【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() { 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; }
