Codeforces Round #425 (Div. 2) D. Misha, Grisha and Underground （LCA

题意：给定一颗树（n<=1e5），并有q（<=1e5）次询问，每次询问指定三个点a，b，c：意思是有两个人任选两个点作为各自起点，剩下的那个点作为终点，两个人各自从起点走向终点，求路径上重合的点数，现在要求在这三个点可能的选择方式中，求重合点数的最大值。

 

做法：两两分别求LCA，找到深度最深的那个点，肯定就是我们要找的终点了，然后max（1，2，3）即可

 

///                 .-~~~~~~~~~-._       _.-~~~~~~~~~-.
///             __.'              ~.   .~              `.__
///           .'//                  \./                  \\`.
///        .'//                     |                     \\`.
///       .'// .-~"""""""~~~~-._     |     _,-~~~~"""""""~-. \\`.
///     .'//.-"                 `-.  |  .-'                 "-.\\`.
///   .'//______.============-..   \ | /   ..-============.______\\`.
/// .'______________________________\|/______________________________`.
//#pragma GCC optimize("Ofast")
#pragma comment(linker, "/STACK:102400000,102400000")
//#pragma GCC target(sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx) 
#include <vector>
#include <iostream>
#include <string>
#include <map>
#include <stack>
#include <cstring>
#include <queue>
#include <list>
#include <stdio.h>
#include <set>
#include <algorithm>
#include <cstdlib>
#include <cmath>
#include <iomanip>
#include <cctype>
#include <sstream>
#include <functional>
#include <stdlib.h>
#include <time.h>
#include <bitset>
using namespace std;

#define pi acos(-1)
#define s_1(x) scanf("%d",&x)
#define s_2(x,y) scanf("%d%d",&x,&y)
#define s_3(x,y,z) scanf("%d%d%d",&x,&y,&z)
#define s_4(x,y,z,X) scanf("%d%d%d%d",&x,&y,&z,&X)
#define S_1(x) scan_d(x)
#define S_2(x,y) scan_d(x),scan_d(y)
#define S_3(x,y,z) scan_d(x),scan_d(y),scan_d(z)
#define PI acos(-1)
#define endl '\n'
#define srand() srand(time(0));
#define me(x,y) memset(x,y,sizeof(x));
#define foreach(it,a) for(__typeof((a).begin()) it=(a).begin();it!=(a).end();it++)
#define close() ios::sync_with_stdio(0); cin.tie(0);
#define FOR(x,n,i) for(int i=x;i<=n;i++)
#define FOr(x,n,i) for(int i=x;i<n;i++)
#define fOR(n,x,i) for(int i=n;i>=x;i--)
#define fOr(n,x,i) for(int i=n;i>x;i--)
#define W while
#define sgn(x) ((x) < 0 ? -1 : (x) > 0)
#define bug printf("***********\n");
#define db double
#define ll long long
#define mp make_pair
#define pb push_back
typedef long long LL;
typedef pair <int, int> ii;
const int INF=0x3f3f3f3f;
const LL LINF=0x3f3f3f3f3f3f3f3fLL;
const int dx[]={-1,0,1,0,1,-1,-1,1};
const int dy[]={0,1,0,-1,-1,1,-1,1};
const int maxn=1e5+5;
//const int maxx=1e6+10;
const double EPS=1e-8;
const double eps=1e-8;
const int mod=1e9+7;
template<class T>inline T min(T a,T b,T c) { return min(min(a,b),c);}
template<class T>inline T max(T a,T b,T c) { return max(max(a,b),c);}
template<class T>inline T min(T a,T b,T c,T d) { return min(min(a,b),min(c,d));}
template<class T>inline T max(T a,T b,T c,T d) { return max(max(a,b),max(c,d));}
template <class T>
inline bool scan_d(T &ret){char c;int sgn;if (c = getchar(), c == EOF){return 0;}
while (c != '-' && (c < '0' || c > '9')){c = getchar();}sgn = (c == '-') ? -1 : 1;ret = (c == '-') ? 0 : (c - '0');
while (c = getchar(), c >= '0' && c <= '9'){ret = ret * 10 + (c - '0');}ret *= sgn;return 1;}

