[BZOJ3224]Tyvj 1728 普通平衡树

[BZOJ3224]Tyvj 1728 普通平衡树

试题描述

您需要写一种数据结构（可参考题目标题），来维护一些数，其中需要提供以下操作：
1. 插入x数
2. 删除x数(若有多个相同的数，因只删除一个)
3. 查询x数的排名(若有多个相同的数，因输出最小的排名)
4. 查询排名为x的数
5. 求x的前驱(前驱定义为小于x，且最大的数)
6. 求x的后继(后继定义为大于x，且最小的数)

输入

第一行为n，表示操作的个数,下面n行每行有两个数opt和x，opt表示操作的序号(1<=opt<=6)

输出

对于操作3,4,5,6每行输出一个数，表示对应答案

输入示例

输出示例

数据规模及约定

1.n的数据范围：n<=100000

2.每个数的数据范围：[-1e7,1e7]

题解

treap 模板题。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cctype>
#include <algorithm>
using namespace std;

int read() {
	int x = 0, f = 1; char c = getchar();
	while(!isdigit(c)){ if(c == '-') f = -1; c = getchar(); }
	while(isdigit(c)){ x = x * 10 + c - '0'; c = getchar(); }
	return x * f;
}

#define maxn 100010
struct Node {
	int v, r, siz;
	Node() {}
	Node(int _, int __): v(_), r(__) {}
} ns[maxn];
int rt, ToT, fa[maxn], ch[2][maxn];
void maintain(int o) {
	ns[o].siz = 1;
	for(int i = 0; i < 2; i++) if(ch[i][o])
		ns[o].siz += ns[ch[i][o]].siz;
	return ;
}
void rotate(int u) {
	int y = fa[u], z = fa[y], l = 0, r = 1;
	if(z) ch[ch[1][z]==y][z] = u;
	if(ch[1][y] == u) swap(l, r);
	fa[u] = z; fa[y] = u; fa[ch[r][u]] = y;
	ch[l][y] = ch[r][u]; ch[r][u] = y;
	maintain(y); maintain(u);
	return ;
}
void insert(int& o, int v) {
	if(!o) {
		ns[o = ++ToT] = Node(v, rand());
		return maintain(o);
	}
	bool d = v > ns[o].v;
	insert(ch[d][o], v); fa[ch[d][o]] = o;
	if(ns[ch[d][o]].r > ns[o].r) {
		int t = ch[d][o];
		rotate(t); o = t;
	}
	return maintain(o);
}
void del(int& o, int v) {
	if(!o) return ;
	if(ns[o].v == v) {
		if(!ch[0][o] && !ch[1][o]) o = 0;
		else if(!ch[0][o]) {
			int t = ch[1][o]; fa[t] = fa[o]; o = t;
		}
		else if(!ch[1][o]) {
			int t = ch[0][o]; fa[t] = fa[o]; o = t;
		}
		else {
			bool d = ns[ch[1][o]].r > ns[ch[0][o]].r;
			int t = ch[d][o]; rotate(t); o = t;
			del(ch[d^1][o], v);
		}
	}
	else {
		bool d = v > ns[o].v ;
		del(ch[d][o], v);
	}
	return maintain(o);
}
int qrank(int o, int v) {
	if(!o) return 0;
	int ls = ch[0][o] ? ns[ch[0][o]].siz : 0;
	if(v > ns[o].v) return ls + 1 + qrank(ch[1][o], v);
	return qrank(ch[0][o], v);
}
#define err -233333333
#define errm 233333333
int qkth(int o, int k) {
	if(!o) return err;
	int ls = ch[0][o] ? ns[ch[0][o]].siz : 0;
	if(k == ls + 1) return ns[o].v;
	if(k > ls + 1) return qkth(ch[1][o], k - ls - 1);
	return qkth(ch[0][o], k);
}
int qlow(int o, int v) {
	if(!o) return err;
	bool d = v > ns[o].v;
	if(d) return max(ns[o].v, qlow(ch[d][o], v));
	return qlow(ch[d][o], v);
}
int qupp(int o, int v) {
	if(!o) return errm;
	bool d = v >= ns[o].v;
	if(!d) return min(ns[o].v, qupp(ch[d][o], v));
	return qupp(ch[d][o], v);
}

