poj3580:SuperMemo（块状链表/Splay）

传送门

题意：

题目要求实现一种数据结构，支持6种操作：
add x,y D：第x个数到第y个数之间的数每个加D；
reverse x y：第x个数到第y个数之间全部数翻转；
revolve x y T：第x个数到第y个数之间的数，向后循环流动T次，即后面T个数变成这段子序列的最前面T个，前面的被挤到后面。
Insert x P：在第x个数后面插入一个数P。
Delete x：删除第x个数。
Min x，y：求第x个数到第y个数之间的最小数字。

题解

1.块状链表。这是很好想而且很好写的，全是暴力操作。感兴趣的可以自己学习学习。（1400ms）

2.Splay。虽然时间复杂度比块状链表优（1087ms，其实也没优什么，主要是Splay常数大），但是代码特别长（块状链表250行，Splay400行）。用Splay主要注意两点，一是打标记（Add，Reverse操作），二是提取区间（即要操作的区间），提取方法很简单，将区间前一位置于rt,将区间后一位置于rt的右儿子，那么对rt右儿子的左儿子操作即可。

主要是Revolve操作有点难写，下面给出做法：

很显然是将[r-c+1,r]的区间提取到[l,r-c]之前，那么先提取前面的区间，再将l-1置为根节点，将l置为l-1的右儿子，将刚才提取的区间置为l左儿子即可。

（注意判断边界以及及时更新。。。）

Code1（块状链表）：1454MS

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
#include <cmath>
using namespace std; inline int read();
const int N = 1e5 + 5, INF = 0x7fffffff, SIZEINT = sizeof(int);
const int SQRTN = 500, B = 1000, SMIN = SQRTN / 2, SMAX = SQRTN * 2;
int n, m, a[N]; typedef struct Block* PBlock;
typedef struct List* PList;
struct Block
{ int a[SQRTN * 5]; int size, tag, rev, ans; inline void calc() { tag = rev = 0; ans = INF; for (int i = 0; i < size; ++i) if (a[i] < ans) ans = a[i]; } inline void downdate() { if (tag != 0){ for (int i = 0; i < size; ++i)a[i] += tag; tag = 0; } if (rev){ rev = 0; for (int i = 0; i << 1 < size; ++i){ int t = a[i]; a[i] = a[size - i - 1]; a[size - i - 1] = t; } } }
}used[B]; PBlock pool, *top, unused[B];
struct List
{ PBlock a; PList last, next;
}USED[B]; PList head, tail, POOL, *TOP, UNUSED[B]; inline PBlock newBlock()
{ if (top != unused) return *--top; return pool++;
} inline void delBlock(PBlock x)
{ *top++ = x;
} inline PList newList()
{ if (TOP != UNUSED) return *--TOP; return POOL++;
} inline void delList(PList x)
{ *TOP++ = x;
} inline void Build(int *a, const int &n, PList *h, PList *t)
{ for (int i = 0; i < n; i += SQRTN) { PList p = newList(); p->a = newBlock(); p->a->size = i + SQRTN < n ? SQRTN : n - i; memcpy(p->a->a, a + i, SIZEINT * p->a->size); p->a->calc(); p->last = *t; p->next = NULL; if (*t != NULL) (*t)->next = p; else *h = p; *t = p; }
} inline void merge(PList x)
{ PList p = x->next; x->a->downdate(); p->a->downdate(); memcpy(x->a->a + x->a->size, p->a->a, SIZEINT * p->a->size); x->a->size += p->a->size; x->a->calc(); x->next = p->next; if (p->next) p->next->last = x; else tail = x; delBlock(p->a); delList(p);
} inline void split(PList x, const int &n)
{ PList p = newList(); p->a = newBlock(); x->a->downdate(); p->a->size = x->a->size - n; memcpy(p->a->a, x->a->a + n, SIZEINT * p->a->size); x->a->size = n; x->a->calc(); p->a->calc(); p->next = x->next; if (x->next) x->next->last = p; else tail = p; x->next = p; p->last = x;
} inline void Balance()
