【BZOJ 3224】 普通平衡树

【题目链接】

          点击打开链接

【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() {
        read(N);
        while (N--) {
                read(opt); read(x);
                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;
    
}