P2486 [SDOI2011]染色 维护区间块数 树链剖分

https://www.luogu.org/problemnew/show/P2486

 

题意

对一个树上维护两种操作，一种是把x到y间的点都染成c色，另一种是求x到y间的点有多少个颜色块，比如112221由“11”，“222”，“1”三块组成。

思路

这题的关键是要如何维护这个颜色块，我们可以利用线段树，记录每个区间的块数，区间左端点，区间右端点的颜色。合并中如果两个区间相邻点颜色相同，个数要减去1.
查询也是一样的，链与链间的相邻点也要考虑清楚。

#include <algorithm>
#include  <iterator>
#include  <iostream>
#include   <cstring>
#include   <cstdlib>
#include   <iomanip>
#include    <bitset>
#include    <cctype>
#include    <cstdio>
#include    <string>
#include    <vector>
#include     <stack>
#include     <cmath>
#include     <queue>
#include      <list>
#include       <map>
#include       <set>
#include   <cassert>
 
/*
 
⊂_ヽ
　 ＼＼ Λ＿Λ  来了老弟
　　 ＼('ㅅ')
　　　 >　⌒ヽ
　　　/ 　 へ＼
　　 /　　/　＼＼
　　 ﾚ　ノ　　 ヽ_つ
　　/　/
　 /　/|
　(　(ヽ
　|　|、＼
　| 丿 ＼ ⌒)
　| |　　) /
'ノ )　　Lﾉ
 
*/
 
using namespace std;
#define lson (l , mid , rt << 1)
#define rson (mid + 1 , r , rt << 1 | 1)
#define debug(x) cerr << #x << " = " << x << "\n";
#define pb push_back
#define pq priority_queue
 
typedef long long ll;
typedef unsigned long long ull;
//typedef __int128 bll;
typedef pair<ll ,ll > pll;
typedef pair<int ,int > pii;
typedef pair<int,pii> p3;
 
//priority_queue<int> q;//这是一个大根堆q
//priority_queue<int,vector<int>,greater<int> >q;//这是一个小根堆q
#define fi first
#define se second
//#define endl '\n'
 
#define boost ios::sync_with_stdio(false);cin.tie(0)
#define rep(a, b, c) for(int a = (b); a <= (c); ++ a)
#define max3(a,b,c) max(max(a,b), c);
#define min3(a,b,c) min(min(a,b), c);
 
const ll oo = 1ll<<;
const ll mos = 0x7FFFFFFF;  //
const ll nmos = 0x80000000;  //-2147483648
const int inf = 0x3f3f3f3f;
const ll inff = 0x3f3f3f3f3f3f3f3f; //
const ll mod = ;
const double esp = 1e-;
const double PI=acos(-1.0);
const double PHI=0.61803399;    //黄金分割点
const double tPHI=0.38196601;
 
template<typename T>
inline T read(T&x){
    x=;int f=;char ch=getchar();
    while (ch<''||ch>'') f|=(ch=='-'),ch=getchar();
    while (ch>=''&&ch<='') x=x*+ch-'',ch=getchar();
    return x=f?-x:x;
}
 
inline void cmax(int &x,int y){if(x<y)x=y;}
inline void cmax(ll &x,ll y){if(x<y)x=y;}
inline void cmin(int &x,int y){if(x>y)x=y;}
inline void cmin(ll &x,ll y){if(x>y)x=y;}
 
/*-----------------------showtime----------------------*/
 
            const int maxn = 1e5+;
            int a[maxn],b[maxn];
            int dp[maxn],sz[maxn],fa[maxn],son[maxn];
            vector<int>mp[maxn];
 
            void dfs1(int u,int f,int deep){
                dp[u] = deep;
                fa[u] = f;
                sz[u] = ;
                int mx = ;
                for(int i=; i<mp[u].size(); i++){
                    int v = mp[u][i];
                    if(v == f) continue;
                    dfs1(v, u, deep+);
                    sz[u] += sz[v];
                    if(sz[v] > mx) {mx = sz[v], son[u] = v;}
                }
            }
 
            int top[maxn],id[maxn],cnt = ;
            void dfs2(int u,int f,int topf){
                top[u] = topf;
                id[u] = ++cnt;
                b[cnt] = a[u];
                if(son[u])dfs2(son[u], u, topf);
                for(int i=; i<mp[u].size(); i++){
                    int v = mp[u][i];
                    if(v == f || v == son[u]) continue;
                    dfs2(v, u, v);
                }
            }
 