{ for (PList p = head; p; p = p->next) { while (p != tail && p->a->size < SMIN)merge(p); if (p->a->size > SMAX)split(p, SQRTN); }
} inline void Delete(PList x)
{ if (x->last != NULL) x->last->next = x->next; else head = x->next; if (x->next != NULL) x->next->last = x->last; else tail = x->last; delBlock(x->a); delList(x);
} inline PList findl(int n)
{ PList p = head; for (; n > p->a->size; p = p->next) n -= p->a->size; if (n != 1) { split(p, n - 1); p = p->next; } return p;
} inline PList findr(int n)
{ PList p = head; for (; n > p->a->size; p = p->next) n -= p->a->size; if (n != p->a->size) split(p, n); return p;
} inline void Init()
{ pool = used; POOL = USED; top = unused; TOP = UNUSED; head = tail = NULL;
} char ch;
inline int read()
{ int res = 0, sgn = 0; while (ch = getchar(), ch < '0' || ch > '9') if (ch == '-') sgn = 1; res = ch - 48; while (ch = getchar(), ch >= '0' && ch <= '9') res = res * 10 + ch - 48; return sgn ? -res : res;
} int main()
{ Init(); n = read(); for (int i = 0; i < n; ++i) a[i] = read(); Build(a, n, &head, &tail); m = read(); char type; int l, r, v; PList fr, en, t; PBlock tmp; while (m--) { Balance(); while (type = getchar(), type < 'A' || type > 'Z'); if (type == 'A') { l = read(); r = read(); v = read(); if (l > r) swap(l, r); fr = findl(l); en = findr(r); for (en = en->next; fr != en; fr = fr->next) { fr->a->tag += v; fr->a->ans += v; } } else if (type == 'I') { l = read(); r = read(); fr = findr(l); fr->a->downdate(); fr->a->a[fr->a->size++] = r; if (r < fr->a->ans) fr->a->ans = r; } else if (type == 'D') { l = read(); fr = findl(l); if (fr->a->size != 1) split(fr, 1); Delete(fr); } else if (type == 'M') { l = read(); r = read(); if (l > r) swap(l, r); fr = findl(l); en = findr(r); int ans = INF; for (en = en->next; fr != en; fr = fr->next) if (fr->a->ans < ans) ans = fr->a->ans; printf("%d\n", ans); } else { getchar(); getchar(); type = getchar(); if (type == 'E') { l = read(); r = read(); if (l > r) swap(l, r); fr = findl(l); en = findr(r); while (fr != en && fr != en->next) { fr->a->rev ^= 1; en->a->rev ^= 1; tmp = fr->a; fr->a = en->a; en->a = tmp; fr = fr->next; en = en->last; } if (fr == en) fr->a->rev ^= 1; } else { l = read(); r = read(); if (l > r) swap(l, r); v = read() % (r - l + 1); if (v == 0 || l == r) continue; v = r - l + 1 - v; fr = findl(l); en = findr(r); for (t = fr; v > t->a->size; t = t->next) v -= t->a->size; if (v != t->a->size) { split(t, v); if (en == t) en = en->next; } PList p1 = fr->last, p2 = fr, p3 = t, p4 = t->next, p5 = en, p6 = en->next; if (p1 != NULL) { p1->next = p4; p4->last = p1; } else head = p4, p4->last = NULL; if (p6 != NULL){ p6->last = p3; p3->next = p6; } else tail = p3, p3->next = NULL; p5->next = p2; p2->last = p5; } } } return 0;
}

