4923: [Lydsy1706月赛]K小值查询 平衡树 非旋转Treap

 1 #include<cstdio>
 2 #include<algorithm>
 3 #include<cstdlib>
 4 const int maxn=1e5+1e2;
 5 
 6 typedef std::pair<int,int> pii;
 7 __inline pii mp(const int &x,const int &y) { return std::make_pair(x,y); }
 8 
 9 int seq[maxn],sql;
10 int stk[maxn],top;
11 
12 struct Treap {
13     int lson[maxn],rson[maxn],lazy[maxn],val[maxn],siz[maxn],fix[maxn],cnt;
14     
15     inline void init(int n) {
16         for(int i=1;i<=n;i++) fix[i] = i;
17         std::random_shuffle(fix+1,fix+1+n);
18     }
19     inline void apply(int pos,int x) {
20         if(pos) lazy[pos] += x , val[pos] -= x;
21     }
22     inline void push(int pos) {
23         if( lazy[pos] ) apply(lson[pos],lazy[pos]) , apply(rson[pos],lazy[pos]) , lazy[pos] = 0;
24     }
25     inline void maintain(int pos) {
26         siz[pos] = siz[lson[pos]] + siz[rson[pos]] + 1;
27     }
28 
29     inline pii split(int pos,int dv) { // left is <= , right is > .
30         if( !pos ) return mp(0,0);
31         push(pos);
32         if(  dv < val[pos] ) {
33             pii spl = split(lson[pos],dv);
34             lson[pos] = spl.second , maintain(pos);
35             return mp(spl.first,pos);
36         } else {
37             pii spr = split(rson[pos],dv);
38             rson[pos] = spr.first , maintain(pos);
39             return mp(pos,spr.second);
40         }
41     }
42     inline int merge(int x,int y) {
43         if( !x || !y ) return x | y;
44         push(x) , push(y);
45         if( val[x] > val[y] ) std::swap(x,y);
46         if( fix[x] > fix[y] ) { // siz[x] is bigger .
47             lson[y] = merge(lson[y],x) , maintain(y);
48             return y;
49         } else {
50             rson[x] = merge(rson[x],y) , maintain(x);
51             return x;
52         }
53     }
54     inline void dfs(int pos) {
55         if( !pos ) return;
56         seq[++sql] = val[pos] , push(pos);
57         dfs(lson[pos]) , dfs(rson[pos]);
58         lson[pos] = rson[pos] = siz[pos] = 0 , stk[++top] = pos;
59     }
60     inline int kth(int pos,int k) { // return the kth value .
61         if( k == siz[lson[pos]] + 1 ) return val[pos];
62         return push(pos) , k <= siz[lson[pos]] ? kth(lson[pos],k) : kth(rson[pos],k-siz[lson[pos]]-1);
63     }
64     inline void insert(int &root,int x) {
65         val[++cnt] = x , siz[cnt] = 1;
66         pii sp = split(root,x);
67         root = merge(sp.first,cnt) , root = merge(root,sp.second);
68     }
69     inline void reinsert(int &root,int x) {
70         int cur = stk[top--];
71         val[cur] = x , siz[cur] = 1;
72         pii sp = split(root,x);
73         root = merge(sp.first,cur) , root = merge(root,sp.second);
74     }
75     
76 }tp;
77 
78 int main() {
79     static int n,m,root,rtl,rtm,rtr;
80     scanf("%d%d",&n,&m) , tp.init(n);
81     for(int i=1,t;i<=n;i++) scanf("%d",&t) , tp.insert(root,t);
82     for(int i=1,o,x;i<=m;i++) {
83         scanf("%d%d",&o,&x);
84         if( o == 1 ) printf("%d\n",tp.kth(root,x));
85         else if( o == 2 ) {
86             pii sp = tp.split(root,x);
87             rtl = sp.first , sp = tp.split(sp.second,x<<1);
88             rtm = sp.first , rtr = sp.second;
89             sql = 0 , tp.dfs(rtm) , tp.apply(rtr,x);
90             for(int i=1;i<=sql;i++) tp.reinsert(rtl,seq[i]-x);
91             root = tp.merge(rtl,rtr);
92         }
93     }
94     return 0;
95 }