洛谷 P3384 【模板】轻重链剖分

题目传送门

解题思路:

树链剖分的板子,写这篇博客只是为了存个代码.

AC代码:

#include<iostream>
#include<cstdio> 
#include<cstring>

using namespace std;

int n,m,rr,p,a[100001],tot,head[100001],rk[100001];
//rk[i]表示dfs中第i个被访问的点是哪个(或者说在线段树上第i号是谁),线段树赋值时有用 
struct xianduanshu {
    int v,l,r,lazy;
}e[400002];
struct bian {
    int to,next;
}c[200001];
struct dian {
    int f,d,son,si,top,id;
}q[100001];
//父亲,相对于根的深度,重儿子,子树大小,链顶,编号(线段树上的) 

inline void build(int rt,int L,int R) {//线段树建树 
    e[rt].l = L;e[rt].r = R;
    if(L == R) {
        e[rt].v = a[rk[L]] % p;
        return ;
    }
    int mid = L + R >> 1;
    build(rt * 2,L,mid);
    build(rt * 2 + 1,mid + 1,R);
    e[rt].v = (e[rt*2].v % p + e[rt*2+1].v % p) % p;
}

inline void add(int x,int y) {
    c[++tot].to = y;
    c[tot].next = head[x];
    head[x] = tot;
}

inline void dfs1(int u,int fa,int deep) {//找重儿子 
    q[u].d = deep;
    q[u].f = fa;
    q[u].si = 1;
    q[u].son = 0;
    for(int i = head[u];i; i = c[i].next) {
        int o = c[i].to;
        if(o == fa) continue;
        dfs1(o,u,deep + 1);
        q[u].si += q[o].si;
        if(q[q[u].son].si < q[o].si) q[u].son = o;
    }
}

inline void dfs2(int rt,int topf) {//找重链 
    q[rt].id = ++tot;
    rk[tot] = rt;
    q[rt].top = topf;
    if(q[rt].son == 0) return ;
    dfs2(q[rt].son,topf);//处理重链 
    for(int i = head[rt];i; i = c[i].next) {
        int o = c[i].to;
        if(o == q[rt].f || o == q[rt].son) continue;
        dfs2(o,o);//处理轻链 
    }
}

inline void pushdown(int rt) {
    if(e[rt].lazy) {
        e[rt*2].v = (e[rt*2].v + e[rt].lazy * (e[rt*2].r - e[rt*2].l + 1) % p) % p;
        e[rt*2+1].v = (e[rt*2+1].v + e[rt].lazy * (e[rt*2+1].r - e[rt*2+1].l + 1) % p) % p;
        e[rt*2].lazy = (e[rt*2].lazy + e[rt].lazy) % p;
        e[rt*2+1].lazy = (e[rt*2+1].lazy + e[rt].lazy) % p;
        e[rt].lazy = 0;
    }
}

inline void pl(int rt,int L,int R,int vv) {
    if(L <= e[rt].l && R >= e[rt].r) {
        e[rt].v = (e[rt].v + vv * (e[rt].r - e[rt].l + 1) % p) % p;
        e[rt].lazy = (e[rt].lazy + vv) % p;
        return ;
    }
    pushdown(rt);
    int mid = e[rt].l + e[rt].r >> 1;
    if(L <= mid) pl(rt * 2,L,R,vv);
    if(R > mid) pl(rt * 2 + 1,L,R,vv);
    e[rt].v = (e[rt*2].v % p + e[rt*2+1].v % p) % p;
}

inline void treeadd(int x,int y,int z) {//区间修改 
    int tx = q[x].top;
    int ty = q[y].top;
    while(tx != ty) {
        if(q[tx].d >= q[ty].d) {
            pl(1,q[tx].id,q[x].id,z);
            x = q[tx].f;tx = q[x].top;
        }
        else {
            pl(1,q[ty].id,q[y].id,z);
            y = q[ty].f;ty = q[y].top;
        }
    }
    if(q[x].d > q[y].d)
        pl(1,q[y].id,q[x].id,z);
    else
        pl(1,q[x].id,q[y].id,z);
}

inline int chaxun(int rt,int L,int R) {
    long long uu = 0;
    if(e[rt].l >= L && e[rt].r <= R) return e[rt].v % p;
    pushdown(rt);
    int mid = e[rt].l + e[rt].r >> 1;
    if(L <= mid) uu += chaxun(rt * 2,L,R),uu %= p;
    if(R > mid) uu += chaxun(rt * 2 + 1,L,R), uu %= p;
    return uu % p;
}

inline int treesum(int x,int y) {//查询 
    long long ans = 0;
    int tx = q[x].top;
    int ty = q[y].top;
    while(tx != ty) {
        if(q[tx].d >= q[ty].d) {
            ans += chaxun(1,q[tx].id,q[x].id);
            ans %= p;
            x = q[tx].f;tx = q[x].top;
        }
        else {
            ans += chaxun(1,q[ty].id,q[y].id);
            ans %= p;
            y = q[ty].f;ty = q[y].top;
        }
    }
    if(q[x].d > q[y].d)
        ans += chaxun(1,q[y].id,q[x].id),ans %= p;
    else
        ans += chaxun(1,q[x].id,q[y].id),ans %= p;
    return ans % p;
}

int main() {
    scanf("%d%d%d%d",&n,&m,&rr,&p);
    for(int i = 1;i <= n; i++)
        scanf("%d",&a[i]);
    for(int i = 1;i < n; i++) {
        int x,y;
        scanf("%d%d",&x,&y);
        add(x,y);
        add(y,x);
    }
    dfs1(rr,0,1);
    tot = 0;
    dfs2(rr,rr);
    build(1,1,n);
    for(int i = 1;i <= m; i++) {
        int x,y,z,ww;
        scanf("%d",&ww);
        if(ww == 1) {
            scanf("%d%d%d",&x,&y,&z);
            treeadd(x,y,z % p);
        }
        if(ww == 2) {
            scanf("%d%d",&x,&y);
            int aa = 0;
            aa = treesum(x,y);
            printf("%d
",aa % p);
        }
        if(ww == 3) {
            scanf("%d%d",&x,&y);
            pl(1,q[x].id,q[x].id + q[x].si - 1,y % p);
        }
        if(ww == 4) {
            scanf("%d",&x);
            printf("%d
",chaxun(1,q[x].id,q[x].id + q[x].si - 1) % p);
        }
    }
    return 0;
}