P10689 学习笔记

省流：又又又又是毒瘤数据结构。

题目传送门

看到操作一我们想到线段树/树状数组，看到操作二我们想到文艺平衡树。

再结合后面的所有操作，这题就是文艺平衡树裸题。

我们需要维护两个 lazy tag，一个翻转标记，一个加法标记即可。

下面给出二十几行的 pushdown ：

void pushdown(ll u){
	if (rev[u]) {
		swap(ls[u], rs[u]);
		rev[ls[u]] ^= 1;
		rev[rs[u]] ^= 1;
		rev[u] = 0;
	}
	if (add[u]) {
		if (ls[u]) {
			add[ls[u]] += add[u];
			minn[ls[u]] += add[u];
			val[ls[u]] += add[u];
		}
		if (rs[u]) {
			add[rs[u]] += add[u];
			minn[rs[u]] += add[u];
			val[rs[u]] += add[u];
		}
		add[u] = 0;
	}
}

其他的就是文艺平衡树板子了。

code

#include <bits/stdc++.h>
#define pub public:
#define pri private:
#define fri friend:
#define Ofile(s) freopen(s".in", "r", stdin), freopen (s".out", "w", stdout)
#define Cfile(s) fclose(stdin), fclose(stdout)
#define fast ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
using namespace std;

using ll = long long;
using ull = unsigned long long;
using lb = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;

constexpr int mod = 998244353;
constexpr int maxn = 2e5 + 5;

ll n, q;
ll x, y, z;
ll root, tot;
ll seed = 1;

ll val[maxn];
ll priority[maxn];
ll siz[maxn];
ll minn[maxn];
ll ls[maxn];
ll rs[maxn];
ll rev[maxn];
ll add[maxn];

string opt;

void pushup(ll);
void pushdown(ll);
void split(ll, ll, ll &, ll &);
ll merge(ll, ll);
void ADD(ll, ll, ll);
void REVERSE(ll, ll);
void REVOLVE(ll, ll, ll);
void INSERT(ll, ll);
void DELETE(ll);
ll MIN(ll, ll);

int main() {
	freopen("std.in", "r", stdin);
	freopen("std.out", "w", stdout);
	fast;
	srand(time(0));
	cin >> n;
	minn[0] = 1e18;
	for (int i = 1, u; i <= n; i++){
		cin >> u;
		INSERT(i - 1, u);
	}
	cin >> q;
	while (q--){
		cin >> opt;
		if (opt == "ADD"){
			cin >> x >> y >> z;
			ADD(x, y, z);
		}
		else if (opt == "REVERSE"){
			cin >> x >> y;
			REVERSE(x, y);
		}
		else if (opt == "REVOLVE"){
			cin >> x >> y >> z;
			REVOLVE(x, y, z);
		}
		else if (opt == "INSERT"){
			cin >> x >> y;
			INSERT(x, y);
		}
		else if (opt == "DELETE"){
			cin >> x;
			DELETE(x);
		}
		else {
			cin >> x >> y;
			cout << MIN(x, y) << endl;
		}
	}
	return 0;
}

void pushup(ll u){
	siz[u] = siz[ls[u]] + siz[rs[u]] + 1;
	minn[u] = min(val[u], min(minn[ls[u]], minn[rs[u]]));
}

void pushdown(ll u){
	if (rev[u]) {
		swap(ls[u], rs[u]);
		rev[ls[u]] ^= 1;
		rev[rs[u]] ^= 1;
		rev[u] = 0;
	}
	if (add[u]) {
		if (ls[u]) {
			add[ls[u]] += add[u];
			minn[ls[u]] += add[u];
			val[ls[u]] += add[u];
		}
		if (rs[u]) {
			add[rs[u]] += add[u];
			minn[rs[u]] += add[u];
			val[rs[u]] += add[u];
		}
		add[u] = 0;
	}
}

void split(ll u, ll v, ll &rootl, ll &rootr){
	if (!u){
		rootl = rootr = 0;
		return ;
	}
	pushdown(u);
	if (siz[ls[u]] + 1 <= v){
		rootl = u;
		split(rs[u], v - siz[ls[u]] - 1, rs[u], rootr);
	}
	else {
		rootr = u;
		split(ls[u], v, rootl, ls[u]);
	}
	pushup(u);
}

ll merge(ll rootl, ll rootr){
	if (!rootl)
		return rootr;
	if (!rootr)
		return rootl;
	pushdown(rootl);
	pushdown(rootr);
	if (priority[rootl] < priority[rootr]){
		rs[rootl] = merge(rs[rootl], rootr);
		pushup(rootl);
		return rootl;
	}
	else {
		ls[rootr] = merge(rootl, ls[rootr]);
		pushup(rootr);
		return rootr;
	}
}

void ADD(ll x, ll y, ll z){
	ll a, b, c;
	split(root, y, b, c);
	split(b, x - 1, a, b);
	add[b] += z;
	minn[b] += z;
	val[b] += z;
	root = merge(merge(a, b), c);
}

void REVERSE(ll x, ll y){
	ll a, b, c;
	split(root, y, b, c);
	split(b, x - 1, a, b);
	rev[b] ^= 1;
	root = merge(merge(a, b), c);
}

void REVOLVE(ll x, ll y, ll z){
	ll a, b, c, d;
	split(root, y, c, d);
	split(c, x - 1, a, c);
	z %= (y - x + 1);
	split(c, y - x + 1 - z, b, c);
	root = merge(merge(merge(a, c), b), d);
}

void INSERT(ll x, ll y){
	++tot;
	val[tot] = y;
	priority[tot] = rand();
	siz[tot] = 1;
	minn[tot] = y;
	ll a, b;
	split(root, x, a, b);
	root = merge(merge(a, tot), b);
}

void DELETE(ll x){
	ll a, b, c;
	split(root, x - 1, a, b);
	split(b, 1, b, c);
	root = merge(a, c);
}

ll MIN(ll x, ll y){
	ll a, b, c;
	split(root, y, b, c);
	split(b, x - 1, a, b);
	ll ans = minn[b];
	root = merge(merge(a, b), c);
	return ans;
}