总结-LCT

题单： https://www.zybuluo.com/xzyxzy/note/1027479

LuoguP3203 [HNOI2010]弹飞绵羊

动态加边，删边

#include <cstdio>
#include <iostream>
#include <cstring>
#include <algorithm>
#include <cmath>
#define R(a,b,c) for(register int a = (b); (a) <= (c); ++(a))
#define nR(a,b,c) for(register int a = (b); (a) >= (c); --(a))
#define Fill(a,b) memset(a, b, sizeof(a))
#define Swap(a,b) ((a) ^= (b) ^= (a) ^= (b))
#define ll long long
#define u32 unsigned int
#define u64 unsigned long long

//#define ON_DEBUGG

#ifdef ON_DEBUGG

#define D_e_Line printf("\n----------\n")
#define D_e(x) cout << (#x) << " : " << x << endl
#define Pause() system("pause")
#define FileOpen() freopen("in.txt", "r", stdin)
#define FileSave() freopen("out.txt", "w", stdout)
#include <ctime>
#define TIME() fprintf(stderr, "\ntime: %.3fms\n", clock() * 1000.0 / CLOCKS_PER_SEC)

#else

#define D_e_Line ;
#define D_e(x) ;
#define Pause() ;
#define FileOpen() ;
#define FileSave() ;
#define TIME() ;
//char buf[1 << 21], *p1 = buf, *p2 = buf;
//#define getchar() (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1 << 21, stdin), p1 == p2) ? EOF : *p1++)

#endif

using namespace std;
struct ios{
    template<typename ATP>inline ios& operator >> (ATP &x){
        x = 0; int f = 1; char ch;
        for(ch = getchar(); ch < '0' || ch > '9'; ch = getchar()) if(ch == '-') f = -1;
        while(ch >= '0' && ch <= '9') x = x * 10 + (ch ^ '0'), ch = getchar();
        x *= f;
        return *this;
    }
}io;

template<typename ATP>inline ATP Max(ATP a, ATP b){
    return a > b ? a : b;
}
template<typename ATP>inline ATP Min(ATP a, ATP b){
    return a < b ? a : b;
}
template<typename ATP>inline ATP Abs(ATP a){
    return a < 0 ? -a : a;
}

const int N = 200007;

int n;
int val[N];

struct Tree{
	int ch[2], fa, val, siz;
	bool rev;
}t[N];
#define ls t[u].ch[0]
#define rs t[u].ch[1]
#define root (n + 1)

inline bool Ident(int u) {
	return u == t[t[u].fa].ch[1];
}

inline bool IsRoot(int u) {
	return t[t[u].fa].ch[0] != u && t[t[u].fa].ch[1] != u;
}

inline void Pushup(int u) {
	t[u].siz = t[ls].siz + t[rs].siz + 1;
}

inline void Pushrev(int u) {
	Swap(ls, rs);
	t[u].rev ^= 1;
}

inline void Pushdown(int u) {
	if(!t[u].rev) return;
	if(ls) Pushrev(ls);
	if(rs) Pushrev(rs);
	t[u].rev = 0;
}

int sta[N], top;

inline void Rotate(int x) {
	int y = t[x].fa, z = t[y].fa, k = Ident(x);
	t[x].fa = z; if(!IsRoot(y)) t[z].ch[Ident(y)] = x;
	t[y].ch[k] = t[x].ch[k ^ 1], t[t[x].ch[k ^ 1]].fa = y;
	t[x].ch[k ^ 1] = y, t[y].fa = x;
	Pushup(y), Pushup(x);
}

inline void Splay(int u){
	int x = u;
	while(!IsRoot(u)){
		sta[++top] = u;
		u = t[u].fa;
	}
	sta[++top] = u;
	while(top) Pushdown(sta[top--]);
	while(!IsRoot(x)) {
		int y = t[x].fa;
		if(!IsRoot(y)){
			Ident(x) == Ident(y) ? Rotate(y) : Rotate(x);
		}
		Rotate(x);
	}
	Pushup(x);
}

inline void Access(int u) {
	for(register int v = 0; u; v = u, u = t[u].fa){
	 	Splay(u);
	 	t[u].ch[1] = v;
	 	Pushup(u);
	}
}

inline void MakeRoot(int u) {
	Access(u);
	Splay(u);
	Pushrev(u);
}

inline int FindRoot(int u) {
	Access(u);
	Splay(u);
	while(ls) u = ls;
	Splay(u);
	return u;
}

