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  • 1064 Complete Binary Search Tree (30 分)完全二叉树

    1064 Complete Binary Search Tree (30 分)

    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 NNN (≤1000le 10001000). Then NNN 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
    思路:
      由于要输出的是一个完全二叉树且是二叉搜索树。所以使用顺序表存储,对各个顶点的编号方法是自左到右,自上而下。所以
    只需要在建立树以后,遍历数组输出即可,当然使用标准的二叉树层次遍历算法也可以。建立树的方法使用中序遍历,因为二叉搜
    索树的中序遍历结果是有序的。
    #include<iostream>
    #include<vector>
    #include<algorithm>
    #include<queue>
    #include<string>
    #include<map>
    #include<set>
    using namespace std;
    int k=1;
    void create(int tree[],int root,int n,int a[])
    {
        if(root>n)
            return;
        create(tree,2*root,n,a);
        tree[root]=a[k++];
        create(tree,2*root+1,n,a);
    }
    
    void level(int tree[],int n)
    {
        queue<int> qu;
        qu.push(1);
        cout<<tree[1];
        while(!qu.empty())
        {
            int temp=qu.front();
            qu.pop();
            if(2*temp<=n)
            {
                qu.push(2*temp);
                cout<<" "<<tree[2*temp];
            }
            if(2*temp+1<=n)
            {
                qu.push(2*temp+1);
                cout<<" "<<tree[2*temp+1];
            }
        }
    }
    
    
    int main()
    {
        int n;
        cin>>n;
        int a[n+1];
        for(int i=1;i<n+1;i++)
            cin>>a[i];
        sort(a+1,a+n+1);
        int tree[n+1];
        create(tree,1,n,a);
        //level(tree,n);
        cout<<tree[1];
        for(int i=2;i<n+1;i++)
            cout<<" "<<tree[i];
        return 0;
    }
     
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  • 原文地址:https://www.cnblogs.com/zhanghaijie/p/10308327.html
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