int main() {
	int q = read();
	while(q--) {
		int tp = read(), v = read();
		if(tp == 1) insert(rt, v);
		if(tp == 2) del(rt, v);
		if(tp == 3) printf("%d\n", qrank(rt, v) + 1);
		if(tp == 4) printf("%d\n", qkth(rt, v));
		if(tp == 5) printf("%d\n", qlow(rt, v));
		if(tp == 6) printf("%d\n", qupp(rt, v));
	}

	return 0;
}

再贴一个替罪羊树版本的。

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <stack>
#include <vector>
#include <queue>
#include <cstring>
#include <string>
#include <map>
#include <set>
using namespace std;

const int BufferSize = 1 << 16;
char buffer[BufferSize], *Head, *Tail;
inline char Getchar() {
	if(Head == Tail) {
		int l = fread(buffer, 1, BufferSize, stdin);
		Tail = (Head = buffer) + l;
	}
	return *Head++;
}
int read() {
	int x = 0, f = 1; char c = Getchar();
	while(!isdigit(c)){ if(c == '-') f = -1; c = Getchar(); }
	while(isdigit(c)){ x = x * 10 + c - '0'; c = Getchar(); }
	return x * f;
}

#define maxn 100010
#define oo 2147483647
struct Node {
	int v, siz, reas, mx, mn;
	bool del;
	Node() {}
	Node(int _): v(_), del(0) {}
} ns[maxn];
int rt, ToT, fa[maxn], ch[maxn][2];
void maintain(int o) {
	ns[o].siz = ns[o].del ^ 1; ns[o].reas = 1;
	ns[o].mx = ns[o].del ? -oo : ns[o].v;
	ns[o].mn = ns[o].del ? oo : ns[o].v;
	for(int i = 0; i < 2; i++) if(ch[o][i])
		ns[o].siz += ns[ch[o][i]].siz,
		ns[o].reas += ns[ch[o][i]].reas,
		ns[o].mx = max(ns[o].mx, ns[ch[o][i]].mx),
		ns[o].mn = min(ns[o].mn, ns[ch[o][i]].mn);
	return ;
}
const double Bili = .6;
bool unbal(int o) {
	return max(ch[o][0] ? ns[ch[o][0]].reas : 0, ch[o][1] ? ns[ch[o][1]].reas : 0) > Bili * ns[o].reas;
}
int rb;
void insert(int& o, int v) {
	if(!o) {
		ns[o = ++ToT] = Node(v);
		return maintain(o);
	}
	bool d = v > ns[o].v;
	insert(ch[o][d], v); fa[ch[o][d]] = o; maintain(o);
	if(unbal(o)) rb = o;
	return ;
}
int cntn, get[maxn];
void getnode(int o) {
	if(!o) return ;
	getnode(ch[o][0]);
	if(!ns[o].del) get[++cntn] = o;
	getnode(ch[o][1]);
	fa[o] = ch[o][0] = ch[o][1] = 0;
	return ;
}
void build(int& o, int l, int r) {
	if(l > r){ o = 0; return ; }
	int mid = l + r >> 1; o = get[mid];
	build(ch[o][0], l, mid - 1); build(ch[o][1], mid + 1, r);
	if(ch[o][0]) fa[ch[o][0]] = o;
	if(ch[o][1]) fa[ch[o][1]] = o;
	return maintain(o);
}
void rebuild(int& o) {
	cntn = 0; getnode(o);
	build(o, 1, cntn);
	return ;
}
void Insert(int v) {
	rb = 0; insert(rt, v);
	if(!rb) return ;
	int frb = fa[rb];
	if(!frb) rebuild(rt), fa[rt] = 0;
	else if(ch[frb][0] == rb) rebuild(ch[frb][0]), fa[ch[frb][0]] = frb;
	else rebuild(ch[frb][1]), fa[ch[frb][1]] = frb;
	return ;
}
bool unbal2(int o) {
