总结-LCT
2024-10-20 13:43:28
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
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