BZOJ1500 : [NOI2005]维修数列-fhq_Treap

题面见这里

 

反正是道平衡树，就拿 fhq_Treap 写了写...

这道题思路基本是围绕“用 Treap 维护中序遍历” 和 中序遍历的性质 来进行的操作

所以就可以类比线段树进行一些操作

1. 建树 & 插入

　　这题也要用到笛卡尔树的建树方式，假的 O(n) 真是相当快啊

　　建树的方式见这里

inline int build(int r) {
    top = 0;
    register int tmp = newnode(a[1]);
    stk[++top] = tmp;
    for(int i = 2; i <= r; ++i) {
        int last = 0, cur = newnode(a[i]);
        while(top and t[stk[top]].prio > t[cur].prio) {
            pushup(stk[top]);
            last = stk[top];
            stk[top--] = 0;
        }
        t[cur].ch[0] = last;
        pushup(cur);
        if(top) {
            t[stk[top]].ch[1] = cur;
            pushup(stk[top]);
        }
        stk[++top] = cur;
    }
    while(top) pushup(stk[top--]);
    return stk[1];
}

　　在本题中呢，由于插入的值不是一个一个给出的而是给出序列，故应先建出一棵小 Treap 再合并过去

　　在这里也要用到上面提到的方式来建这棵小树

inline void Insert(int pos, int tot) {
    int newrt = build(tot);
    pair<int, int> x = Split(Root, pos);
    Root = Merge(Merge(x.first, newrt), x.second);
    return;
}

2.删除

　　此题的删除也是删除一段序列，直接 Split 出来即可

　　不过这里注意到任何时刻数列中最多含有 5e5 个数，多写一个内存回收就好了

inline int Malloc(){
    register int x;
    return (!delpool.empty()) ? (t[x = delpool.front()].clear(), delpool.pop(), x) : (++poolcur); 
}
inline int newnode(int val) {
    register int cur = Malloc();
    t[cur].val = t[cur].sum = t[cur].prtmx = val;
    t[cur].lmx = t[cur].rmx = max(0, val);
    t[cur].prio = rand();
    t[cur].siz = 1;
    return cur;
}
void Recycle(int cur) {
    if(!cur) return;
    if(lson) Recycle(lson);
    delpool.push(cur);
    if(rson) Recycle(rson);
    return;
}
inline void Remove(int pos, int tot) {
    pair<int, int> x = Split(Root, pos + tot - 1);
    pair<int, int> y = Split(x.first, pos - 1);
    Recycle(y.second);
    Root = Merge(y.first, x.second);
    return;
}

　　觉得递归不优美的可以手写栈模拟

3.区间修改

　　打标记

inline void cover(int pos, int tot, int val) {
    pair<int, int> x = Split(Root, pos + tot - 1);
    pair<int, int> y = Split(x.first, pos - 1);
    t[y.second].val = t[y.second].cvr = val;
    t[y.second].sum = val * t[y.second].siz;
    t[y.second].lmx = t[y.second].rmx = max(0, t[y.second].sum);
    t[y.second].prtmx = max(t[y.second].val, t[y.second].sum);
    t[y.second].rvrs = false;
    Root = Merge(Merge(y.first, y.second), x.second);
    return;
}

　

4.翻转区间

　　比较基础的操作

inline void Reverse(int pos, int tot) {
    pair<int, int> x = Split(Root, pos + tot - 1);
    pair<int, int> y = Split(x.first, pos - 1);
    t[y.second].rvrs ^= 1;
    swap(t[y.second].lmx, t[y.second].rmx);
    swap(t[y.second].ch[0], t[y.second].ch[1]);
    Root = Merge(Merge(y.first, y.second), x.second);
    return;
}

