题目链接：http://www.lydsy.com/JudgeOnline/problem.php?id=3224
!解锁新技能：替罪羊树
一道无论平衡树是否平衡都可以过的题
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#include<bits/stdc++.h> #define MAXN 100010 #define inf 1000000007 typedef long long ll; typedef double db; using namespace std; inline int rd(){ int x=0,y=1;char c=getchar(); while(c<'0' || c>'9'){if(c=='-')y=-y;c=getchar();} while(c>='0'&&c<='9')x=x*10+c-'0',c=getchar(); return x*y; } int nums[MAXN]; struct ScapeGoatTree{ int son[MAXN][2],sz[MAXN],fa[MAXN],key[MAXN]; int root,tot,sum; db alpha; void init(){ sum=0; alpha=0.75; tot=2,root=1; key[1]=-inf,sz[1]=2,son[1][1]=2,fa[1]=0; key[2]=inf,sz[2]=1,fa[2]=1; } int getlr(int x){ return son[fa[x]][1]==x; } bool balance(int x){ return (db)sz[x]*alpha>=(db)sz[son[x][0]] && (db)sz[x]*alpha>=(db)sz[son[x][1]]; } void dfs(int x){ if(!x)return; dfs(son[x][0]); nums[++sum]=x; dfs(son[x][1]); } int build(int l,int r){ if(l>r)return 0; int mid=(l+r)/2,tmp=nums[mid]; fa[son[tmp][0]=build(l,mid-1)]=tmp; fa[son[tmp][1]=build(mid+1,r)]=tmp; sz[tmp]=sz[son[tmp][0]]+sz[son[tmp][1]]+1; return tmp; } void rebuild(int x){ sum=0;dfs(x); int which=getlr(x),f=fa[x]; int tmp=build(1,sum); fa[tmp]=f; son[f][which]=tmp; if(root==x)root=tmp; } void ins(int x){ int tmp=root,f=0; key[++tot]=x,sz[tot]=1; while(tmp){ sz[tmp]++; f=tmp; tmp=son[tmp][key[tmp]<=x]; if(!tmp){ fa[tot]=f; son[f][key[f]<=x]=tot; break; } } int reb=0; for(int i=tot; i; i=fa[i])if(!balance(i))reb=i; if(reb)rebuild(reb); } int findrk(int x){ int tmp=root,ret=0; while(tmp){ if(key[tmp]>=x)tmp=son[tmp][0]; else ret+=sz[son[tmp][0]]+1,tmp=son[tmp][1]; } return ret; } int findkth(int x){ int tmp=root; while(tmp){ if(sz[son[tmp][0]]==x-1)break; else if(sz[son[tmp][0]]>=x)tmp=son[tmp][0]; else x-=sz[son[tmp][0]]+1,tmp=son[tmp][1]; } return key[tmp]; } int getnum(int x){ int tmp=root; while(tmp){ if(key[tmp]==x)return tmp; tmp=son[tmp][key[tmp]<x]; } } int pre(int x){ int tmp=root,ret=-inf; while(tmp){ if(key[tmp]<x)ret=max(ret,key[tmp]),tmp=son[tmp][1]; else tmp=son[tmp][0]; } return ret; } int nxt(int x){ int tmp=root,ret=inf; while(tmp){ if(key[tmp]>x)ret=min(ret,key[tmp]),tmp=son[tmp][0]; else tmp=son[tmp][1]; } return ret; } void del(int x){ x=getnum(x); if(son[x][0] && son[x][1]){ int tmp=son[x][0]; while(son[tmp][1])tmp=son[tmp][1]; key[x]=key[tmp]; x=tmp; } int ss=son[x][0]?son[x][0]:son[x][1],which=getlr(x); son[fa[x]][which]=ss; fa[ss]=fa[x]; for(int i=x; i; i=fa[i])sz[i]--; if(x==root)root=ss; } }tree; int main(){ int n=rd(); tree.init(); while(n--){ int op=rd(),x=rd(); if(op==1)tree.ins(x); if(op==2)tree.del(x); if(op==3)printf("%d\n",tree.findrk(x)); if(op==4)printf("%d\n",tree.findkth(x+1)); if(op==5)printf("%d\n",tree.pre(x)); if(op==6)printf("%d\n",tree.nxt(x)); } return 0; } |
太神辣QwQ
orz orz
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