二叉平衡树

  1 # include<iostream>

  2 # include<stdio.h>
  3 # include<algorithm>
  4 # include<string>
  5 using namespace std;
  6 /*建树的过程和二叉树大差不差*/
  7 const int  N = 100010, INF = 1e8;
  8 
  9 int n;
 10 struct node {
 11     int l, r;
 12     int key, val;
 13     int cnt, size;
 14 } tr[N];
 15 
 16 int root, idx;
 17 
 18 void pushup(int p) {
 19     tr[p].size = tr[tr[p].l].size + tr[tr[p].r].size + tr[p].cnt;
 20 }/*用子树的数据来维护父节点的数据*/
 21 
 22 int get_node(int key) {
 23     tr[++idx].key = key;
 24     tr[idx].val = rand();
 25     tr[idx].cnt = tr[idx].size = 1;
 26     return idx;
 27 }
 28 
 29 void zig(int &p) { /*右旋*/
 30     int q = tr[p].l;
 31     tr[p].l = tr[q].r;
 32     tr[q].r = p;
 33     p = q;
 34     pushup(tr[p].r), pushup(p);
 35 }
 36 
 37 void zag(int &p) { /*左旋*/
 38     int q = tr[p].r;
 39     tr[p].r = tr[q].l;
 40     tr[q].l  = p;
 41     p = q;
 42     pushup(tr[p].l), pushup(p); 
 43 }
 44 
 45 void build() {
 46     get_node(-INF), get_node(INF);
 47     root = 1;
 48     tr[1].r = 2;
 49     pushup(root);
 50     if (tr[1].val < tr[2].val) zag(root);
 51 }
 52 
 53 void insert(int &p, int key) {
 54     if (!p) p = get_node(key);
 55     else if (tr[p].key == key) tr[p].cnt++;
 56     else if (tr[p].key > key) {
 57         insert(tr[p].l, key);
 58         if (tr[tr[p].l].val > tr[p].val) zig(p);
 59     } else {
 60         insert(tr[p].r, key);
 61         if (tr[tr[p].r].val > tr[p].val) zag(p);
 62     }
 63     pushup(p);
 64 }
 65 
 66 void remove(int &p, int key) {
 67     if (!p) return;
 68     if (tr[p].key == key) {
 69         if (tr[p].cnt > 1)
 70             tr[p].cnt--;
 71         else if (tr[p].l || tr[p].r) {
 72             if (!tr[p].r || tr[tr[p].l].val > tr[tr[p].r].val) {
 73                 zig(p);
 74                 remove(tr[p].r, key);
 75             } else {
 76                 zag(p);
 77                 remove(tr[p].l, key);
 78             }
 79         } else p = 0;
 80     } else if (tr[p].key > key) remove(tr[p].l, key);
 81     else remove(tr[p].r, key);
 82     pushup(p);
 83 }
 84 
 85 int get_rank_by_key(int p, int key) {
 86     if (!p) return 0;
 87     if (tr[p].key == key) return tr[tr[p].l].size + 1;
 88     if (tr[p].key > key) return get_rank_by_key(tr[p].l, key);
 89     return tr[tr[p].l].size + tr[p].cnt + get_rank_by_key(tr[p].r, key);
 90 }
 91 
 92 int get_key_by_rank(int p, int rank) {
 93     if (!p) return INF;
 94     if (tr[tr[p].l].size >= rank) return get_key_by_rank(tr[p].l, rank);
 95     if (tr[tr[p].l].size + tr[p].cnt >= rank) return tr[p].key;
 96     return get_key_by_rank(tr[p].r, rank - tr[tr[p].l].size - tr[p].cnt);
 97 }
 98 
 99 int get_prev(int p, int key) {
100     if (!p) return -INF;
101     if (tr[p].key >= key) return get_prev(tr[p].l, key);
102     return max(tr[p].key, get_prev(tr[p].r, key));
103 }
104 
105 int get_next(int p, int key) {
106     if (!p) return INF;
107     if (tr[p].key <= key) return get_next(tr[p].r, key);
108     return min(tr[p].key, get_next(tr[p].l, key));
109 }
110 
111 int main() {
112     build();
113 
114     scanf("%d", &n);
115     while (n--) {
116         int op, x;
117         scanf("%d%d", &op, &x);
118         if (op == 1) insert(root, x);
119         else if (op == 2) remove(root, x);
120         else if (op == 3) printf("%d\n", get_rank_by_key(root, x) - 1);
121         else if (op == 4) printf("%d\n", get_key_by_rank(root, x + 1));
122         else if (op == 5) printf("%d\n", get_prev(root, x));
123         else printf("%d\n", get_next(root, x));
124     }
125 
126 
127 
128     return 0;
129 }