【BIT套主席树】COGS257-动态排名系统

#include<iostream>
#include<cstdio>
#include<cstring>
#include<vector>
#include<algorithm>
#define lson l,m
#define rson m+1,r
using namespace std;
const int MAXN=60000+50;//注意要开60000，原来50000个数加修改操作中可能另外出现的10000个数
int n,q,tot,m,d;
struct node
{
int l,r,k,Q;
}op[MAXN];
int a[MAXN<<2],hash[MAXN<<2],T[MAXN<<2],S[MAXN<<2],use[MAXN<<2];
int L[MAXN<<5],R[MAXN<<5],sum[MAXN<<5];

int lowbit(int x)
{
return (x&(-x));
}

int build(int l,int r)
{
int rt=++tot;
sum[rt]=0;
if (l!=r)
{
int m=(l+r)>>1;
L[rt]=build(lson);
R[rt]=build(rson);
}
return rt;
}

int update(int pre,int l,int r,int x,int op)
{
int rt=++tot;
L[rt]=L[pre],R[rt]=R[pre],sum[rt]=sum[pre]+op;
if (l<r)
{
int m=(l+r)>>1;
if (x<=m) L[rt]=update(L[pre],lson,x,op);
else R[rt]=update(R[pre],rson,x,op);
}
return rt;
}

int Sum(int x)
{
int ret=0;
while (x>0)
{
ret+=sum[L[use[x]]];
x-=lowbit(x);
}
return ret;
}

int query(int Sl,int Sr,int Tl,int Tr,int l,int r,int k)
{
if (l==r) return l;
int m=(l+r)>>1;
int tmp=Sum(Sr)-Sum(Sl)+sum[L]-sum[L[Tl]];
if (tmp>=k)
{
for (int i=Sl;i;i-=lowbit(i)) use[i]=L[use[i]];
for (int i=Sr;i;i-=lowbit(i)) use[i]=L[use[i]];
return query(Sl,Sr,L[Tl],L,lson,k);
}
else
{
for (int i=Sl;i;i-=lowbit(i)) use[i]=R[use[i]];
for (int i=Sr;i;i-=lowbit(i)) use[i]=R[use[i]];
return query(Sl,Sr,R[Tl],R,rson,k-tmp);
}
}

void modify(int x,int p,int delta)
{
while (x<=n)
{
S[x]=update(S[x],1,d,p,delta);
x+=lowbit(x);
}
}

void init()
{
tot=0;
m=0;
d=0;
scanf("%d%d",&n,&q);
for (int i=1;i<=n;i++) scanf("%d",&a[i]),hash[++m]=a[i];
for (int i=0;i<q;i++)
{
char s[10];
scanf("%s",s);
if (s[0]=='Q')    scanf("%d%d%d",&op[i].l,&op[i].r,&op[i].k),op[i].Q=1;
else
{
scanf("%d%d",&op[i].l,&op[i].r);
op[i].Q=0;
hash[++m]=op[i].r;
}
}

sort(hash+1,hash+m+1);
d=unique(hash+1,hash+1+m)-hash-1;

T[0]=build(1,d);
for (int i=1;i<=n;i++)
{
int x=lower_bound(hash+1,hash+d+1,a[i])-hash;
T[i]=update(T[i-1],1,d,x,1);
}

for (int i=1;i<=n;i++) S[i]=T[0];
}

void solve()
{
//不要忘记了离散化之后的范围上界为d而不是m
for (int i=0;i<q;i++)
{
if (op[i].Q)
{
for (int j=op[i].l-1;j;j-=lowbit(j)) use[j]=S[j];
for (int j=op[i].r;j;j-=lowbit(j)) use[j]=S[j];
int ans=query(op[i].l-1,op[i].r,T[op[i].l-1],T[op[i].r],1,d,op[i].k);
printf("%d\n",hash[ans]);
}
else
{
int x=lower_bound(hash+1,hash+d+1,a[op[i].l])-hash;
int y=lower_bound(hash+1,hash+d+1,op[i].r)-hash;
modify(op[i].l,x,-1);
modify(op[i].l,y,1);
a[op[i].l] =op[i].r;
}
}
}

int main()
{
freopen("dynrank.in","r",stdin);
freopen("dynrank.out","w",stdout);
int T;
scanf("%d",&T);
while (T--)
{
init();
solve();
}
return 0;
}