Treap + 无旋转Treap 学习笔记
普通的Treap模板
今天自己实现成功
/* * @Author: chenkexing * @Date: 2019-08-02 20:30:39 * @Last Modified by: chenkexing * @Last Modified time: 2019-08-02 22:33:17 */ // #pragma GCC optimize(2) // #pragma GCC optimize(3) // #pragma GCC optimize(4) #include <algorithm> #include <iterator> #include <iostream> #include <cstring> #include <cstdlib> #include <iomanip> #include <bitset> #include <cctype> #include <cstdio> #include <string> #include <vector> #include <stack> #include <cmath> #include <queue> #include <list> #include <map> #include <set> #include <cassert> // #include<bits/extc++.h> // using namespace __gnu_pbds; using namespace std; #define pb push_back #define fi first #define se second #define debug(x) cerr<<#x << " := " << x << endl; #define bug cerr<<"-----------------------"<<endl; #define FOR(a, b, c) for(int a = b; a <= c; ++ a) typedef long long ll; typedef long double ld; typedef pair<int, int> pii; typedef pair<ll, ll> pll; const int inf = 0x3f3f3f3f; const ll inff = 0x3f3f3f3f3f3f3f3f; const int mod = 998244353; template<typename T> inline T read(T&x){ x=0;int f=0;char ch=getchar(); while (ch<'0'||ch>'9') f|=(ch=='-'),ch=getchar(); while (ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar(); return x=f?-x:x; } /**********showtime************/ struct Node{ Node * ch[2]; int r; int v; int s; int cnt; Node(int val = 0){ ch[0] = ch[1] = NULL; v = val; r = rand(); s = 1; cnt = 1; } int cmp(int x) const{ if(x == v) return -1; return x < v ? 0 : 1; } void maintain(){ s = cnt; if(ch[0] != NULL) s+=ch[0]->s; if(ch[1] != NULL) s+=ch[1]->s; } }*rt; void rotate(Node* &o, int d) { Node* k = o->ch[d^1]; o ->ch[d ^ 1] = k -> ch[d]; k -> ch[d] = o; o->maintain(); k->maintain(); o = k; } void insert(Node* &o, int x) { if(o == NULL) {o = new Node(x);} else if(o->v == x) {o->cnt++;} else { int d = o->cmp(x); insert(o->ch[d], x); if(o->ch[d] -> r > o->r) rotate(o, d^1); } o->maintain(); } void remove(Node* &o, int x) { int d = o->cmp(x); if(d == -1) { if(o->cnt > 1) o->cnt --; else if(o->ch[0] == NULL) o = o->ch[1]; else if(o->ch[1] == NULL) o = o->ch[0]; else { int d2 = (o->ch[0] -> r > o->ch[1] -> r ? 1 : 0); rotate(o, d2); remove(o->ch[d2], x); } } else remove(o->ch[d], x); if(o != NULL) o->maintain(); } int find(Node* o, int x) { while(o != NULL) { int d = o->cmp(x); if(d == -1) return o->cnt; else o = o->ch[d]; } return 0; } //返回第k小的数，不存在返回-inf int kth(Node* o, int k){ if(o == NULL || k <= 0 || k > o->s) return -inf; int s = (o->ch[0] == NULL ? 0 : o->ch[0]->s); if(s + 1 <= k && s + o->cnt >= k) return o->v; else if(s >= k) return kth(o->ch[0], k); else return kth(o->ch[1], k - s - o->cnt); } //返回比x值小的个数 int rannk(Node* o, int x) { if(o == NULL) return 0; int s = (o->ch[0] == NULL ? 