_tree],now);
        Calc(aim[i],x);
    }
}

int main()
{
    cin >> points >> edges >> cost;
    for(int i = 1; i <= points; ++i)
        f[i] = i;
    for(int x,y,z,i = 1; i <= edges; ++i) {
        scanf("%d%d%d",&x,&y,&z);
        ++x,++y;
        Add(x,y,z),Add(y,x,z);
        int fx = Find(x),fy = Find(y);
        if(fx != fy)
            f[fx] = fy;
    }
    int ans = 0;
    int max_1 = 0,max_2 = 0,max_3 = 0;
    for(int i = 1; i <= points; ++i)
        if(f[i] == i) {
            ++cnt;
            now_tree = i;
            DFS(i,0);
            g[i] = 0;
            __max[i] = __min[i] = max_length[i];
            Calc(i,0);
            ans = max(ans,__max[i]);
            if(__min[i] > max_1) {
                max_3 = max_2;
                max_2 = max_1;
                max_1 = __min[i];
            }
            else if(__min[i] > max_2) {
                max_3 = max_2;
                max_2 = __min[i];
            }
            else
                max_3 = max(max_3,__min[i]);
        }
    if(cnt > 1) ans = max(ans,max_1 + max_2 + cost);
    if(cnt > 2) ans = max(ans,max_2 + max_3 + (cost << 1));
    cout << ans << endl;
    return 0;
}