前言
代码
P3369 【模板】普通平衡树 - 洛谷
package class150; // 替罪羊树的实现(java版) // 实现一种结构，支持如下操作，要求单次调用的时间复杂度O(log n) // 1，增加x，重复加入算多个词频 // 2，删除x，如果有多个，只删掉一个 // 3，查询x的排名，x的排名为，比x小的数的个数+1 // 4，查询数据中排名为x的数 // 5，查询x的前驱，x的前驱为，小于x的数中最大的数，不存在返回整数最小值 // 6，查询x的后继，x的后继为，大于x的数中最小的数，不存在返回整数最大值 // 所有操作的次数 <= 10^5 // -10^7 <= x <= +10^7 // 测试链接 : https://www.luogu.com.cn/problem/P3369 // 提交以下的code，提交时请把类名改成"Main"，可以通过所有测试用例 import java.io.BufferedReader; import java.io.IOException; import java.io.InputStreamReader; import java.io.OutputStreamWriter; import java.io.PrintWriter; import java.io.StreamTokenizer; import java.util.Arrays; public class Code02_ScapeGoat1 { // 平衡因子 public static double ALPHA = 0.7; // 空间的最大使用量 public static int MAXN = 100001; // 整棵树的头节点编号 public static int head = 0; // 空间使用计数 public static int cnt = 0; // 节点的key值 public static int[] key = new int[MAXN]; // 节点key的计数 public static int[] count = new int[MAXN]; // 左孩子 public static int[] left = new int[MAXN]; // 右孩子 public static int[] right = new int[MAXN]; // 数字总数 public static int[] size = new int[MAXN]; // 节点总数 public static int[] diff = new int[MAXN]; // 中序收集节点的数组 public static int[] collect = new int[MAXN]; // 中序收集节点的计数 public static int ci; // 最上方的不平衡节点 public static int top; // top的父节点 public static int father; // top是父节点的什么孩子，1代表左孩子，2代表右孩子 public static int side; public static int init(int num) { key[++cnt] = num; left[cnt] = right[cnt] = 0; count[cnt] = size[cnt] = diff[cnt] = 1; return cnt; } public static void up(int i) { size[i] = size[left[i]] + size[right[i]] + count[i]; diff[i] = diff[left[i]] + diff[right[i]] + (count[i] > 0 ? 1 : 0); } public static void inorder(int i) { if (i != 0) { inorder(left[i]); if (count[i] > 0) { collect[++ci] = i; } inorder(right[i]); } } public static int build(int l, int r) { if (l > r) { return 0; } int m = (l + r) / 2; int h = collect[m]; left[h] = build(l, m - 1); right[h] = build(m + 1, r); up(h); return h; } public static void rebuild() { if (top != 0) { ci = 0; inorder(top); if (ci > 0) { if (father == 0) { head = build(1, ci); } else if (side == 1) { left[father] = build(1, ci); } else { right[father] = build(1, ci); } } } } public static boolean balance(int i) { return ALPHA * diff[i] >= Math.max(diff[left[i]], diff[right[i]]); } public static void add(int i, int f, int s, int num) { if (i == 0) { if (f == 0) { head = init(num); } else if (s == 1) { left[f] = init(num); } else { right[f] = init(num); } } else { if (key[i] == num) { count[i]++; } else if (key[i] > num) { add(left[i], i, 1, num); } else { add(right[i], i, 2, num); } up(i); if (!balance(i)) { top = i; father = f; side = s; } } } public static void add(int num) { top = father = side = 0; add(head, 0, 0, num); rebuild(); } public static int small(int i, int num) { if (i == 0) { return 0; } if (key[i] >= num) { return small(left[i], num); } else { return size[left[i]] + count[i] + small(right[i], num); } } public static int rank(int num) { return small(head, num) + 1; } public static int index(int i, int x) { if (size[left[i]] >= x) { return index(left[i], x); } else if (size[left[i]] + count[i] < x) { return index(right[i], x - size[left[i]] - count[i]); } return key[i]; } public static int index(int x) { return index(head, x); } public static int pre(int num) { int kth = rank(num); if (kth == 1) { return Integer.MIN_VALUE; } else { return index(kth - 1); } } public static int post(int num) { int kth = rank(num + 1); if (kth == size[head] + 1) { return Integer.MAX_VALUE; } else { return index(kth); } } public static void remove(int i, int f, int s, int num) { if (key[i] == num) { count[i]--; } else if (key[i] > num) { remove(left[i], i, 1, num); } else { remove(right[i], i, 2, num); } up(i); if (!balance(i)) { top = i; father = f; side = s; } } public static void remove(int num) { if (rank(num) != rank(num + 1)) { top = father = side = 0; remove(head, 0, 0, num); rebuild(); } } public static void clear() { Arrays.fill(key, 1, cnt + 1, 0); Arrays.fill(count, 1, cnt + 1, 0); Arrays.fill(left, 1, cnt + 1, 0); Arrays.fill(right, 1, cnt + 1, 0); Arrays.fill(size, 1, cnt + 1, 0); Arrays.fill(diff, 1, cnt + 1, 0); cnt = 0; head = 0; } public static void main(String[] args) throws IOException { BufferedReader br = new BufferedReader(new InputStreamReader(System.in)); StreamTokenizer in = new StreamTokenizer(br); PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out)); in.nextToken(); int n = (int) in.nval; for (int i = 1, op, x; i <= n; i++) { in.nextToken(); op = (int) in.nval; in.nextToken(); x = (int) in.nval; if (op == 1) { add(x); } else if (op == 2) { remove(x); } else if (op == 3) { out.println(rank(x)); } else if (op == 4) { out.println(index(x)); } else if (op == 5) { out.println(pre(x)); } else { out.println(post(x)); } } clear(); out.flush(); out.close(); br.close(); } }