	return Bili * ns[o].reas > ns[o].siz;
}
void del(int o, int k) {
	if(!o) return ;
	int ls = ch[o][0] ? ns[ch[o][0]].siz : 0;
	if(k == ls + 1 && !ns[o].del) {
		ns[o].del = 1; maintain(o);
		if(unbal2(o)) rb = o;
		return ;
	}
	if(k > ls + (ns[o].del ^ 1)) {
		del(ch[o][1], k - ls - (ns[o].del ^ 1)); maintain(o);
		if(unbal2(o)) rb = o;
		return ;
	}
	del(ch[o][0], k); maintain(o);
	if(unbal2(o)) rb = o;
	return ;
}
int Find(int o, int v) {
	if(!o) return 0;
	int ls = ch[o][0] ? ns[ch[o][0]].siz : 0;
	if(v <= ns[o].v) return Find(ch[o][0], v);
	return ls + (ns[o].del ^ 1) + Find(ch[o][1], v);
}
void Delete(int v) {
	int id = Find(rt, v) + 1;
	rb = 0; del(rt, id);
	int tmp = ns[rt].reas;
	if(!rb) return ;
	int frb = fa[rb];
	if(!frb) rebuild(rt), fa[rt] = 0;
	else if(ch[frb][0] == rb) rebuild(ch[frb][0]), fa[ch[frb][0]] = frb;
	else rebuild(ch[frb][1]), fa[ch[frb][1]] = frb;
	return ;
}
int qkth(int o, int k) {
	if(!o) return 0;
	int ls = ch[o][0] ? ns[ch[o][0]].siz : 0;
	if(k == ls + 1 && !ns[o].del) return ns[o].v;
	if(k > ls + (ns[o].del ^ 1)) return qkth(ch[o][1], k - ls - (ns[o].del ^ 1));
	return qkth(ch[o][0], k);
}
int qlow(int o, int v) {
	if(!o) return -oo;
	if(ns[o].v < v) return max(max(ns[o].del ? -oo : ns[o].v, ch[o][0] ? ns[ch[o][0]].mx : -oo), qlow(ch[o][1], v));
	return qlow(ch[o][0], v);
}
int qupp(int o, int v) {
	if(!o) return oo;
	if(ns[o].v > v) return min(min(ns[o].del ? oo : ns[o].v, ch[o][1] ? ns[ch[o][1]].mn : oo), qupp(ch[o][0], v));
	return qupp(ch[o][1], v);
}

int main() {
	int q = read();
	while(q--) {
		int tp = read(), x = read();
		if(tp == 1) Insert(x);
		if(tp == 2) Delete(x);
		if(tp == 3) printf("%d\n", Find(rt, x) + 1);
		if(tp == 4) printf("%d\n", qkth(rt, x));
		if(tp == 5) printf("%d\n", qlow(rt, x));
		if(tp == 6) printf("%d\n", qupp(rt, x));
	}

	return 0;
}

懒惰删除真的一点都不懒惰！！！打了删除标记反而更难处理了。。。太多细节要考虑。

再贴一个 fhq treap 的版本。

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cctype>
#include <algorithm>
#include <cassert>
using namespace std;
#define rep(i, s, t) for(int i = (s), mi = (t); i <= mi; i++)
#define dwn(i, s, t) for(int i = (s), mi = (t); i >= mi; i--)

const int BufferSize = 1 << 16;
char buffer[BufferSize], *Head, *Tail;
inline char Getchar() {
    if(Head == Tail) {
        int l = fread(buffer, 1, BufferSize, stdin);
        Tail = (Head = buffer) + l;
    }
    return *Head++;
}
int read() {
    int x = 0, f = 1; char c = Getchar();
    while(!isdigit(c)){ if(c == '-') f = -1; c = Getchar(); }
    while(isdigit(c)){ x = x * 10 + c - '0'; c = Getchar(); }
    return x * f;
}

