【LG3721】[HNOI2017]单旋

【LG3721】[HNOI2017]单旋

题面

洛谷

题解

20pts

直接模拟\(spaly\)的过程即可。

100pts

可以发现单旋最大、最小值到根，手玩是有显然规律的，发现只需要几次\(link,cut\)，那么我们维护原树的父子关系以及一颗\(LCT\)。

对于插入操作，由于插入的值肯定在前驱的右儿子或后继的左儿子，用\(set\)维护前驱后继即可。

建议自己独立找出规律，这里不再赘述，这题其实细节还是挺多的。

代码

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <set>
#include <map>
using namespace std;
inline int gi() {
    register int data = 0, w = 1;
    register char ch = 0;
    while (!isdigit(ch) && ch != '-') ch = getchar();
    if (ch == '-') w = -1, ch = getchar();
    while (isdigit(ch)) data = 10 * data + ch - '0', ch = getchar();
    return w * data;
}
const int MAX_N = 2e5 + 5;
struct Node { int ch[2], fa, size; bool rev; } t[MAX_N];
struct Clone { int v, ls, rs, fa; } _t[MAX_N];
int root, tot;
bool get(int x) { return t[t[x].fa].ch[1] == x; }
bool nroot(int x) { return t[t[x].fa].ch[0] == x || t[t[x].fa].ch[1] == x; }
void pushup(int x) { t[x].size = t[t[x].ch[0]].size + t[t[x].ch[1]].size + 1; }
void putrev(int x) { swap(t[x].ch[0], t[x].ch[1]); t[x].rev ^= 1; }
void pushdown(int x) {
	if (!t[x].rev) return ;
	if (t[x].ch[0]) putrev(t[x].ch[0]);
	if (t[x].ch[1]) putrev(t[x].ch[1]);
	t[x].rev = 0;
}
void rotate(int x) {
	int y = t[x].fa, z = t[y].fa, k = get(x);
	if (nroot(y)) t[z].ch[get(y)] = x;
	t[x].fa = z;
	t[t[x].ch[k ^ 1]].fa = y, t[y].ch[k] = t[x].ch[k ^ 1];
	t[y].fa = x, t[x].ch[k ^ 1] = y;
	pushup(y), pushup(x);
}
void splay(int x) {
	static int stk[MAX_N], top;
	stk[top = 1] = x;
	for (int i = x; nroot(i); i = t[i].fa) stk[++top] = t[i].fa;
	for (int i = top; i; --i) pushdown(stk[i]);
	while (nroot(x)) {
		int y = t[x].fa;
		if (nroot(y)) get(x) ^ get(y) ? rotate(x) : rotate(y);
		rotate(x);
	}
}
void access(int x) { for (int y = 0; x; y = x, x = t[x].fa) splay(x), t[x].ch[1] = y, pushup(x); }
void makeroot(int x) { access(x); splay(x); putrev(x); }
void link(int x, int y) { makeroot(x); t[x].fa = y; }
void split(int x, int y) { makeroot(x); access(y); splay(y); }
void cut(int x, int y) { split(x, y); t[x].fa = t[y].ch[0] = 0; pushup(y); }
set<int> st;
map<int, int> mp;
void insert(int v) {
	int x = ++tot;
	mp[v] = x, _t[x].v = v;
	if (st.size() == 0) return st.insert(v), root = x, (void)puts("1");
	set<int> :: iterator ite = st.upper_bound(v);
	if (ite == st.end() || _t[mp[*ite]].ls) {
		--ite;
		int tmp = mp[*ite];
		link(x, tmp), _t[tmp].rs = x, _t[x].fa = tmp;
	} else {
		int tmp = mp[*ite];
		link(x, tmp), _t[tmp].ls = x, _t[x].fa = tmp;
	}
	st.insert(v);
	return split(x, root), (void)printf("%d\n", t[root].size);
}
void splay_min() {
	int x = mp[*st.begin()];
	if (x == root) return (void)puts("1");
	split(x, root); printf("%d\n", t[root].size);
	cut(x, _t[x].fa); if (_t[x].rs) cut(x, _t[x].rs);
	link(x, root); if (_t[x].rs) link(_t[x].fa, _t[x].rs);
	_t[_t[x].fa].ls = _t[x].rs; if (_t[x].rs) _t[_t[x].rs].fa = _t[x].fa;
	_t[x].fa = 0, _t[root].fa = x, _t[x].rs = root;
	root = x;
}
void splay_max() {
    int x = mp[*st.rbegin()];
    if (x == root) return (void)puts("1");
    split(x, root); printf("%d\n", t[root].size);
    cut(x, _t[x].fa); if (_t[x].ls) cut(x, _t[x].ls);
    link(x, root); if (_t[x].ls) link(_t[x].ls, _t[x].fa);
    _t[_t[x].fa].rs = _t[x].ls; if (_t[x].ls) _t[_t[x].ls].fa = _t[x].fa;
    _t[x].fa = 0, _t[root].fa = x, _t[x].ls = root;
    root = x;
}
void del_min() {
    int x = mp[*st.begin()];
    if (root == x) {
		puts("1");
		if (_t[x].rs) cut(x, _t[x].rs);
		_t[_t[x].rs].fa = 0, root = _t[x].rs;
		st.erase(st.begin());
		return ;
	}
    split(x, root); printf("%d\n", t[root].size);
    cut(x, _t[x].fa); if (_t[x].rs) cut(x, _t[x].rs);
    if (_t[x].rs) link(_t[x].fa, _t[x].rs);
    _t[_t[x].fa].ls = _t[x].rs; if (_t[x].rs) _t[_t[x].rs].fa = _t[x].fa;
    st.erase(st.begin());
}
void del_max() {
    int x = mp[*st.rbegin()];
    if (root == x) {
		puts("1");
		if (_t[x].ls) cut(x, _t[x].ls);
		_t[_t[x].ls].fa = 0, root = _t[x].ls;
		st.erase(--st.end());
		return;
	}
    split(x, root); printf("%d\n", t[root].size);
    cut(x, _t[x].fa); if (_t[x].ls) cut(x, _t[x].ls);
    if (_t[x].ls) link(_t[x].ls, _t[x].fa);
    _t[_t[x].fa].rs = _t[x].ls; if(_t[x].ls) _t[_t[x].ls].fa = _t[x].fa;
    st.erase(--st.end());
}
int main () {
#ifndef ONLINE_JUDGE
    freopen("cpp.in", "r", stdin);
#endif
	int M = gi();
    for (int i = 1; i <= M; i++) {
        int op = gi();
        switch (op) {
            case 1: insert(gi()); break;
            case 2: splay_min(); break;
            case 3: splay_max(); break;
            case 4: del_min(); break;
            case 5: del_max(); break;
        }
    }
	return 0;
}