0 : o->ch[0]->s); if(o->v == x) return rannk(o->ch[0], x); else if(o->v > x)return rannk(o->ch[0], x); else return s + o->cnt + rannk(o->ch[1], x); } //合并两个Treap void mergeto(Node* &src, Node* &dest) { if(src->ch[0] != NULL) mergeto(src->ch[0], dest); if(src->ch[1] != NULL) mergeto(src->ch[1], dest); insert(dest, src->v); delete src; src = NULL; } //清空树 void removetree(Node* &x) { if(x->ch[0] != NULL) removetree(x->ch[0]); if(x->ch[1] != NULL) removetree(x->ch[1]); delete x; x = NULL; } int main(){ srand(time(0)); int m; scanf("%d", &m); while(m --) { int op,x; scanf("%d%d", &op, &x); if(op == 1) insert(rt, x); else if(op == 2) remove(rt, x); else if(op == 3) printf("%d\n", rannk(rt, x) + 1); else if(op == 4) printf("%d\n", kth(rt, x)); else if(op == 5) { int k = rannk(rt, x); printf("%d\n", kth(rt, k)); } else { int k = rannk(rt, x); k += find(rt, x); printf("%d\n", kth(rt, k+1)); } } return 0; }
参考和学习：https://www.cnblogs.com/BCOI/p/9072444.html
对了，参考的blog中删点他应该写错了。
这个是按照val 进行切分的treap
写了模板普通平衡树
#include <algorithm> #include <iterator> #include <iostream> #include <cstring> #include <cstdlib> #include <iomanip> #include <bitset> #include <cctype> #include <cstdio> #include <string> #include <vector> #include <stack> #include <cmath> #include <queue> #include <list> #include <map> #include <set> #include <cassert> using namespace std; //#pragma GCC optimize(3) //#pragma comment(linker, "/STACK:102400000,102400000") //c++ // #pragma GCC diagnostic error "-std=c++11" // #pragma comment(linker, "/stack:200000000") // #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") // #pragma GCC optimize("-fdelete-null-pointer-checks,inline-functions-called-once,-funsafe-loop-optimizations,-fexpensive-optimizations,-foptimize-sibling-calls,-ftree-switch-conversion,-finline-small-functions,inline-small-functions,-frerun-cse-after-loop,-fhoist-adjacent-loads,-findirect-inlining,-freorder-functions,no-stack-protector,-fpartial-inlining,-fsched-interblock,-fcse-follow-jumps,-fcse-skip-blocks,-falign-functions,-fstrict-overflow,-fstrict-aliasing,-fschedule-insns2,-ftree-tail-merge,inline-functions,-fschedule-insns,-freorder-blocks,-fwhole-program,-funroll-loops,-fthread-jumps,-fcrossjumping,-fcaller-saves,-fdevirtualize,-falign-labels,-falign-loops,-falign-jumps,unroll-loops,-fsched-spec,-ffast-math,Ofast,inline,-fgcse,-fgcse-lm,-fipa-sra,-ftree-pre,-ftree-vrp,-fpeephole2",3) #define lson (l , mid , rt << 1) #define rson (mid + 1 , r , rt << 1 | 1) #define debug(x) cerr << #x << " = " << x << "\n"; #define pb push_back #define pq priority_queue typedef long long ll; typedef unsigned long long ull; typedef pair<ll ,ll > pll; typedef pair<int ,int > pii; typedef pair<int,pii> p3; //priority_queue<int> q;//这是一个大根堆q //priority_queue<int,vector<int>,greater<int> >q;//这是一个小根堆q #define fi first #define se second //#define endl '\n' #define OKC ios::sync_with_stdio(false);cin.tie(0) #define FT(A,B,C) for(int A=B;A <= C;++A) //用来压行 #define REP(i , j , k) for(int i = j ; i < k ; ++i) #define max3(a,b,c) max(max(a,b), c); //priority_queue<int ,vector<int>, greater<int> >que; const ll mos = 0x7FFFFFFF; //2147483647 const ll nmos = 0x80000000; //-2147483648 const int inf = 0x3f3f3f3f; const ll inff = 0x3f3f3f3f3f3f3f3f; //18 const int mod = 1e9+7; const double esp = 1e-8; const double PI=acos(-1.0); const double PHI=0.61803399; //黄金分割点 const double tPHI=0.38196601; template<typename T> inline T read(T&x){ x=0;int f=0;char ch=getchar(); while (ch<'0'||ch>'9') f|=(ch=='-'),ch=getchar(); while (ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar(); return x=f?