Zoj 3765 Lights (stretching tree)

Test instructions: A row of lights have light and dark, each light has a value;

Five types of operations:

Q L R SS Seek the GCD of the light in the [L,r] interval in which the state is SS;

I I value SS inserts a value after the first light for the value state for the SS Light;

D I delete the first light;

R I change the state of the first light;

M I x change the value of the first light to X;

Reference: Http://wenku.baidu.com/link?url=EEwhlUPp2_U05mJEcbskt0_e3scLHpZ5gfS2s4OEvuAObTB2CgB4_TUroeccorOEGMxzzKk9SA_ Qt2w3k06xbg6p1qlpr8plgymusfhfocg

Idea: involving the insertion and deletion of arrays generally think of stretching tree splay, typical application; a binary search tree;

In order to make the whole search time smaller, those items with high frequency are often placed near the root of the tree. This is the advantage of stretching the tree; averaging complexity O (logn)

The core operation of the stretching tree is rotation, and each operation requires the number of operations to rotate to the ch[ch[root][1]][0] position near the root node;

Super-awesome data structure.

#include <cstdio>#include<cstring>#include<algorithm>using namespacestd;#defineKey_value Ch[ch[root][1]][0]Const intmaxn=500010;Const intinf=0x3f3f3f3f;intpre[maxn],ch[maxn][2],KEY[MAXN],SIZ[MAXN];//parent node, child node, number, subtree sizeintroot,tot1;intSUM0[MAXN],SUM1[MAXN];//current GCD for two statesintST[MAXN];//the on or off state of the nodeintS[maxn],tot2;//memory pool, capacityinta[maxn],status[maxn],n,q;Long LonggcdLong LongALong Longb) {  if(b==0)returnA; returnGCD (b,a%b);}voidNewNode (int&r,intFatherintKintSS) {//Establishing Nodes  if(Tot2) r=s[tot2--]; Elser=++tot1; PRE[R]=father; ch[r][0]=ch[r][1]=0; KEY[R]=k;//valueSt[r]=ss;//Light Status  if(ss==0) sum0[r]=k,sum1[r]=0; Elsesum0[r]=0, sum1[r]=K; SIZ[R]=1;}voidPushup (intR) {//Update parent node, update up    intlson=ch[r][0],rson=ch[r][1]; SIZ[R]=siz[lson]+siz[rson]+1; SUM0[R]=sum1[r]=0; SUM0[R]=gcd (Sum0[lson],sum0[rson]); SUM1[R]=gcd (Sum1[lson],sum1[rson]); if(St[r]) sum1[r]=gcd (Sum1[r],key[r]); Elsesum0[r]=gcd (Sum0[r],key[r]);}voidBuildint&x,intLintRintFather) {//two fork Tree achievements    if(L>r)return; intMid= (L+R)/2;    NewNode (X,father,a[mid],status[mid]); Build (ch[x][0],l,mid-1, x); Build (ch[x][1],mid+1, r,x); Pushup (x);}voidInit () {//InitializeRoot=tot1=tot2=0; ch[root][0]=ch[root][1]=siz[root]=pre[root]=0; Sum0[root]=sum1[root]=0; NewNode (Root,0,0,0); NewNode (ch[root][1],root,0,0);//establish the root node     for(intI=0; i<n;i++) scanf ("%d%d",&a[i],&Status[i]); Build (Key_value,0, N-1, ch[root][1]);//AchievementsPushup (ch[root][1]); Pushup (root);}voidRotate (intXintKind) {//Rotate    inty=Pre[x]; ch[y][!kind]=Ch[x][kind]; Pre[ch[x][kind]]=y; if(Pre[y]) ch[pre[y]][ch[pre[y]][1]==y]=x; PRE[X]=Pre[y]; Ch[x][kind]=y; Pre[y]=x; Pushup (y);}voidSplay (intRintGoal) {//stretching    while(pre[r]!=goal) {      if(pre[pre[r]]==goal) {Rotate (r,ch[pre[r]][0]==R); }      Else{        inty=Pre[r]; intkind=ch[pre[y]][0]==y; if(ch[y][kind]==R) {Rotate (R,!kind);        Rotate (R,kind); }        Else{Rotate (y,kind);        Rotate (R,kind);   }}} pushup (r); if(goal==0) root=R;}intGet_kth (intRintK) {//query in sequence traversal K large    intt=siz[ch[r][0]]+1; if(t==k)returnR; if(t>k)returnGet_kth (ch[r][0],k); Else returnGet_kth (ch[r][1],k-t);}voidInsert (intPosintValintSS) {splay (get_kth (Root,pos+1),0); Splay (get_kth (Root,pos+2), root); NewNode (key_value,ch[root][1],val,ss); Pushup (ch[root][1]); Pushup (root);}voidEraseintR) {   if(!R)return; s[++tot2]=R; Erase (ch[r][0]); Erase (ch[r][1]);}voidDelete (intPOS) {//Delete a nodeSplay (Get_kth (Root,pos),0); Splay (get_kth (Root,pos+2), root);   Erase (Key_value); Pre[key_value]=0; Key_value=0; Pushup (ch[root][1]); Pushup (root);}voidChangeintPOS) {//FlipSplay (Get_kth (Root,pos),0); Splay (get_kth (Root,pos+2), root); St[key_value]^=1;    Pushup (Key_value); Pushup (ch[root][1]); Pushup (root);}voidModifyintPosintVal) {//ModifySplay (Get_kth (Root,pos),0); Splay (get_kth (Root,pos+2), root); Key[key_value]=Val;    Pushup (Key_value); Pushup (ch[root][1]); Pushup (root);}intQueryintLintRintSS) {//Query GCD    intans; Splay (Get_kth (root,l),0); Splay (get_kth (Root,r+2), root); if(ss==0) ans=Sum0[key_value]; Elseans=Sum1[key_value]; if(ans==0) ans=-1; returnans;}intMain () {inti,j,k; Charch[ the];  while(SCANF ("%d%d", &n,&q)! =EOF)        {init ();  while(q--) {scanf ("%s", CH); if(ch[0]=='Q'){                intL,r,ss; scanf ("%d%d%d",&l,&r,&SS); printf ("%d\n", Query (L,R,SS)); }            Else if(ch[0]=='I'){                intPos,val,ss; scanf ("%d%d%d",&pos,&val,&SS);            Insert (POS,VAL,SS); }            Else if(ch[0]=='D'){                intPOS; scanf ("%d",&POS);            Delete (POS); }            Else if(ch[0]=='R'){                intPOS; scanf ("%d",&POS);            Change (POS); }            Else if(ch[0]=='M'){                intPos,val; scanf ("%d%d",&pos,&val);            Modify (Pos,val); }        }    }    return 0;}

Zoj 3765 Lights (stretching tree)