inline void Split(int u, int v) {
	MakeRoot(u);
	Access(v);
	Splay(v);
}

inline void Link(int u, int v) {
	Split(u, v);
	t[u].fa = v;
}

inline void Cut(int u, int v) {
	MakeRoot(u);
	if(FindRoot(v) == u && t[v].fa == u && !t[v].ch[0]){
		t[v].fa = t[u].ch[1] = 0;
		Pushup(u);
	}
}

inline void Modify(int u, int w) {
//	Access(u); // no access
	Splay(u);
	t[u].val = w;
	Pushup(u);
}

inline int Query(int u) {
	MakeRoot(u);
	Access(root);
	Splay(root);
	return t[root].siz - 1;
}

int main(){
FileOpen();
FileSave();
	int m;
	io >> n;
	R(i,1,n){
		io >> val[i];
		if(i + val[i] <= n)
			Link(i, i + val[i]);
		else
			Link(i, root);
	}

	io >> m;

	while(m--){
		int opt;
		io >> opt;
		if(opt == 1){
			int x;
			io >> x;
			++x;
			printf("%d\n", Query(x));
		}
		else{
			int x, w;
			io >> x >> w;
			++x;
			Cut(x, x + val[x] <= n ? x + val[x] : root);
			Modify(x, w);
			Link(x, x + w <= n ? x + w : root);
			val[x] = w;
		}
	}
	TIME();
	return 0;
}

LuoguP2387 [NOI2014]魔法森林

边权拆点两端，一维偏序排序，二维偏序类似\(Kruskal\)

#include <cstdio>
#include <iostream>
#include <cstring>
#include <algorithm>
#include <cmath>
#define R(a,b,c) for(register int a = (b); (a) <= (c); ++(a))
#define nR(a,b,c) for(register int a = (b); (a) >= (c); --(a))
#define Fill(a,b) memset(a, b, sizeof(a))
#define Swap(a,b) ((a) ^= (b) ^= (a) ^= (b))
#define ll long long
#define u32 unsigned int
#define u64 unsigned long long

#define ON_DEBUGG

#ifdef ON_DEBUGG

#define D_e_Line printf("\n----------\n")
#define D_e(x) cout << (#x) << " : " << x << endl
#define Pause() system("pause")
#define FileOpen() freopen("in.txt", "r", stdin)
#define FileSave() freopen("out.txt", "w", stdout)
#include <ctime>
#define TIME() fprintf(stderr, "\ntime: %.3fms\n", clock() * 1000.0 / CLOCKS_PER_SEC)

#else

#define D_e_Line ;
#define D_e(x) ;
#define Pause() ;
#define FileOpen() ;
#define FileSave() ;
#define TIME() ;
//char buf[1 << 21], *p1 = buf, *p2 = buf;
//#define getchar() (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1 << 21, stdin), p1 == p2) ? EOF : *p1++)

#endif

using namespace std;
struct ios{
    template<typename ATP>inline ios& operator >> (ATP &x){
        x = 0; int f = 1; char ch;
        for(ch = getchar(); ch < '0' || ch > '9'; ch = getchar()) if(ch == '-') f = -1;
        while(ch >= '0' && ch <= '9') x = x * 10 + (ch ^ '0'), ch = getchar();
        x *= f;
        return *this;
    }
}io;

template<typename ATP>inline ATP Max(ATP a, ATP b){
    return a > b ? a : b;
}
template<typename ATP>inline ATP Min(ATP a, ATP b){
    return a < b ? a : b;
}
template<typename ATP>inline ATP Abs(ATP a){
    return a < 0 ? -a : a;
}

const int N = 5e4 + 7;
const int M = 1e5 + 7;

struct Node{
	int x, y, valA, valB;
	bool operator < (const Node &com) const{
		if(valA != com.valA) return valA < com.valA;
		return valB < com.valB;
	}
}a[M];

int fa[N];
inline int Find(int x) {
	return x == fa[x] ? x : fa[x] = Find(fa[x]);
}

struct Tree{
	int ch[2], fa, val, mx; // mx : maxPos
	bool rev;
}t[N * 3];