-x:x; } /*-----------------------showtime----------------------*/ const int maxn = 100009; int tot = 0,root,r1,r2,r3; struct node{ int sz,val,rd,cnt; int ch[2]; }tr[maxn]; int newNode(int v){ tot++; tr[tot].sz = 1; tr[tot].val = v;tr[tot].rd = rand(); tr[tot].cnt = 1; return tot; } void update(int x){ tr[x].sz = tr[tr[x].ch[0]].sz + tr[tr[x].ch[1]].sz + tr[x].cnt; } void split(int x,int val, int &a, int &b){ if(!x) {a = b = 0;return;} if(tr[x].val <= val){ a = x; split(tr[x].ch[1], val, tr[x].ch[1], b); } else { b = x; split(tr[x].ch[0], val, a, tr[x].ch[0]); } update(x); } int merge(int x,int y){ if(x == 0 || y == 0)return x+y; if(tr[x].rd <= tr[y].rd){ tr[x].ch[1] = merge(tr[x].ch[1], y); update(x); return x; } else { tr[y].ch[0] = merge(x, tr[y].ch[0]); update(y); return y; } } void insert(int val){ split(root, val, r1,r2); root = merge(r1, merge(newNode(val), r2)); } void delet(int val){ r1 = r2 = r3 = 0;split(root,val,r1,r3); split(r1,val-1,r1,r2); r2 = merge(tr[r2].ch[0], tr[r2].ch[1]); root = merge(merge(r1,r2), r3); } int Rank(int val){ split(root,val-1,r1,r2); int res = tr[r1].sz + 1; merge(r1,r2); return res; } int kth(int rt,int k){ int x = rt; while(true){ if(x == 0)return -1; if(k <= tr[tr[x].ch[0]].sz){ x = tr[x].ch[0]; } else if(k > tr[tr[x].ch[0]].sz + tr[x].cnt){ k = k - tr[tr[x].ch[0]].sz - tr[x].cnt; x = tr[x].ch[1]; } else return tr[x].val; } } int pre(int val){ r1 = r2 = 0; split(root, val-1,r1,r2); int res = kth(r1, tr[r1].sz); merge(r1,r2); return res; } int nxt(int val){ r1 = r2 = 0; split(root,val,r1,r2); int res = kth(r2,1); merge(r1,r2); return res; } int main(){ srand(time(0)); int t; scanf("%d", &t); while(t--){ int op,x; scanf("%d%d", &op, &x); if(op == 1) insert(x); else if(op == 2 )delet(x); else if(op == 3)printf("%d\n", Rank(x)); else if(op == 4)printf("%d\n", kth(root,x)); else if(op == 5)printf("%d\n", pre(x)); else if(op == 6)printf("%d\n", nxt(x)); } }
换了个新的FHQ_TREE
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include <bits/stdc++.h> using namespace std; #define pb push_back #define fi first #define se second #define debug(x) cerr<<#x << " := " << x << endl; #define bug cerr<<"-----------------------"<<endl; #define FOR(a, b, c) for(int a = b; a <= c; ++ a) typedef long long ll; typedef long double ld; typedef pair<int, int> pii; typedef pair<ll, ll> pll; template<typename T> inline T read(T&x){ x=0;int f=0;char ch=getchar(); while (ch<'0'||ch>'9') f|=(ch=='-'),ch=getchar(); while (ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar(); return x=f?