5.求和 & 最大子段和

　　这里一开始不敢这么写，其实是可以的

　　在提取一个区间的过程中，是在不断 pushup 和 pushdown 的，故提取/合并后并不会出什么差错

　　像线段树一样维护，一些维护的的值在 Reverse 后注意更新

inline void rvrs(int cur) {
    swap(lson, rson);
    swap(t[cur].lmx, t[cur].rmx);
    t[cur].rvrs ^= 1;
    return;
}
inline void cvr(int cur, int val) {
    t[cur].cvr = t[cur].val = val;
    t[cur].sum = t[cur].siz * val;
    t[cur].prtmx = max(t[cur].val, t[cur].sum);
    t[cur].lmx = t[cur].rmx = max(0, t[cur].sum);
    return;
}
inline void pushup(int cur) {
    t[cur].siz = t[lson].siz + t[rson].siz + 1;
    t[cur].sum = t[cur].val + t[lson].sum + t[rson].sum;
    t[cur].lmx = max(0, max(t[lson].lmx, t[lson].sum + t[rson].lmx + t[cur].val));
    t[cur].rmx = max(0, max(t[rson].rmx, t[rson].sum + t[lson].rmx + t[cur].val));
    t[cur].prtmx = max(t[cur].val, t[lson].rmx + t[rson].lmx + t[cur].val);
    if(lson) t[cur].prtmx = max(t[cur].prtmx, t[lson].prtmx);
    if(rson) t[cur].prtmx = max(t[cur].prtmx, t[rson].prtmx);
    return;
}
inline void pushdown(int cur) {
    if(t[cur].rvrs) {
        if(lson) rvrs(lson);
        if(rson) rvrs(rson);
    }
    if(t[cur].cvr != inf) {
        if(lson) cvr(lson, t[cur].cvr);
        if(rson) cvr(rson, t[cur].cvr);
    }
    t[cur].rvrs = false;
    t[cur].cvr = inf;
    return;
}

　　

完整的代码

#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cctype>
#include<cstdio>
#include<cmath>
#include<queue>
#include<ctime>
#define lson t[cur].ch[0]
#define rson t[cur].ch[1]
using namespace std;

const int MAXN = 500010, inf = 2333;

struct Node{
    int ch[2], siz, val, prio, lmx, rmx, sum, prtmx;
    int cvr;
    bool rvrs;
    Node(){ch[0] = ch[1] = siz = val = sum = 0; cvr = inf; rvrs = false;}
    void clear(){
        ch[0] = ch[1] = siz = val = sum = 0;
        cvr = inf;
        rvrs = false;
        return;
    }
}t[MAXN];
int n, m, poolcur, Root;
int a[MAXN], stk[MAXN], top;
queue<int> delpool;
char que[20];