Code2（Splay）:1047ms

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<string>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
const int Maxn=2e5+50;
const int INF=0x3f3f3f3f;
inline int read()
{char ch=getchar();int i=0,f=1;while(!isdigit(ch)){if(ch=='-')f=-1;ch=getchar();}while(isdigit(ch)){i=(i<<1)+(i<<3)+ch-'0';ch=getchar();}return i*f;
}struct node
{node *fa,*lc,*rc;int val,taga,tagr,mn,sze;node():fa(NULL),lc(NULL),rc(NULL){}inline void upt(){sze=(lc?lc->sze:0)+(rc?rc->sze:0)+1;mn=min(val,min(lc?lc->mn:INF,rc?rc->mn:INF));}
}POOL[Maxn],*pool=POOL,*rt,*que[Maxn];int n,m,a[Maxn],bg,ed;
char ch[10];inline void add(node *now,int val)
{now->val+=val;now->mn+=val;now->taga+=val;
}inline void addr(node *now)
{swap(now->lc,now->rc);now->tagr^=1;
}inline node* newnode(int val)
{++pool;pool->val=val;pool->mn=val;pool->sze=1;return pool;
}inline void build(node *&now,int l,int r)
{int mid=(l+r)>>1;now=newnode(a[mid]);if(l<mid)build(now->lc,l,mid-1);if(r>mid)build(now->rc,mid+1,r);if(now->lc)now->lc->fa=now;if(now->rc)now->rc->fa=now;now->upt();
}inline void pushdown(node *now)
{if(now->taga){if(now->lc){now->lc->mn+=now->taga;now->lc->val+=now->taga;now->lc->taga+=now->taga;}if(now->rc){now->rc->mn+=now->taga;now->rc->val+=now->taga;now->rc->taga+=now->taga;}now->taga=0;}if(now->tagr){if(now->lc){swap(now->lc->lc,now->lc->rc);now->lc->tagr^=1;}if(now->rc){swap(now->rc->lc,now->rc->rc);now->rc->tagr^=1;}now->tagr^=1;   }
}inline node* find(node *now,int k)
{pushdown(now);now->upt();if((now->lc?now->lc->sze:0)==k-1)return now;else if((now->lc?now->lc->sze:0)>k-1)return find(now->lc,k);else return find(now->rc,k-(now->lc?now->lc->sze:0)-1);
}inline void Rotate(node *x)
{node *y=x->fa,*z=y->fa;y->fa=x;x->fa=z;if(z){((z->lc==y)?(z->lc):(z->rc))=x;}if(y->lc==x){node* b=x->rc;if(b)b->fa=y;y->lc=b;x->rc=y;}else{node* b=x->lc;if(b)b->fa=y;y->rc=b;x->lc=y;}y->upt();x->upt();
}inline bool which(node* x)
{return x->fa->lc==x;
}inline void Splay(node* x,node* tar=NULL)
{que[ed=1]=x;for(node* y=x;y!=rt;y=y->fa)que[++ed]=y->fa;for(int i=ed;i>=1;i--){node* y=que[i];pushdown(y);}while(x->fa!=tar){node* y=x->fa,*z=y->fa;if(z!=tar){if(which(x)^which(y))Rotate(x);else Rotate(y);}Rotate(x);}if(!tar)rt=x;
}inline node* split(int l,int r)
{if(l&&r<=n){node *t1=find(rt,l);node *t2=find(rt,r);Splay(t1);Splay(t2,rt);node *t3=t2->lc;t2->lc=NULL;t2->upt();t3->fa=NULL;return t3;}else if(!l){node *t2=find(rt,r);Splay(t2);node *t3=t2->lc;t2->lc=NULL;t2->upt();t3->fa=NULL;return t3;}else{node *t1=find(rt,l);Splay(t1);node *t3=t1->rc;t3->fa=NULL;t1->rc=NULL;t1->upt();return t3;}
}int buf[50];
inline void W(int x)
{if(!x){putchar('0');return;}if(x<0)putchar('-'),x=-x;while(x)buf[++buf[0]]=x%10,x/=10;while(buf[0])putchar('0'+buf[buf[0]--]);return;
}int main()
{n=read();for(int i=1;i<=n;i++){a[i]=read();}build(rt,1,n);m=read();while(m--){scanf("%s",ch+1);if(ch[1]=='A'){int l=read(),r=read(),v=read();if(l==1&&r==n)add(rt,v);else if(l==1){node* t2=find(rt,r+1);Splay(t2);add(rt->lc,v);rt->upt();}else if(r==n){node* t1=find(rt,l-1);Splay(t1);add(rt->rc,v);rt->upt();}else {node* t1=find(rt,l-1);node* t2=find(rt,r+1);Splay(t1);Splay(t2,rt);add(t2->lc,v);t2->upt();t1->upt();}}else if(ch[1]=='I'){int x=read(),y=read();if(x!=0&&x!=n){node* t1=find(rt,x);node* t2=find(rt,x+1);Splay(t1);Splay(t2,rt);t2->lc=newnode(y);t2->lc->fa=t2;t2->upt();t1->upt();n++;}else if(x!=0){node* t1=find(rt,x);Splay(t1);t1->rc=newnode(y);t1->rc->fa=t1;t1->upt();n++;}else{node* t2=find(rt,x+1);t2->lc=newnode(y);t2->lc->fa=t2;t2->upt();n++;}       }else if(ch[1]=='D'){int pos=read();if(pos!=1&&pos!=n){node* t1=find(rt,pos-1);node* t2=find(rt,pos+1);Splay(t1);Splay(t2,rt);t2->lc->fa=NULL;t2->lc=NULL;t2->upt();rt->upt();n--;}else if(pos!=1){node* t1=find(rt,pos-1);Splay(t1);t1->rc->fa=NULL;t1->rc=NULL;t1->upt();n--;}else{node* t2=find(rt,pos+1);Splay(t2);t2->lc->fa=NULL;t2->lc=NULL;t2->upt();n--;}}else if(ch[1]=='M'){int l=read(),r=read();if(l==1&&r==n)W(rt->mn),putchar('\n');else if(l==1){node* t2=find(rt,r+1);Splay(t2);W(rt->lc->mn),putchar('\n');}else if(r==n){node* t1=find(rt,l-1);Splay(t1);W(rt->rc->mn),putchar('\n');}else {node* t1=find(rt,l-1);node* t2=find(rt,r+1);Splay(t1);Splay(t2,rt);W(t2->lc->mn),putchar('\n');}}else if(ch[4]=='E'){int l=read(),r=read();if(l==1&&r==n)addr(rt);else if(l==1){node* t2=find(rt,r+1);Splay(t2);addr(rt->lc);}else if(r==n){node* t1=find(rt,l-1);Splay(t1);addr(rt->rc);}else {node* t1=find(rt,l-1);node* t2=find(rt,r+1);Splay(t1);Splay(t2,rt);addr(t2->lc);}}else{int x=read(),y=read(),c=read();int l=(y-x+1);c%=l;if(c==0)continue;node* t1=split(y-c,y+1);if(x!=1){node* t2=find(rt,x-1);node* t3=find(rt,x);Splay(t2);Splay(t3,rt);t3->lc=t1;t1->fa=t3;t3->upt();t2->upt();}else{node* t3=find(rt,x);Splay(t3);t3->lc=t1;t1->fa=t3;t3->upt();}}}
}

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poj3580:SuperMemo（块状链表/Splay）

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