-x:x; } const int inf = 0x3f3f3f3f; const ll inff = 0x3f3f3f3f3f3f3f3f; const int mod = 998244353; /**********showtime************/ struct fhq_treap { static const int N = 1e5 + 5; struct Node { int val, key, lc, rc, sz, mx; }tree[N]; int rt, tot; inline void init() { rt = tot = 0; tree[rt].sz = tree[rt].val = tree[rt].lc = tree[rt].rc = 0; srand(time(0)); } inline void update(int rt) { tree[rt].sz = tree[tree[rt].lc].sz + 1 + tree[tree[rt].rc].sz; tree[rt].mx = max(tree[tree[rt].lc].mx,max(tree[rt].val,tree[tree[rt].rc].mx)); } void split_val(int rt, int &a, int &b, int val) { if(rt == 0) {a = b = 0; return ;} if(max(tree[rt].val , tree[tree[rt].lc].mx) <= val) { a = rt; split_val(tree[rt].rc, tree[a].rc, b, val); } else { b = rt; split_val(tree[rt].lc, a, tree[b].lc, val); } update(rt); } void split_sz(int rt, int &a, int &b, int sz) { if(rt == 0) {a = b = 0; return ;} if(tree[tree[rt].lc].sz + 1 > sz) { b = rt; split_sz(tree[rt].lc, a, tree[b].lc, sz); } else { a = rt; split_sz(tree[rt].rc, tree[a].rc, b, sz - 1 - tree[tree[rt].lc].sz); } update(rt); } void merge(int &rt, int a, int b) { if(a==0 || b==0) { rt = a+b; return ; } if(tree[a].key < tree[b].key) { rt = a; merge(tree[rt].rc, tree[a].rc, b); } else { rt = b; merge(tree[rt].lc, a, tree[b].lc); } update(rt); } inline int new_node(int val) { tree[++tot].sz = 1; tree[tot].val = val; tree[tot].lc = tree[tot].rc = 0; tree[tot].key = rand(); tree[tot].mx = val; return tot; } void ins(int &rt, int val) { int x = 0, y = 0, node = new_node(val); merge(rt, rt, node); } void delete_node(int &rt, int val) { int x = 0, y = 0, z = 0; split_val(rt, x, y, val); split_val(x, x, z, val-1); merge(z, tree[z].lc, tree[z].rc); merge(x, x, z); merge(rt, x, y); } inline int get_kth(int rt, int k) { while(tree[tree[rt].lc].sz+1 != k) { if(tree[tree[rt].lc].sz >= k) rt = tree[rt].lc; else k -= tree[tree[rt].lc].sz+1, rt = tree[rt].rc; } return tree[rt].val; } int get_rnk(int &rt, int val) { int x = 0, y = 0; split_val(rt, x, y, val-1); int tmp = tree[x].sz+1; merge(rt, x, y); return tmp; } int get_pre(int &rt, int val) { int x = 0, y = 0; split_val(rt, x, y, val-1); int tmp = get_kth(x, tree[x].sz); merge(rt, x, y); return tmp; } int get_scc(int &rt, int val) { int x = 0, y = 0; split_val(rt, x, y, val); int tmp = get_kth(y, 1); merge(rt, x, y); return tmp; } }t; const int maxn = 1e5+9; int n,m; int a[maxn]; void display(int x) { if(t.tree[x].lc) display(t.tree[x].lc); if(t.tree[x].rc) display(t.tree[x].rc); } void solve(int le, int mid ,int ri) { int x, y, z; t.split_sz(t.rt, x, z, ri); t.split_sz(x, x, y, mid); int tmp; int r = 0; while(x && y) { int p = t.get_kth(x, 1); int q = t.get_kth(y, 1); if(p > q) swap(p, q), swap(x, y); t.split_val(x, tmp, x, q); t.merge(r,r, tmp); } t.merge(r, r, x); t.merge(r, r, y); t.merge(r, r, z); t.rt = r; } int main(){ t.init(); scanf("%d%d", &n, &m); for(int i=1; i<=n; i++) { scanf("%d", &a[i]); t.ins(t.rt, a[i]); } while(m--){ int op; scanf("%d", &op); if(op == 2) { int x; scanf("%d", &x); printf("%d\n", t.get_kth(t.rt, x)); } else { int le, mid, ri; scanf("%d%d%d", &le, &mid, &ri); solve(le, mid, ri); } } return 0; } /* 5 10 3 2 1 5 4 1 1 2 5 */
skr
