树的直径

树的直径

【定义】
我们将一棵树T = ( V，E )的直径定义为maxδ ( u，v ) ( u，v ∈ V )，也就是说，树中所有最短路径距离的最大值即为树的直径。
poj1985-添加链接描述
【做法】
做法1：2遍DFS
先从任意一点P出发，找离它最远的点Q，再从点Q出发，找离它最远的点W，W到Q的距离就是是的直径。
DFS从当前节点出发到达最远的点
第一次DFS返回的point肯定是直径的端点，在DFS一遍即可

//#pragma GCC optimize(3,"Ofast","inline")  	//G++
#include<bits/stdc++.h>
#define mem(a,x) memset(a,x,sizeof(a))
#define debug(x) cout << #x << ": " << x << endl;
#define ios ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define fcout cout<<setprecision(4)<<fixed
using namespace std;
typedef long long ll;
typedef pair<int,int> pi;

const int inf=0x3f3f3f3f;
const ll INF=0x7fffffffffffffff;
const int mod=1e9+7;
const int maxn = 1e6+5;
const double eps=1e-8;

template<typename T> void read(T &x){
    x = 0;char ch = getchar();ll f = 1;
    while(!isdigit(ch)){if(ch == '-')f*=-1;ch=getchar();}
    while(isdigit(ch)){x = x*10+ch-48;ch=getchar();}x*=f;
}
template<typename T, typename... Args> void read(T &first, Args& ... args) {
    read(first);
    read(args...);
}

int n,m,ans;
vector<pi> edge[maxn];
void add(int x,int y,int val){
    edge[x].push_back({y,val});
    edge[y].push_back({x,val});
}
ll point,dis[maxn];
void dfs(int u,int fa){
    if(dis[u]>ans){
        ans = dis[u];
        point = u;
    }
    for(int i=0;i<(int)edge[u].size();i++){
        int v = edge[u][i].first, val = edge[u][i].second;
        if(v==fa) continue;
        dis[v] = dis[u] + val;
        dfs(v,u);
    }
}
int main()
{
    char op[10];
    read(n,m);
    for (int i = 1;i<=m;i++){
        int x, y,val;
        read(x,y,val);
        cin >> op;
        add(x, y,val);
    }
    dfs(1, 0);
    ans = 0;
    for (int i = 1;i<=n;i++)
        dis[i] = 0;
    dfs(point, 0);

    cout << ans << "\n";
}

做法2：
树形DP 统计每个点到达的最远距离和次远距离 ans=max（ans，dp[i][0]+dp[i][1]）；

#pragma GCC optimize(3,"Ofast","inline")  	//G++
#include<bits/stdc++.h>
#define mem(a, x) memset(a, x, sizeof(a))
using namespace std;
typedef long long ll;
typedef pair<int, int> pi;

const int inf = 0x3f3f3f3f;
const int mod = 1e9 + 7;
const int maxn = 1e6 + 5;
const double eps = 1e-8;

template<typename T> void read(T &x){
    x = 0;char ch = getchar();ll f = 1;
    while(!isdigit(ch)){if(ch == '-')f*=-1;ch=getchar();}
    while(isdigit(ch)){x = x*10+ch-48;ch=getchar();}x*=f;
}
template<typename T, typename... Args> void read(T &first, Args& ... args) {
    read(first);
    read(args...);
}

int n, m, ans;
vector<pi> edge[maxn];
void add(int x, int y, int val)
{
    edge[x].push_back({y, val});
    edge[y].push_back({x, val});
}
int dp[maxn][2]; // 0最长 1次长
void dfs(int u, int fa)
{
    //    for(auto it:edge[u]){
    for (int i = 0; i < edge[u].size(); i++)
    {
        int v = edge[u][i].first, val = edge[u][i].second;
        if (v == fa)
            continue;
        dfs(v, u);
        if (dp[v][0] + val > dp[u][0])
            dp[u][1] = dp[u][0], dp[u][0] = dp[v][0] + val;
        else if (dp[v][0] + val > dp[u][1])
            dp[u][1] = dp[v][0] + val;
    }
    ans = max(dp[u][0] + dp[u][1], ans);
}
int main()
{
    char op[10];
    read(n, m);
    for (int i = 1; i <= m; i++)
    {
        int x, y, val;
        read(x, y, val);
        cin >> op;
        add(x, y, val);
    }
    dfs(1, 0);
    cout << ans << "\n";
}

练习题—牛客小白周赛22
添加链接描述

#pragma GCC optimize(3,"Ofast","inline")  	//G++
#include<bits/stdc++.h>
#define mem(a,x) memset(a,x,sizeof(a))
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pi;

const ll inf=0x3f3f3f3f;
const ll maxn = 1e6+5;

template<typename T> void read(T &x){
    x = 0;char ch = getchar();ll f = 1;
    while(!isdigit(ch)){if(ch == '-')f*=-1;ch=getchar();}
    while(isdigit(ch)){x = x*10+ch-48;ch=getchar();}x*=f;
}
template<typename T, typename... Args> void read(T &first, Args& ... args) {
    read(first);
    read(args...);
}

ll n, m;
ll ans=-1e15;
vector<ll> edge[maxn];
void add(ll x,ll y){
    edge[x].push_back(y);
    edge[y].push_back(x);
}
ll dp[maxn][2];// 0最长 1次长
ll a[maxn];
void dfs(ll u,ll fa){

    dp[u][0]  =a[u];
    dp[u][1] = -inf;
    for(auto v:edge[u]){
        if(v==fa) continue;
        dfs(v,u);
        if(dp[v][0]+a[u]>dp[u][0]) dp[u][1]=dp[u][0],dp[u][0]=dp[v][0]+a[u];
        else if(dp[v][0]+a[u]>dp[u][1])
            dp[u][1] = dp[v][0] + a[u];
    }
    ans = max(dp[u][0] + dp[u][1]-a[u], ans);
}
main()
{
    read(n);
    for (ll i = 1; i <= n;i++){
        read(a[i]);
        ans = max(a[i], ans);
        //   dp[i][0] = dp[i][1] = -inf;
    }
    for (ll i = 1; i <= n - 1; i++)
    {
        ll x, y;
        read(x, y);
        add(x, y);
    }
    dfs(1, 0);
    cout << ans << "\n";
}

现场赛没做出来，，，，好多人都会5555