#define ls t[u].ch[0]
#define rs t[u].ch[1]

inline int Ident(int u) {
	return t[t[u].fa].ch[1] == u;
}

inline bool IsRoot(int u) {
	return t[t[u].fa].ch[0] != u && t[t[u].fa].ch[1] != u;
}

inline void Pushup(int u) {
	t[u].mx = u;
	if(ls && t[t[ls].mx].val > t[t[u].mx].val) t[u].mx = t[ls].mx;
	if(rs && t[t[rs].mx].val > t[t[u].mx].val) t[u].mx = t[rs].mx;
}

inline void Pushrev(int u) {
	Swap(ls, rs);
	t[u].rev ^= 1;
}

inline void Pushdown(int u) {
	if(!t[u].rev) return;
	if(ls) Pushrev(ls);
	if(rs) Pushrev(rs);
	t[u].rev = 0;
}

inline void Rotate(int x) {
	int y = t[x].fa, z = t[y].fa, k = Ident(x);
	t[x].fa = z; if(!IsRoot(y)) t[z].ch[Ident(y)] = x;
	t[y].ch[k] = t[x].ch[k ^ 1], t[t[x].ch[k ^ 1]].fa = y;
	t[x].ch[k ^ 1] = y, t[y].fa = x;
	Pushup(y), Pushup(x);
}

int sta[N], top;

inline void Splay(int u) {
	int x = u;
	while(!IsRoot(u)){
		sta[++top] = u;
		u = t[u].fa; //
	}
	sta[++top] = u;
	while(top) Pushdown(sta[top--]);
	while(!IsRoot(x)){
		int y = t[x].fa;
		if(!IsRoot(y)){
			Ident(x) == Ident(y) ? Rotate(y) : Rotate(x);
		}
		Rotate(x);
	}
	Pushup(x);
}

inline void Access(int u) {
	for(register int v = 0; u; v = u, u = t[u].fa){ //
		Splay(u);
		t[u].ch[1] = v;
		Pushup(u);
	}
}

inline void MakeRoot(int u) {
	Access(u);
	Splay(u);
	Pushrev(u);
}

inline void Split(int u, int v) {
	MakeRoot(u);
	Access(v);
	Splay(v);
}

inline void Link(int u, int v) {
	Split(u, v);
	t[u].fa = v;
}

inline void Cut(int u, int v) {
	Split(u, v);
	t[u].fa = t[v].ch[1] = 0;
	Pushup(v);
}

int main() {
	int n, m;
	io >> n >> m;
	int tot = 0;
	R(i,1,m){
		int u, v, A, B;
		io >> u >> v >> A >> B;
		if(u == v) continue;
		a[++tot] = (Node){ u, v, A, B};
	}

	m = tot;
	sort(a + 1, a + m + 1);

	R(i,1,n) fa[i] = i; //
	R(i,n,n + m) t[i].val = a[i - n].valB;

	int ans = 0x7fffffff;

	R(i,1,m){

		int u = a[i].x, v = a[i].y;
		int p = Find(u), q = Find(v);
		if(p == q){
			Split(u, v);
			int j = t[v].mx - n;
			if(a[j].valB <= a[i].valB) continue;
			Cut(a[j].x, j + n), Cut(a[j].y, j + n);
			Link(u, i + n), Link(v, i + n);
		}
		else{
			fa[p] = q;
			Link(u, i + n), Link(v, i + n);
		}
		if(Find(1) == Find(n)){
			Split(1, n);
			int j = t[n].mx - n;
			ans = Min(ans, a[i].valA + a[j].valB);
		}
	}

	printf("%d", ans == 0x7fffffff ? -1 : ans);

	return 0;
}

LuoguP4234 最小差值生成树

“亲爱的边，你喜欢LCT维护吗”

“不喜欢呀”

“那你就tmd给我变成点吧”

“呜呜呜”

“排了你，从小往大单调着走”

“嘤嘤嘤”

“然后就是最小生成树，LCT版本的呢”

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#define R(a,b,c) for(register int a = (b); a <= (c); ++a)
#define nR(a,b,c) for(register int a = (b); a >= (c); --a)
#define Fill(a,b) memset(a, b, sizeof(a))
#define Swap(a,b) ((a) ^= (b) ^= (a) ^= (b))

#define ON_DEBUGG

#ifdef ON_DEBUGG

#define D_e_Line printf("\n-----------\n")
#define D_e(x) std::cout << (#x) << " : " <<x << "\n"
#define FileOpen() freopen("in.txt", "r", stdin)
#define FileSave() freopen("out.txt", "w", stdout)
#define Pause() system("pause")
#include <ctime>
#define TIME() fprintf(stderr, "\nTIME :　%.3lfms\n", clock() * 1000.0 / CLOCKS_PER_SEC)

#else

#define D_e_Line ;
#define D_e(x) ;
#define FileOpen() ;
#define FilSave ;
#define Pause() ;
#define TIME() ;