inline int Malloc(){
    register int x;
    return (!delpool.empty()) ? (t[x = delpool.front()].clear(), delpool.pop(), x) : (++poolcur); 
}
inline int newnode(int val) {
    register int cur = Malloc();
    t[cur].val = t[cur].sum = t[cur].prtmx = val;
    t[cur].lmx = t[cur].rmx = max(0, val);
    t[cur].prio = rand();
    t[cur].siz = 1;
    return cur;
}
inline void pushup(int cur) {
    t[cur].siz = t[lson].siz + t[rson].siz + 1;
    t[cur].sum = t[cur].val + t[lson].sum + t[rson].sum;
    t[cur].lmx = max(0, max(t[lson].lmx, t[lson].sum + t[rson].lmx + t[cur].val));
    t[cur].rmx = max(0, max(t[rson].rmx, t[rson].sum + t[lson].rmx + t[cur].val));
    t[cur].prtmx = max(t[cur].val, t[lson].rmx + t[rson].lmx + t[cur].val);
    if(lson) t[cur].prtmx = max(t[cur].prtmx, t[lson].prtmx);
    if(rson) t[cur].prtmx = max(t[cur].prtmx, t[rson].prtmx);
    return;
}
inline void rvrs(int cur) {
    swap(lson, rson);
    swap(t[cur].lmx, t[cur].rmx);
    t[cur].rvrs ^= 1;
    return;
}
inline void cvr(int cur, int val) {
    t[cur].cvr = t[cur].val = val;
    t[cur].sum = t[cur].siz * val;
    t[cur].prtmx = max(t[cur].val, t[cur].sum);
    t[cur].lmx = t[cur].rmx = max(0, t[cur].sum);
    return;
}
inline void pushdown(int cur) {
    if(t[cur].rvrs) {
        if(lson) rvrs(lson);
        if(rson) rvrs(rson);
    }
    if(t[cur].cvr != inf) {
        if(lson) cvr(lson, t[cur].cvr);
        if(rson) cvr(rson, t[cur].cvr);
    }
    t[cur].rvrs = false;
    t[cur].cvr = inf;
    return;
}
inline int build(int r) {
    top = 0;
    register int tmp = newnode(a[1]);
    stk[++top] = tmp;
    for(int i = 2; i <= r; ++i) {
        int last = 0, cur = newnode(a[i]);
        while(top and t[stk[top]].prio > t[cur].prio) {
            pushup(stk[top]);
            last = stk[top];
            stk[top--] = 0;
        }
        t[cur].ch[0] = last;
        pushup(cur);
        if(top) {
            t[stk[top]].ch[1] = cur;
            pushup(stk[top]);
        }
        stk[++top] = cur;
    }
    while(top) pushup(stk[top--]);
    return stk[1];
}
pair<int, int> Split(int cur, int k) {
    if(!cur or !k) return make_pair(0, cur);
    pushdown(cur);
    pair<int, int> res;
    if(t[lson].siz >= k) {
        res = Split(lson, k);
        lson = res.second;
        pushup(cur);
        res.second = cur;
    } else {
        res = Split(rson, k - t[lson].siz - 1);
        rson = res.first;
        pushup(cur);
        res.first = cur;
    }
    return res;
}
int Merge(int x, int y) {
    if(x) pushdown(x); if(y) pushdown(y);
    if(!x) return y; if(!y) return x;
    if(t[x].prio < t[y].prio) {
        t[x].ch[1] = Merge(t[x].ch[1], y);
        pushup(x);
        return x;
    } else {
        t[y].ch[0] = Merge(x, t[y].ch[0]);
        pushup(y);
        return y;
    }
}
void Recycle(int cur) {
    if(!cur) return;
    if(lson) Recycle(lson);
    delpool.push(cur);
    if(rson) Recycle(rson);
    return;
}
inline void Insert(int pos, int tot) {
    int newrt = build(tot);
    pair<int, int> x = Split(Root, pos);
    Root = Merge(Merge(x.first, newrt), x.second);
    return;
}
inline void Remove(int pos, int tot) {
    pair<int, int> x = Split(Root, pos + tot - 1);
    pair<int, int> y = Split(x.first, pos - 1);
    Recycle(y.second);
    Root = Merge(y.first, x.second);
    return;
}
inline void Reverse(int pos, int tot) {
    pair<int, int> x = Split(Root, pos + tot - 1);
    pair<int, int> y = Split(x.first, pos - 1);
    t[y.second].rvrs ^= 1;
    swap(t[y.second].lmx, t[y.second].rmx);
    swap(t[y.second].ch[0], t[y.second].ch[1]);
    Root = Merge(Merge(y.first, y.second), x.second);
    return;
}
inline void cover(int pos, int tot, int val) {
    pair<int, int> x = Split(Root, pos + tot - 1);
    pair<int, int> y = Split(x.first, pos - 1);
    t[y.second].val = t[y.second].cvr = val;
    t[y.second].sum = val * t[y.second].siz;
    t[y.second].lmx = t[y.second].rmx = max(0, t[y.second].sum);
    t[y.second].prtmx = max(t[y.second].val, t[y.second].sum);
    t[y.second].rvrs = false;
    Root = Merge(Merge(y.first, y.second), x.second);
    return;
}
inline int getsum(int pos, int tot) {
    pair<int, int> x = Split(Root, pos + tot - 1);
    pair<int, int> y = Split(x.first, pos - 1);
    int ans = t[y.second].sum;
    Root = Merge(Merge(y.first, y.second), x.second);
    return ans;
}
void rdstr(char s[]) {
    register int sz = 0;
    register char c = getchar();
    while(!isalpha(c) and c != '-') c = getchar();
    while(isalpha(c) || (c == '-')) {
        s[sz++] = c;
        c = getchar();
    }
    return;
}
inline int rd() {
    register int x = 0;
    register char c = getchar();
    register bool f = false;
    while(!isdigit(c)) {
        if(c == '-') f = true;
        c = getchar();
    }
    while(isdigit(c)) {
        x = x * 10 + (c ^ 48);
        c = getchar();
    }
    return f ? -x : x;
}

int main() {
    srand(time(NULL));
    n = rd(); m = rd();
    for(int i = 1; i <= n; ++i) a[i] = rd();
    Root = build(n);
    int pos, tot, val;
    while(m--) {
        rdstr(que);
        switch(que[0]) {
            case 'I':{
                pos = rd(); tot = rd();
                for(int i = 1; i <= tot; ++i) a[i] = rd();
                Insert(pos, tot);
                break;
            }
            case 'D':{
                pos = rd(); tot = rd();
                Remove(pos, tot);
                break;
            }
            case 'R':{
                pos = rd(); tot = rd();
                Reverse(pos, tot);
                break;
            }
            case 'G':{
                pos = rd(); tot = rd();
                printf("%d\n", getsum(pos, tot));
                break;
            }
            case 'M':{
                if(que[2] == 'K') {
                    pos = rd(); tot = rd(); val = rd();
                    cover(pos, tot, val);
                } else {
                    printf("%d\n", t[Root].prtmx);
                }
                break;
            }
        }
    }
    return 0;
}