# 【BZOJ 3224】 普通平衡树

【题目链接】

【算法】

本题是Splay模板题，值得一做！

【代码】

#include<bits/stdc++.h>
using namespace std;
#define MAXN 100000

int N,opt,x;

template <typename T> inline void read(T &x) {
int f = 1; x = 0;
char c = getchar();
for (; !isdigit(c); c = getchar()) { if (c == '-') f = -f; }
for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0';
x *= f;
}

template <typename T> inline void write(T x) {
if (x < 0) { putchar('-'); x = -x; }
if (x > 9) write(x/10);
putchar(x%10+'0');
}

template <typename T> inline void writeln(T x) {
write(x);
puts("");
}

struct Splay {
int root,total;
struct Node {
int fa,son[2],val,cnt,size;
} Tree[MAXN+10];
bool get(int x) {
return Tree[Tree[x].fa].son[1] == x;
}
inline void new_node(int index,int f,int x) {
Tree[index].fa = f;
Tree[index].son[0] = Tree[index].son[1] = 0;
Tree[index].val = x;
Tree[index].cnt = Tree[index].size = 1;
}
inline void update(int index) {
Tree[index].size = Tree[index].cnt;
Tree[index].size += Tree[Tree[index].son[0]].size;
Tree[index].size += Tree[Tree[index].son[1]].size;
}
inline void rotate(int x) {
int f = Tree[x].fa,g = Tree[f].fa,
tmpx = get(x),tmpf = get(f);
if (!f) return;
Tree[f].son[tmpx] = Tree[x].son[tmpx^1];
if (Tree[x].son[tmpx^1]) Tree[Tree[x].son[tmpx^1]].fa = f;
Tree[x].son[tmpx^1] = f;
Tree[f].fa = x;
Tree[x].fa = g;
if (g) Tree[g].son[tmpf] = x;
update(f);
update(x);
}
inline void splay(int x) {
int f;
for (f = Tree[x].fa; (f = Tree[x].fa); rotate(x))
rotate((get(x) == get(f)) ? (f) : (x));
root = x;
}
inline void Insert(int x) {
int index = root;
bool tmp;
if (!root) {
new_node(++total,0,x);
root = total;
return;
}
while (true) {
if (Tree[index].val == x) {
++Tree[index].cnt;
splay(index);
return;
}
tmp = Tree[index].val < x;
if (!Tree[index].son[tmp]) {
new_node(++total,index,x);
Tree[index].son[tmp] = total;
splay(total);
return;
} else index = Tree[index].son[tmp];
}
}
inline int query_max(int index) {
while (true) {
if (!Tree[index].son[1]) return index;
index = Tree[index].son[1];
}
}
inline int query_min(int index) {
while (true) {
if (!Tree[index].son[0]) return index;
index = Tree[index].son[0];
}
}
inline void join(int x,int y) {
int pos = query_max(x);
splay(pos);
Tree[pos].son[1] = y;
Tree[y].fa = pos;
}
inline void erase(int x) {
int index = root;
bool tmp;
while (true) {
if (Tree[index].val == x) {
if (Tree[index].cnt > 1) {
--Tree[index].cnt;
splay(index);
return;
}
splay(index);
break;
}
tmp = Tree[index].val < x;
index = Tree[index].son[tmp];
}
if ((!Tree[index].son[0]) && (!Tree[index].son[1])) {
root = 0;
return;
}
if (!Tree[index].son[0]) {
root = Tree[index].son[1];
Tree[root].fa = 0;
return;
}
if (!Tree[index].son[1]) {
root = Tree[index].son[0];
Tree[root].fa = 0;
return;
}
join(Tree[index].son[0],Tree[index].son[1]);
}
inline int query_rank(int x) {
int index = root,ans=1;
while (true) {
if (Tree[index].val <= x) {
ans += Tree[Tree[index].son[0]].size;
if (Tree[index].val == x) {
splay(index);
return ans;
}
ans += Tree[index].cnt;
index = Tree[index].son[1];
} else index = Tree[index].son[0];
}
}
inline int rank(int x) {
int index = root;
while (true) {
if (x <= Tree[Tree[index].son[0]].size) index = Tree[index].son[0];
else {
x -= Tree[Tree[index].son[0]].size;
if (x <= Tree[index].cnt) {
splay(index);
return Tree[index].val;
}
x -= Tree[index].cnt;
index = Tree[index].son[1];
}
}
}
inline int pred(int x) {
int ans;
Insert(x);
ans = Tree[query_max(Tree[root].son[0])].val;
erase(x);
return ans;
}
inline int succ(int x) {
int ans;
Insert(x);
ans = Tree[query_min(Tree[root].son[1])].val;
erase(x);
return ans;
}
} T;

int main() {
while (N--) {
if (opt == 1) T.Insert(x);
else if (opt == 2) T.erase(x);
else if (opt == 3) writeln(T.query_rank(x));
else if (opt == 4) writeln(T.rank(x));
else if (opt == 5) writeln(T.pred(x));
else if (opt == 6) writeln(T.succ(x));
}

return 0;

}

posted @ 2018-02-27 20:52  evenbao  阅读(194)  评论(0编辑  收藏  举报