#define maxn 100010
#define oo 2147483647
#define pii pair <int, int>
#define x first
#define y second
#define mp(x, y) make_pair(x, y)

struct Node {
    int v, r, siz;
    Node() {}
    Node(int _v): v(_v), r(rand()), siz(1) {}
} ns[maxn];
int ToT, rt, ch[maxn][2];

void maintain(int o) {
    if(!o) return ;
    ns[o].siz = 1;
    if(ch[o][0]) ns[o].siz += ns[ch[o][0]].siz;
    if(ch[o][1]) ns[o].siz += ns[ch[o][1]].siz;
    return ;
}
int merge(int a, int b) { // max{a} <= min{b}
    if(!a) return maintain(b), b;
    if(!b) return maintain(a), a;
    if(ns[a].r > ns[b].r) return ch[a][1] = merge(ch[a][1], b), maintain(a), a;
    return ch[b][0] = merge(a, ch[b][0]), maintain(b), b;
}
pii split(int o, int k) {
    if(!o) return mp(0, 0);
    if(!k) return mp(0, o);
    int ls = ch[o][0] ? ns[ch[o][0]].siz : 0;
    if(k <= ls) {
        pii pr = split(ch[o][0], k);
        ch[o][0] = pr.y; maintain(o);
        return mp(pr.x, o);
    }
    pii pr = split(ch[o][1], k - ls - 1);
    ch[o][1] = pr.x; maintain(o);
    return mp(o, pr.y);
}
int Find(int o, int v) {
    if(!o) return 0;
    int ls = ch[o][0] ? ns[ch[o][0]].siz : 0;
    if(v <= ns[o].v) return Find(ch[o][0], v);
    return ls + 1 + Find(ch[o][1], v);
}
void Insert(int v) {
    int rnk = Find(rt, v);
    pii pr = split(rt, rnk);
    ns[++ToT] = Node(v);
    rt = merge(pr.x, ToT);
    rt = merge(rt, pr.y);
    return ;
}
void Delete(int& o, int v) {
    if(!o) return ;
    if(ns[o].v == v) return (void)(o = merge(ch[o][0], ch[o][1]));
    if(v < ns[o].v) Delete(ch[o][0], v);
    else Delete(ch[o][1], v);
    return maintain(o);
}
int qkth(int o, int k) {
    assert(o);
    int ls = ch[o][0] ? ns[ch[o][0]].siz : 0;
    if(k == ls + 1) return ns[o].v;
    if(k <= ls) return qkth(ch[o][0], k);
    return qkth(ch[o][1], k - ls - 1);
}
int qpre(int o, int v) {
    if(!o) return -oo;
    if(ns[o].v < v) return max(ns[o].v, qpre(ch[o][1], v));
    return qpre(ch[o][0], v);
}
int qnxt(int o, int v) {
    if(!o) return oo;
    if(ns[o].v > v) return min(ns[o].v, qnxt(ch[o][0], v));
    return qnxt(ch[o][1], v);
}

int main () {
    srand(5);
    int q = read();
    while(q--) {
        int tp = read();
        if(tp == 1) Insert(read());
        if(tp == 2) Delete(rt, read());
        if(tp == 3) printf("%d\n", Find(rt, read()) + 1);
        if(tp == 4) printf("%d\n", qkth(rt, read()));
        if(tp == 5) printf("%d\n", qpre(rt, read()));
        if(tp == 6) printf("%d\n", qnxt(rt, read()));
    }

    return 0;
}