            int tag[maxn<<],lazy[maxn<<],ly[maxn<<],rz[maxn<<];
            void pushup(int rt){
                tag[rt] = tag[rt<<] + tag[rt<<|];
                rz[rt] = rz[rt<<];
                ly[rt] = ly[rt<<|];
                if(ly[rt<<] == rz[rt<<|])tag[rt] --;
            }
            void build(int l,int r,int rt){
                if(l == r){
                    tag[rt] = ;
                    ly[rt] = rz[rt] = b[l];
                    return ;
                }
                int mid = (l + r) >> ;
                build(l, mid, rt<<);
                build(mid+,r,rt<<|);
                pushup(rt);
                // cout<<l<<" "<<r<<" "<<rz[rt] << "  " << ly[rt]<<endl;
            }
            void pushdown(int l,int r,int rt){
                tag[rt<<] = tag[rt<<|] = ;
                ly[rt<<] = rz[rt<<] = lazy[rt];
                ly[rt<<|] = rz[rt<<|] = lazy[rt];
                lazy[rt<<] = lazy[rt<<|] = lazy[rt];
                lazy[rt] = ;
            }
            void update(int L, int R, int c, int l, int r,int rt){
                if(l >= L && r <= R){
                    tag[rt] = ;
                    ly[rt] = rz[rt] = c;
                    lazy[rt] = c;
                    return;
                }
                int mid = (l + r) >> ;
                if(lazy[rt]) pushdown(l, r, rt);
                if(mid >= L) update(L, R, c, l, mid, rt<<);
                if(mid < R) update(L,R,c,mid+,r,rt<<|);
                pushup(rt);
            }
            int n,m;
            void solve(int x,int y,int c){
                while(top[x] != top[y]){
                    if(dp[top[x]] < dp[top[y]]) swap(x, y);
                    update(id[top[x]], id[x], c, , n, );
                    x = fa[top[x]];
                }
                if(dp[x] > dp[y]) swap(x, y);
                update(id[x], id[y], c, , n, );
            }
 
            int query(int L,int R, int l,int r,int rt,int &tmpl,int &tmpr){
                    if(l >= L && r<= R){
                        if(l == L) tmpl = rz[rt];
                        if(r == R) tmpr = ly[rt];
 
                        return tag[rt];
                    }
                    int mid = (l + r) >> ;
                    if(lazy[rt])pushdown(l, r, rt);
                    int res = ;
                    int ql = -, qr = -;
                    if(mid >= L) {
                        res += query(L, R, l, mid, rt<<,tmpl,tmpr);
                        ql = ly[rt<<];
                    }
                    if(mid < R){
                        res += query(L, R, mid +, r, rt<<|,tmpl,tmpr);
                        qr = rz[rt<<|];
                    }
                    if(ql == qr && ql != -) res --;
                    pushup(rt);
                    return res;
            }
            int cal(int x,int y){
                int res = ,lax = -,lay=-;
 
                while(top[x] != top[y]){
                    int tmpl = -,tmpr=-;
                    if(dp[top[x]] > dp[top[y]]) {
                        res += query(id[top[x]], id[x], , n, , tmpl, tmpr);//tmp,flag 1,r
                        if(lax == tmpr) res--;
                        lax = tmpl;
                        x = fa[top[x]];
                    }
                    else {
                        res += query(id[top[y]], id[y], , n, ,tmpl,tmpr);
                        if(lay == tmpr) res--;
                        lay = tmpl;
                        y = fa[top[y]];
                    }
 
                    // cout<<tmpl<<" !! "<<tmpr<<endl;
                }
 
                if(dp[x] > dp[y]){
                    int tmpl = -,tmpr=-;
                    res += query(id[y], id[x], , n, ,tmpl,tmpr);
                    if(tmpr == lax) res--;
                    if(tmpl == lay) res--;
                }
                else {
                    int tmpl = -,tmpr=-;
                    res += query(id[x], id[y], , n, ,tmpl,tmpr);
                    if(tmpl == lax) res--;
                    if(tmpr == lay) res--;
                }   
 
                return res;
            }
int main(){
            scanf("%d%d", &n, &m);
            rep(i, , n) scanf("%d", &a[i]);
            rep(i, , n-) {
                int u,v;
                scanf("%d%d", &u, &v);
                mp[u].pb(v);
                mp[v].pb(u);
            }
            dfs1(, , );
            dfs2(, , );
            build(, n, );
 
            while(m--){
                char str[];
                scanf("%s", str);
                if(str[] == 'C') {
                    int x,y,z;
                    scanf("%d%d%d", &x, &y, &z);
                    solve(x, y, z);
                }
                else {
                    int x,y;
                    scanf("%d%d", &x, &y);
                    printf("%d\n", cal (x,y));
                }
 
            }
            return ;
}