【学习笔记】数据结构全家桶

前言

2025.10.28：
一时兴起建了这个，原因是刚刚学了KTT qwq
我如果塞完这个东西应该都大学几年级了吧
没事慢慢弄

正文

线段树

KTT

KTT

//https://www.luogu.com.cn/problem/P5693
#include<bits/stdc++.h>
#define rep(i, l, r) for(int i(l);i<=(r);++i)
#define per(i, r, l) for(int i(r);i>=(l);--i)
using namespace std;
namespace IO{
template <typename T>
inline void read(T &x){
	x = 0;
	static char c;
	static bool f;
	c = getchar(), f = 0;
	while(c<'0'||c>'9'){ if(c == '-')f = 1; c = getchar(); }
	while('0'<=c&&c<='9')x = (x << 3) + (x << 1) + (c ^ 48), c = getchar();
	x = f ? -x : x;
}
template <typename T,typename ...Types>
inline void read(T &x, Types &...y){
	read(x), read(y...);
}
}using namespace IO;

using ll = long long;
const int N = 4e5 + 10;
const ll inf = 1e15;

template <typename T>
inline void ckmin(T &x, T y){ (x > y) && (x = y); }

int n,a[N],qcnt;

namespace KTT{

struct Func{
	int k; ll b;
	inline friend Func operator +(const Func &a,const Func &b){ return (Func){a.k+b.k,a.b+b.b}; }
	inline void add(ll v){ b += k * v; }
};
inline pair<Func, ll> max(Func a, Func b){
	if(a.k < b.k || (a.k == b.k && a.b < b.b))swap(a, b);
	if(a.b >= b.b)return {a, inf};
	return {b, (b.b-a.b)/(a.k-b.k)};
}
struct node{
	Func lm, rm, tot, sum;
	ll iter;//yu zhi
	inline friend node operator +(const node &a,const node &b){
		node res; pair<Func, ll> tmp;
		
		res.iter = min(a.iter, b.iter);
		
		tmp = max(a.lm, b.lm + a.sum);
		res.lm = tmp.first, ckmin(res.iter, tmp.second);
		
		tmp = max(b.rm, a.rm + b.sum);
		res.rm = tmp.first, ckmin(res.iter, tmp.second);
		
		tmp = max(a.tot, b.tot);
		ckmin(res.iter, tmp.second);
		tmp = max(tmp.first, a.rm + b.lm);
		ckmin(res.iter, tmp.second);
		res.tot = tmp.first;
		
		res.sum = a.sum + b.sum;
		
		return res;
	}
}tr[N << 2];
ll tag[N << 2];


#define ls (p << 1)
#define rs (p << 1 | 1)
inline void pup(int p){ tr[p] = tr[ls] + tr[rs]; }
inline void ptag(int p,ll v){
	tag[p] += v;
	tr[p].iter -= v;
	tr[p].lm.add(v),tr[p].rm.add(v),tr[p].tot.add(v),tr[p].sum.add(v);
}
inline void pdown(int p){
	if(tag[p]){
		ptag(ls, tag[p]), ptag(rs, tag[p]);
		tag[p] = 0;
	}
}
void build(int p,int l,int r){
	if(l == r){
		Func tmp = {1, a[l]};
		tr[p] = {tmp, tmp, tmp, tmp, inf};
		return ;
	}
	int mid = (l + r) >> 1;
	build(ls, l, mid), build(rs, mid+1, r);
	pup(p);
}
void defeat(int p,int l,int r,ll v){
	if(v > tr[p].iter){
		int mid = (l + r) >> 1;
		defeat(ls, l, mid, tag[p]+v);
		defeat(rs, mid+1, r, tag[p]+v);
		tag[p] = 0, pup(p);
	}else ptag(p, v);
}
void upd(int p,int l,int r,int L,int R,int k){
	if(L <= l && r <= R)return defeat(p, l, r, k);
	pdown(p);
	int mid = (l + r) >> 1;
	if(L <= mid)upd(ls, l, mid, L, R, k);
	if(mid < R)upd(rs, mid+1, r, L, R, k);
	pup(p);
}
node qry(int p,int l,int r,int L,int R){
	if(L <= l && r <= R)return tr[p];
	pdown(p); int mid = (l + r) >> 1;
	if(R <= mid)return qry(ls, l, mid, L, R);
	if(L > mid)return qry(rs, mid+1, r, L, R);
	return qry(ls, l, mid, L, R) + qry(rs, mid+1, r, L, R);
}
#undef ls
#undef rs
}using namespace KTT;


int main(){
	read(n), read(qcnt);
	rep(i, 1, n)read(a[i]);
	build(1, 1, n);
	int op, l, r, v;
	while(qcnt--){
		read(op);
		if(op == 1){
			read(l, r, v);
			upd(1, 1, n, l, r, v);
		}else{
			read(l, r);
			printf("%lld\n",max(0ll,qry(1, 1, n, l, r).tot.b));
		}
	}
	return 0;
}

