luoguP3871 [TJOI2010]中位数

题目链接

luoguP3871 [TJOI2010]中位数

题解

平衡树

代码

#include<vector>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define LL long long
inline int read() {
    int x = 0,f = 1;char c = getchar();
    while(c < '0'||c > '9'){if(c == '-')f = -1;c = getchar();}
    while(c <= '9' &&c >= '0')x = x * 10 + c - '0',c = getchar();
    return x * f;
}
#define root ch[0][1]
const int maxn = 1000007;
int n,a[maxn],Num = 0,val[maxn],fa[maxn],siz[maxn],ch[maxn][2],num[maxn]; 

inline int ident(int x) { return x == ch[fa[x]][0] ? 0 : 1;  } 

inline void connect(int x,int y,int which) {fa[x] = y,ch[fa[x]][which] = x;} 

inline void update(int x) {
	siz[x] = siz[ch[x][1]] + siz[ch[x][0]] + num[x];
}
void rotate(int x) {
	int y = fa[x],z = fa[y];
	int yson = ident(x),zson = ident(y);
	int ixson = ch[x][yson ^ 1];
	connect(ixson,y,yson);
	connect(x,z,zson);
	connect(y,x,yson ^ 1);
	update(y); update(x);
}
void splay(int x,int to) {
	to = fa[to] ;
	while(fa[x] != to) {
		int y = fa[x];
		if(fa[y] == to) rotate(x);
		else if(ident(x) == ident(y)) rotate(y),rotate(x);
		else rotate(x),rotate(x);
		//rotate(x);
	}
}
int newnode(int Fa,int x) {
	val[++ Num] = x;
	fa[Num] = Fa;
	num[Num] = siz[Num] = 1; return Num;
}
void insert(int x) {
	if(!root) {root = newnode(0,x);return ;}
	int now = root;
	while(now ) {
		siz[now] ++;
		if(val[now] == x) {num[now] ++ ;return;}
		int nxt = val[now] < x ? 1 : 0;
		if(!ch[now][nxt] ){ch[now][nxt] = newnode(now,x); splay(ch[now][nxt],root);return;}
		now = ch[now][nxt];
	}
}
int Arank(int x) {
	int now = root;
	while(now) {
		int used = siz[now] - siz[ch[now][1]];
		if(x > siz[ch[now][0]] && x <= used) return val[now];
		if(used < x) x -= used,now = ch[now][1];
		else now = ch[now][0];
	}
}
int main() {
	n = read();
	for(int i = 1;i <= n;++ i) insert(read());
	int q = read();
	char op[10];
	for(int i = 1;i <= q;++ i) {
		scanf("%s",op + 1);
		if(op[1] == 'a') {
			insert(read()); n ++;
		} else {
			printf("%d\n",Arank(n / 2 + (n & 1)) );
		}
	}
	return 0;
}