PAT甲級1064

1064. Complete Binary Search Tree (30)

時間限制

100 ms

記憶體限制

65536 kB

代碼長度限制

16000 B

判題程式

Standard

作者

CHEN, Yue

A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:

• The left subtree of a node contains only nodes with keys less than the node's key.
• The right subtree of a node contains only nodes with keys greater than or equal to the node's key.
• Both the left and right subtrees must also be binary search trees.

A Complete Binary Tree (CBT) is a tree that is completely filled, with the possible exception of the bottom level, which is filled from left to right.

Now given a sequence of distinct non-negative integer keys, a unique BST can be constructed if it is required that the tree must also be a CBT. You are supposed to output the level order traversal sequence of this BST.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (<=1000). Then N distinct non-negative integer keys are given in the next line. All the numbers in a line are separated by a space and are no greater than 2000.

Output Specification:

For each test case, print in one line the level order traversal sequence of the corresponding complete binary search tree. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line.

Sample Input:

10

1 2 3 4 5 6 7 8 9 0

Sample Output:

6 3 8 1 5 7 9 0 2 4

#include<cstdio>
#include<algorithm>
#include<vector>
#include<queue>
using namespace std;
struct node
{
  int data;
  node*l, *r;
  node():l(NULL),r(NULL){}
};
void createCBT(node*&root,int N)
{
  queue<node*> Q;
  if (!root)
  {
    root = new node;
    N--;
    if (!N)
      return;
    Q.push(root);
  }
  while (!Q.empty())
  {
    node* t = Q.front();
    Q.pop();
    if (!t->l)
    {
      t->l = new node;
      Q.push(t->l);
      N--;
      if (!N)
        return;
    }
    if (!t->r)
    {
      t->r = new node;
      Q.push(t->r);
      N--;
      if (!N)
        return;
    }
  }
}
vector<int> v; int index = 0;
void inorder(node* &root)
{
  if (!root)
    return;
  inorder(root->l);
  root->data = v[index++];
  inorder(root->r);
}
void levelorder(node*root)
{
  queue<node*> Q;
  if (root)
  {
    printf("%d", root->data);
    Q.push(root);
  }
  while (!Q.empty())
  {
    node*f = Q.front();
    Q.pop();
    if (f->l)
    {
      printf(" %d", f->l->data);
      Q.push(f->l);
    }
    if (f->r)
    {
      printf(" %d", f->r->data);
      Q.push(f->r);
    }
  }
}
int main()
{
  int N;
  scanf("%d", &N);
  node*root = NULL;
  int t;
  for (int i = 0; i <N; i++)
  {
    scanf("%d", &t);
    v.push_back(t);
  }
  createCBT(root, N);//先造出未裝填資料的完全二叉樹
  sort(v.begin(), v.end());//利用BST的中序周遊是遞增序列
  inorder(root);//對完全二叉樹進行中序周遊并往其中填資料
  levelorder(root);
  return 0;
}