#endif

struct ios {
	template<typename ATP> ios& operator >> (ATP &x) {
		x = 0; int f = 1; char c;
		for(c = getchar(); c < '0' || c > '9'; c = getchar()) if(c == '-') f = -1;
		while(c >= '0' && c <= '9') x = x * 10 + (c ^ '0'), c = getchar();
		x *= f;
		return *this;
	}
}io;

using namespace std;

template<typename ATP> inline ATP Min(ATP a, ATP b) {
	return a < b ? a : b;
}
template<typename ATP> inline ATP Max(ATP a, ATP b) {
	return a > b ? a : b;
}
template<typename ATP> inline ATP Abs(ATP a) {
	return a < 0 ? -a : a;
}

const int N = 250007;

int n;

struct E {
	int x, y, w;
	bool operator < (const E &com) const {
		return w < com.w;
	}
} e[N];

struct Tree {
	int ch[2], fa, id;
	bool rev;
} t[N];
#define ls t[u].ch[0]
#define rs t[u].ch[1]

inline int Ident(int u) {
	return t[t[u].fa].ch[1] == u;
}

inline bool IsRoot(int u) {
	return t[t[u].fa].ch[1] != u && t[t[u].fa].ch[0] != u;
}

inline void Pushup(int u) {
	t[u].id = u;
    if(t[ls].id > n && (t[u].id <= n || t[u].id > t[ls].id)) t[u].id = t[ls].id;
    if(t[rs].id > n && (t[u].id <= n || t[u].id > t[rs].id)) t[u].id = t[rs].id;
}

inline void Pushrev(int u) {
	Swap(ls, rs);
	t[u].rev ^= 1;
}

inline void Pushdown(int u) {
	if(!t[u].rev) return;
	if(ls) Pushrev(ls);
	if(rs) Pushrev(rs);
	t[u].rev = 0;
}

inline void Rotate(int x) {
	int y = t[x].fa, z = t[y].fa, k = Ident(x);
	t[x].fa = z; if(!IsRoot(y)) t[z].ch[Ident(y)] = x;
	t[y].ch[k] = t[x].ch[k ^ 1], t[t[x].ch[k ^ 1]].fa = y;
	t[x].ch[k ^ 1] = y, t[y].fa = x;
	Pushup(y), Pushup(x);
}

int sta[N], top;

inline void Splay(int u) {
	int x = u;
	while(!IsRoot(u)){ //
		sta[++top] = u;
		u = t[u].fa;
	}
	sta[++top] = u;
	while(top) Pushdown(sta[top--]);
	while(!IsRoot(x)){
		int y = t[x].fa;
		if(!IsRoot(y)){
			Ident(x) == Ident(y) ? Rotate(y) : Rotate(x);
		}
		Rotate(x);
	}
	Pushup(x);
}

inline void Access(int u) {
	for(register int v = 0; u; v = u, u = t[u].fa){
		Splay(u);
		t[u].ch[1] = v;
		Pushup(u);
	}
}

inline void MakeRoot(int u) {
	Access(u);
	Splay(u);
	Pushrev(u);
}

inline int FindRoot(int u) {
	Access(u);
	Splay(u);
	while(ls) u = ls;
	Splay(u);
	return u;
}

inline void Split(int u, int v) {
	MakeRoot(u);
	Access(v);
	Splay(v);
}

inline void Link(int u, int v) {
	Split(u, v);
	t[u].fa = v;
}

inline bool Check(int x, int y) {
	MakeRoot(x);
	return FindRoot(y) != x;
}

int vis[N];
int main() {
	int m;
	io >> n >> m;
	int idx = n, ans = 0x7fffffff;

	R(i,1,m){
		io >> e[i].x >> e[i].y >> e[i].w;
	}

	sort(e + 1, e + m + 1);

	int tot = 1, l = 1;
	R(i,1,m){
		++idx;
		int x = e[i].x, y = e[i].y;
		if(x == y){
			vis[i] = 1;
			continue;
		}
		if(Check(x, y)){
			Link(x, idx), Link(idx, y);
			++tot;
		}
		else{
			Split(x, y);
			int root = t[y].id;
			vis[root - n] = 1;
			Splay(root);
			t[t[root].ch[0]].fa = t[t[root].ch[1]].fa = 0;
			Link(x, idx), Link(idx, y);
		}
		while(l < i && vis[l]) ++l;
		if(tot >= n) ans = Min(ans, e[i].w - e[l].w);
	}

	printf("%d", ans);

	return 0;
}

没看的了，咕了