inline bool scan_lf(double &num){char in;double Dec=0.1;bool IsN=false,IsD=false;in=getchar();if(in==EOF) return false;
while(in!='-'&&in!='.'&&(in<'0'||in>'9'))in=getchar();if(in=='-'){IsN=true;num=0;}else if(in=='.'){IsD=true;num=0;}
else num=in-'0';if(!IsD){while(in=getchar(),in>='0'&&in<='9'){num*=10;num+=in-'0';}}
if(in!='.'){if(IsN) num=-num;return true;}else{while(in=getchar(),in>='0'&&in<='9'){num+=Dec*(in-'0');Dec*=0.1;}}
if(IsN) num=-num;return true;}

void Out(LL a){if(a < 0) { putchar('-'); a = -a; }if(a >= 10) Out(a / 10);putchar(a % 10 + '0');}
void print(LL a){ Out(a),puts("");}
//freopen( "in.txt" , "r" , stdin );
//freopen( "data.txt" , "w" , stdout );
//cerr << "run time is " << clock() << endl;

int up[maxn][23], maxx[maxn][23];
int dep[maxn], dis[maxn];
int cnt, head[maxn];
struct node {
    int to, next, w;
}e[maxn<<1];
void init() {
    me(head,-1); me(dis,0);
    me(up,0); me(dep,0);
    cnt = 0; me(maxx, 0);
}
void add(int u, int v, int w) {
    e[cnt] = node{v, head[u], w};
    head[u] = cnt++;
}
void dfs(int u,int fa,int d) {
    dep[u] = d + 1;
    for(int i = 1 ; i < 20 ; i ++) {
        up[u][i] = up[up[u][i-1]][i-1];
       // maxx[u][i] = max(maxx[up[u][i-1]][i-1], maxx[u][i-1]);
    }
    for(int i = head[u] ; ~i ; i = e[i].next) {
        int to = e[i].to;
        if(to == fa) continue;
        dis[to] = dis[u] + e[i].w;
        up[to][0] = u;
       // maxx[to][0] = e[i].w;
        dfs(to, u, d+1);
    }
}
int LCA_BZ(int u,int v) {
    int mx = 0;
    if(dep[u] < dep[v]) swap(u,v);
    int k = dep[u] - dep[v];
    for(int i = 19 ; i >= 0 ; i --) {
        if((1<<i) & k) {
        //  mx = max(mx, maxx[u][i]);
            u = up[u][i];
        }
    }
    if(u == v) return u;
    for(int i = 19 ; i >= 0 ; i --) {
        if(up[u][i] != up[v][i]){
        //  mx = max(mx, maxx[u][i]);
        //  mx = max(mx, maxx[v][i]);
            u = up[u][i];
            v = up[v][i];
        }
    }
//     return max(mx, max(maxx[u][0], maxx[v][0]));
    return up[u][0];
}

int len(int u,int v) {
	return dis[u] + dis[v] - 2 * dis[LCA_BZ(u,v)];
}

int n,q;
void solve() {
	init();
	s_2(n,q);
	FOR(2,n,i) {
		int x;
		s_1(x);
		add(x,i,1);
		add(i,x,1);
	}
	dfs(1,-1,0);
	W(q--) {
		int a,b,c;
		s_3(a,b,c);
		int x1=LCA_BZ(a,b),x2=LCA_BZ(a,c),x3=LCA_BZ(b,c);
		int ans=dep[x1]>dep[x2]?x1:x2;
		ans=dep[ans]>dep[x3]?ans:x3;
		ans=max(len(ans,a),len(ans,b),len(ans,c))+1;
		print(ans);
	}
}
int main() {
    //freopen( "1.in" , "r" , stdin );
    //freopen( "1.out" , "w" , stdout );
    int t=1;
    //init();
    //s_1(t);
    for(int cas=1;cas<=t;cas++) {
        //printf("Case #%d: ",cas);
        solve();
    }
}