1064. Complete Binary Search Tree (30)

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.

10
1 2 3 4 5 6 7 8 9 0

6 3 8 1 5 7 9 0 2 4

思路

1.二叉搜索樹的中序遍歷是一個遞增的序列，所以先將輸入後的節點數組升序排序。
2.完全二叉樹以數組描述時，索引為i的節點的左右孩子的索引分別為2 * i和2 * i + 1。
3.將排好序的節點以中序遍歷的形式來構造完全二叉搜索樹。
4.遍歷構造好的數組即為這棵樹的層次遍歷

代碼

#include<iostream>
#include<algorithm>
#include<vector>
using namespace std;

const int MAX = 1010;
vector<int> nodes(MAX);
vector<int> tree(MAX);
int N,index;   //number of nodes && index of Nodes

void buildtree(int root)
{
    if(root > N)
        return;
    int left = root*2,right = root*2 + 1;
    buildtree(left);
    tree[root] = nodes[index++];
    buildtree(right);

}

int main()
{
   while(cin >> N)
   {
    //input
     for(int i = 1; i <= N;i++)
        cin >> nodes[i];
     sort(nodes.begin() + 1,nodes.begin() + 1 + N);
     //build tree
     index = 1;
     buildtree(1);

     //print tree
     cout << tree[1];
     for(int i = 2;i <= N;i++)
        cout <<" " << tree[i];
     cout << endl;
   }
}

PAT1064: Compelte Binary Search Tree