数据结构板子——splay

维护数列 https://www.acwing.com/problem/content/957/
线段树能写的splay都能写，不过splay常数较大。时间复杂度大概是线段树的三倍

#include<bits/stdc++.h>
using namespace std;
const int N = 500010,INF = 1e9;
int n,m;
struct Node
{
    int s[2],p,v;
    int rev,same;
    int size,sum,ms,ls,rs;

    void init(int _v,int _p)//初始化点
    {
        s[0] = s[1] = 0,p = _p,v = _v;
        rev = same = 0;
        size = 1,sum = ms = v;
        ls = rs = max(v,0);
    }
}tr[N];

int root,nodes[N],tt;
int w[N];

void pushup(int x)
{
    auto &u = tr[x], &l = tr[u.s[0]], &r = tr[u.s[1]];
    u.size = l.size + r.size + 1;
    u.sum = l.sum + r.sum + u.v;
    u.ls = max(l.ls, l.sum + u.v + r.ls);
    u.rs = max(r.rs, r.sum + u.v + l.rs);
    u.ms = max(max(l.ms, r.ms), l.rs + u.v + r.ls);
}

void pushdown(int x)
{
    auto &u = tr[x], &l = tr[u.s[0]], &r = tr[u.s[1]];
    if (u.same)
    {
        u.same = u.rev = 0;
        if (u.s[0]) l.same = 1, l.v = u.v, l.sum = l.v * l.size;
        if (u.s[1]) r.same = 1, r.v = u.v, r.sum = r.v * r.size;
        if (u.v > 0)
        {
            if (u.s[0]) l.ms = l.ls = l.rs = l.sum;
            if (u.s[1]) r.ms = r.ls = r.rs = r.sum;
        }
        else
        {
            if (u.s[0]) l.ms = l.v, l.ls = l.rs = 0;
            if (u.s[1]) r.ms = r.v, r.ls = r.rs = 0;
        }
    }
    else if (u.rev)
    {
        u.rev = 0, l.rev ^= 1, r.rev ^= 1;
        swap(l.ls, l.rs), swap(r.ls, r.rs);
        swap(l.s[0], l.s[1]), swap(r.s[0], r.s[1]);
    }
}
void rotate(int x)
{
    int y = tr[x].p,z = tr[y].p;
    int k = tr[y].s[1] == x;//看是y的哪个儿子
    tr[z].s[tr[z].s[1]==y] = x,tr[x].p = z;
    tr[y].s[k] = tr[x].s[k^1],tr[tr[x].s[k^1]].p = y;
    tr[x].s[k^1] = y,tr[y].p = x;
    pushup(y);pushup(x);
}
void splay(int x,int k)//转到k的下面
{
    while (tr[x].p!=k)
    {
        int y = tr[x].p,z = tr[y].p;
        if (z!=k) 
            if ((tr[y].s[1]==x)^(tr[z].s[1]==y)) rotate(x);//如果不是直线型，那么就转两次x
            else rotate(y);
        rotate(x);
    }
    if (!k) root = x;//如果转到顶了
}
int get_k(int k)//第k大个数的坐标
{
    int u = root;
    while (u)
    {
        pushdown(u);
        if (tr[tr[u].s[0]].size>=k) u = tr[u].s[0];
        else if (tr[tr[u].s[0]].size+1==k) return u;
        else k-=tr[tr[u].s[0]].size+1,u = tr[u].s[1];
    }
}
int build(int l,int r,int p)//模仿线段树建树
{
    int mid = l+r>>1;
    int u = nodes[tt--];
    tr[u].init(w[mid],p);
    if (l<mid) tr[u].s[0] = build(l,mid-1,u);
    if (r>mid) tr[u].s[1] = build(mid+1,r,u);
    pushup(u);
    return u;
}
void dfs(int u)
{
    if (tr[u].s[0]) dfs(tr[u].s[0]);
    if (tr[u].s[1]) dfs(tr[u].s[1]);
    nodes[ ++ tt ] = u;//删除回收机制
}
int main()
{
    for (int i = 1;i<N;i++) nodes[++tt] = i;
    scanf("%d%d",&n,&m);
    tr[0].ms = w[0] = w[n+1] = -INF;//哨兵
    for (int i = 1;i<=n;i++) scanf("%d",&w[i]);
    root = build(0,n+1,0);
    
    char op[20];
    while (m--)
    {
        scanf("%s",op);
        if (!strcmp(op,"INSERT"))
        {
            int posi,tot;
            scanf("%d%d",&posi,&tot);
            for (int i = 0;i<tot;i++) scanf("%d",&w[i]);
            int l = get_k(posi+1),r = get_k(posi+2);
            splay(l,0);splay(r,l);
            int u = build(0,tot-1,r);
            tr[r].s[0] = u;
            pushup(r);pushup(l);
        }
        else if (!strcmp(op,"DELETE"))
        {
            int posi,tot;
            scanf("%d%d",&posi,&tot);
            int l = get_k(posi),r = get_k(posi+tot+1);
            splay(l,0),splay(r,l);
            dfs(tr[r].s[0]);
            tr[r].s[0] = 0;
            pushup(r);pushup(l);
        }
        else if (!strcmp(op,"MAKE-SAME"))
        {
            int posi,tot,c;
            scanf("%d%d%d",&posi,&tot,&c);
            int l = get_k(posi),r = get_k(posi+tot+1);
            splay(l,0);splay(r,l);
            auto &son = tr[tr[r].s[0]];
            son.same = 1,son.v = c,son.sum = c * son.size;
            if (c>0) son.ms = son.ls = son.rs = son.sum;
            else son.ms = c,son.ls = son.rs = 0;
            pushup(r);pushup(l);
        }
        else if (!strcmp(op, "REVERSE"))
        {
            int posi,tot;
            scanf("%d%d",&posi,&tot);
            int l = get_k(posi),r = get_k(posi+tot+1);
            splay(l,0);splay(r,l);
            auto &son = tr[tr[r].s[0]];
            son.rev^=1;
            swap(son.ls,son.rs);
            swap(son.s[0],son.s[1]);
            pushup(r);pushup(l);
        }
        else if (!strcmp(op, "GET-SUM"))
        {
            int posi,tot;
            scanf("%d%d",&posi,&tot);
            int l = get_k(posi), r = get_k(posi + tot + 1);
            splay(l, 0), splay(r, l);
            printf("%d\n", tr[tr[r].s[0]].sum);
        }
        else printf("%d\n",tr[root].ms);
    }
}**
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174