P4315 月下“毛景树”

题目描述
毛毛虫经过及时的变形，最终逃过的一劫，离开了菜妈的菜园。 毛毛虫经过千山万水，历尽千辛万苦，最后来到了小小的绍兴一中的校园里。

爬啊爬~爬啊爬毛毛虫爬到了一颗小小的“毛景树”下面，发现树上长着他最爱吃的毛毛果~ “毛景树”上有N个节点和N-1条树枝，但节点上是没有毛毛果的，毛毛果都是长在树枝上的。但是这棵“毛景树”有着神奇的魔力，他能改变树枝上毛毛果的个数：

Change k w：将第k条树枝上毛毛果的个数改变为w个。

Cover u v w：将节点u与节点v之间的树枝上毛毛果的个数都改变为w个。

Add u v w：将节点u与节点v之间的树枝上毛毛果的个数都增加w个。 由于毛毛虫很贪，于是他会有如下询问：

Max u v：询问节点u与节点v之间树枝上毛毛果个数最多有多少个。

Solution

树剖
注意线段树下推标记时分清楚对子节点标记的影响

Code

#include<iostream>
#include<cstdio>
#include<queue>
#include<cstring>
#include<algorithm>
#define LL long long
#define REP(i, x, y) for(int i = (x);i <= (y);i++)
using namespace std;
int RD(){
    int out = 0,flag = 1;char c = getchar();
    while(c < '0' || c >'9'){if(c == '-')flag = -1;c = getchar();}
    while(c >= '0' && c <= '9'){out = out * 10 + c - '0';c = getchar();}
    return flag * out;
    }
const int maxn = 100019,INF = 1e9 + 19;
int head[maxn],nume = 1;
struct Node{
    int v,dis,nxt;
    }E[maxn << 3];
void add(int u,int v,int dis){
    E[++nume].nxt = head[u];
    E[nume].v = v;
    E[nume].dis = dis;
    head[u] = nume;
    }
int num;
int size[maxn], wson[maxn], dep[maxn], fa[maxn], val[maxn];
int top[maxn], pos[maxn], ori[maxn], tot;
void dfs1(int u, int F){
    size[u] = 1;
    for(int i = head[u];i;i = E[i].nxt){
        int v = E[i].v;
        if(v == F)continue;
        val[v] = E[i].dis;
        dep[v] = dep[u] + 1;
        fa[v] = u;
        dfs1(v, u);
        size[u] += size[v];
        if(size[v] > size[wson[u]])wson[u] = v;
        }
    }
void dfs2(int u, int TP){
    top[u] = TP;
    pos[u] = ++tot;
    ori[tot] = u;
    if(!wson[u])return ;
    dfs2(wson[u], TP);
    for(int i = head[u];i;i = E[i].nxt){
        int v = E[i].v;
        if(v == fa[u] || v == wson[u])continue;
        dfs2(v, v);
        }
    }
#define lid (id << 1)
#define rid (id << 1) | 1
struct seg_tree{
    int l, r;
    int max;
    int add, set;
    }tree[maxn << 2];
void pushup(int id){tree[id].max = max(tree[lid].max, tree[rid].max);}
void build(int id, int l, int r){
    tree[id].l = l, tree[id].r = r, tree[id].set = -1;
    if(l == r){
        tree[id].max = val[ori[l]];
        return ;
        }
    int mid = (l + r) >> 1;
    build(lid, l, mid), build(rid, mid + 1, r);
    pushup(id);
    }
void pushdown(int id){
    if(tree[id].set != -1){
        int v = tree[id].set;
        tree[lid].max = tree[rid].max = v;
        tree[lid].set = tree[rid].set = v;
        tree[lid].add = tree[rid].add = 0;
        tree[id].add = 0;
        tree[id].set = -1;
        }
    if(tree[id].add != 0){
        int v = tree[id].add;
        tree[lid].max += v;
        tree[rid].max += v;
        if(tree[lid].set != -1)tree[lid].set += v;
        if(tree[rid].set != -1)tree[rid].set += v;
        tree[lid].add += v;
        tree[rid].add += v;
        tree[id].add = 0;
        }
    }
void update(int id, int v, int l, int r, int o){
    pushdown(id);
    if(tree[id].l == l && tree[id].r == r){
        if(o == 1){//1为全改变
            tree[id].max = v;
            tree[id].set = v;
            }
        else{//0为区间加
            tree[id].max += v;
            tree[id].add += v;
            }
        return ;
        }
    int mid = (tree[id].l + tree[id].r) >> 1;
    if(mid < l)update(rid, v, l, r, o);
    else if(mid >= r)update(lid, v, l, r, o);
    else update(lid, v, l, mid, o), update(rid, v, mid + 1, r, o);
    pushup(id);
    }
int query(int id, int l, int r){
    pushdown(id);
    if(tree[id].l == l && tree[id].r == r)return tree[id].max;
    int mid = (tree[id].l + tree[id].r) >> 1;
    if(mid < l)return query(rid, l, r);
    else if(mid >= r)return query(lid, l, r);
    else return max(query(lid, l, mid), query(rid, mid + 1, r));
    }
void uprange(int x, int y, int v, int o){
    while(top[x] != top[y]){
        if(dep[top[x]] < dep[top[y]])swap(x, y);
        update(1, v, pos[top[x]], pos[x], o);
        x = fa[top[x]];
        }
    if(x == y)return ;
    if(dep[x] > dep[y])swap(x, y);
    update(1, v, pos[x] + 1, pos[y], o);
    }
int Q_max(int x, int y){
    int ret = 0;
    while(top[x] != top[y]){
        if(dep[top[x]] < dep[top[y]])swap(x, y);
        ret = max(ret, query(1, pos[top[x]], pos[x]));
        x = fa[top[x]];
        }
    if(x == y)return ret;
    if(dep[x] > dep[y])swap(x, y);
    ret = max(ret, query(1, pos[x] + 1, pos[y]));
    return ret;
    }
struct EDG{int x, y;}I[maxn];
void init(){
    num = RD();
    REP(i, 1, num - 1){
        int u = RD(), v = RD(), dis = RD();
        I[i] = (EDG){u, v};
        add(u, v, dis), add(v, u, dis);
        }
    dep[1] = 1;
    dfs1(1, -1);
    dfs2(1, 1);
    build(1, 1, num);
    }
void solve(){
    char cmd[19];
    while(1){
        scanf("%s", cmd);
        if(cmd[0] == 'S')return ;
        else if(cmd[0] == 'C' && cmd[1] == 'h'){
            int k = RD(), w = RD();
            uprange(I[k].x, I[k].y, w, 1);
            }
        else if(cmd[0] == 'C' && cmd[1] == 'o'){
            int x = RD(), y = RD(), w = RD();
            uprange(x, y, w, 1);
            }
        else if(cmd[0] == 'A'){
            int x = RD(), y = RD(), w = RD();
            uprange(x, y, w, 0);
            }
        else{
            int x = RD(), y = RD();
            printf("%d\n", Q_max(x, y));
            }
        }
    }
int main(){
    init();
    solve();
    return 0;
    }

原文地址：https://www.cnblogs.com/Tony-Double-Sky/p/9895580.html