【JLOI2015】城池攻占

左偏树与Lazy标记
本文介绍了一种结合左偏树与懒惰传播技术的数据结构实现方法,该方法能够高效地处理区间更新与查询操作。通过具体的代码示例,详细展示了如何在左偏树中应用懒惰标记来优化区间更新效率。

左偏树加lazy操作即可

# include <stdio.h>
# include <stdlib.h>
# include <string.h>
# include <iostream>
# include <algorithm>
# define ll long long
# define RG register
# define IL inline
# define Fill(a, b) memset(a, b, sizeof(a))
using namespace std;

IL ll Read(){
    RG ll x = 0, z = 1; RG char c = getchar();
    for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1;
    for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + c - '0';
    return x * z;
}

const int MAXN(300010);
struct Left{
    int id, dis;
    ll lazy_c, lazy_j;
    Left *ch[2];
    IL Left(RG int pos){
        id = pos;
        lazy_c = dis = 1;
        lazy_j = 0;
    }
} *rt[MAXN];
struct Edge{
    int to, nt;
} edge[MAXN];
int die[MAXN], up[MAXN], ft[MAXN], a[MAXN], n, m, cnt, deep[MAXN] = {0, 1}, c[MAXN];
ll h[MAXN], s[MAXN], v[MAXN];

IL void Add(RG int u, RG int to){
    edge[cnt] = (Edge){to, ft[u]}; ft[u] = cnt++;
}

IL int Dis(RG Left *x){
    return x == NULL ? 0 : x -> dis;
}

IL void Updata(RG Left *x){
    if(Dis(x -> ch[0]) < Dis(x -> ch[1])) swap(x -> ch[0], x -> ch[1]);
    x -> dis = Dis(x -> ch[1]) + 1;
}

IL void Cov(RG Left *x, RG ll add, RG ll mul){
    if(x == NULL) return;
    x -> lazy_c *= mul; (x -> lazy_j *= mul) += add;
    (s[x -> id] *= mul) += add;
}

IL void Pushdown(RG Left *x){
    if(x -> lazy_c == 1 && !x -> lazy_j) return;
    Cov(x -> ch[0], x -> lazy_j, x -> lazy_c);
    Cov(x -> ch[1], x -> lazy_j, x -> lazy_c);
    x -> lazy_j = 0; x -> lazy_c = 1;
}

IL Left *Merge(RG Left *x, RG Left *y){
    if(x == NULL) return y;
    if(y == NULL) return x;
    Pushdown(x); Pushdown(y);
    if(s[x -> id] > s[y -> id]) swap(x, y);
    x -> ch[1] = Merge(x -> ch[1], y);
    Updata(x);
    return x;
}

IL void Pop(RG Left *&x){
    RG Left *tmp = x;
    Pushdown(x);
    x = Merge(x -> ch[0], x -> ch[1]);
    delete tmp;
}

IL void Dfs(RG int u){
    for(RG int e = ft[u]; e != -1; e = edge[e].nt){
        RG int to = edge[e].to;
        deep[to] = deep[u] + 1;
        Dfs(to);
        rt[u] = Merge(rt[u], rt[to]);
    }
    while(rt[u] != NULL && s[rt[u] -> id] < h[u]){
        up[rt[u] -> id] = deep[c[rt[u] -> id]] - deep[u];
        die[u]++; Pop(rt[u]);
    }
    if(a[u]) Cov(rt[u], 0, v[u]);
    else Cov(rt[u], v[u], 1);
}

int main(){
    Fill(ft, -1);
    n = Read(); m = Read();
    for(RG int i = 1; i <= n; i++)
        h[i] = Read();
    for(RG int i = 2, f; i <= n; i++){
        f = Read(); a[i] = Read(); v[i] = Read();
        if(f) Add(f, i);
    }
    for(RG int i = 1; i <= m; i++){
        s[i] = Read(); c[i] = Read();
        RG Left *tmp = new Left(i);
        rt[c[i]] = Merge(rt[c[i]], tmp);
    }
    Dfs(1);
    while(rt[1] != NULL) up[rt[1] -> id] = deep[c[rt[1] -> id]], Pop(rt[1]);
    for(RG int i = 1; i <= n; i++)
        printf("%d\n", die[i]);
    for(RG int i = 1; i <= m; i++)
        printf("%d\n", up[i]);
    return 0;
}
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