KTT+吉司机

//https://www.luogu.com.cn/problem/P6792
#include<bits/stdc++.h>
#define rep(i, l, r) for(int i(l);i<=(r);++i)
#define per(i, r, l) for(int i(r);i>=(l);--i)
using namespace std;
namespace IO{
template <typename T>
inline void read(T &x){
	x = 0;
	static char c;
	static bool f;
	c = getchar(), f = 0;
	while(c<'0'||c>'9'){ if(c == '-')f = 1; c = getchar(); }
	while('0'<=c&&c<='9')x = (x << 3) + (x << 1) + (c ^ 48), c = getchar();
	x = f ? -x : x;
}
template <typename T,typename ...Types>
inline void read(T &x, Types &...y){
	read(x), read(y...);
}
}using namespace IO;

using ll = long long;
const int N = 4e5 + 10;
const ll inf = 1e15;

template <typename T>
inline void ckmin(T &x, T y){ (x > y) && (x = y); }

int n,a[N],qcnt;

namespace KTT{

struct Func{
	int k; ll b;
	inline friend Func operator +(const Func &a,const Func &b){ return (Func){a.k+b.k,a.b+b.b}; }
	inline void add(ll v){ b += k * v; }
	inline void set(){ k = 0; }
};
inline pair<Func, ll> max(Func a, Func b){
	if(a.k < b.k || (a.k == b.k && a.b < b.b))swap(a, b);
	if(a.b >= b.b)return {a, inf};
	return {b, (b.b-a.b)/(a.k-b.k)};
}
struct node{
	Func lm, rm, tot, sum;
	ll iter;//yu zhi
	inline friend node operator +(const node &a,const node &b){
		node res; pair<Func, ll> tmp;
		
		res.iter = min(a.iter, b.iter);
		
		tmp = max(a.lm, b.lm + a.sum);
		res.lm = tmp.first, ckmin(res.iter, tmp.second);
		
		tmp = max(b.rm, a.rm + b.sum);
		res.rm = tmp.first, ckmin(res.iter, tmp.second);
		
		tmp = max(a.tot, b.tot);
		ckmin(res.iter, tmp.second);
		tmp = max(tmp.first, a.rm + b.lm);
		ckmin(res.iter, tmp.second);
		res.tot = tmp.first;
		
		res.sum = a.sum + b.sum;
		
		return res;
	}
	inline node set(){
		node a = *this;
		a.lm.set(), a.rm.set(), a.tot.set(), a.sum.set();
		return a;
	}
}tr[N << 2];

ll tag[N << 2], mn[N << 2], se[N << 2];


#define ls (p << 1)
#define rs (p << 1 | 1)
inline void pup(int p){
	if(mn[ls] == mn[rs]){
		mn[p] = mn[ls];
		se[p] = min(se[ls], se[rs]);
		tr[p] = tr[ls] + tr[rs];
	}
	if(mn[ls] < mn[rs]){
		mn[p] = mn[ls];
		se[p] = min(se[ls], mn[rs]);
		tr[p] = tr[ls] + tr[rs].set();
	}
	if(mn[ls] > mn[rs]){
		mn[p] = mn[rs];
		se[p] = min(mn[ls], se[rs]);
		tr[p] = tr[ls].set() + tr[rs];
	}
}
inline void ptag(int p,ll v){
	if(v <= mn[p])return ;
	ll w = v - mn[p];
	mn[p] = v;
	tag[p] = std::max(tag[p], v);
	tr[p].iter -= w;
	tr[p].lm.add(w),tr[p].rm.add(w),tr[p].tot.add(w),tr[p].sum.add(w);
}
inline void pdown(int p){
	if(tag[p] != -inf){
		ptag(ls, tag[p]), ptag(rs, tag[p]);
		tag[p] = -inf;
	}
}
void build(int p,int l,int r){
	tag[p] = -inf;
	if(l == r){
		Func tmp = {1, a[l]};
		tr[p] = {tmp, tmp, tmp, tmp, inf};
		mn[p] = a[l], se[p] = inf;
		return ;
	}
	int mid = (l + r) >> 1;
	build(ls, l, mid), build(rs, mid+1, r);
	pup(p);
}
void defeat(int p,int l,int r,ll v){
	tag[p] = std::max(tag[p], v);
	if(v - mn[p] > tr[p].iter){
		int mid = (l + r) >> 1;
		defeat(ls, l, mid, v);
		defeat(rs, mid+1, r, v);
		pup(p);
	}else ptag(p, v);
}
void upd(int p,int l,int r,int L,int R,int k){
	if(mn[p] >= k)return ;
	if(L <= l && r <= R && k < se[p])return defeat(p, l, r, k);
	pdown(p);
	int mid = (l + r) >> 1;
	if(L <= mid)upd(ls, l, mid, L, R, k);
	if(mid < R)upd(rs, mid+1, r, L, R, k);
	pup(p);
}
node qry(int p,int l,int r,int L,int R){
	if(L <= l && r <= R)return tr[p];
	pdown(p); int mid = (l + r) >> 1;
	if(R <= mid)return qry(ls, l, mid, L, R);
	if(L > mid)return qry(rs, mid+1, r, L, R);
	return qry(ls, l, mid, L, R) + qry(rs, mid+1, r, L, R);
}
#undef ls
#undef rs
}using namespace KTT;


int main(){
	read(n), read(qcnt);
	rep(i, 1, n)read(a[i]);
	build(1, 1, n);
	int op, l, r, v;
	while(qcnt--){
		read(op);
		if(!op){
			read(l, r, v);
			upd(1, 1, n, l, r, v);
		}else{
			read(l, r);
			printf("%lld\n",max(0ll,qry(1, 1, n, l, r).tot.b));
		}
	}
	return 0;
}