1064. Complete Binary Search Tree (30)
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题目如下:
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:101 2 3 4 5 6 7 8 9 0Sample Output:
6 3 8 1 5 7 9 0 2 4
题目要求对给定的序列建立完全二叉搜索树,所谓完全二叉搜索树就是要满足完全二叉树的搜索树。
我们知道,完全二叉树的结点i如果从1开始编号,那么左儿子为2*i,右儿子为2*i+1;而二叉搜索树的中序遍历为升序,因此只需要对输入序列按照升序排序,然后对完全二叉树进行中序遍历,填入相应的元素即可。
#include <iostream>#include <vector>#include <stdio.h>#include <algorithm>using namespace std;vector<int> tree;vector<int> nodes;int N;void buildTree(int root){ static int index = 1; if(root > N) return; buildTree(root * 2); tree[root] = nodes[index++]; buildTree(root * 2 + 1);}int main(){ cin >> N; nodes.resize(N+1); tree.resize(N+1); for(int i = 1; i <= N; i++){ scanf("%d",&nodes[i]); } sort(nodes.begin(),nodes.end()); buildTree(1); printf("%d",tree[1]); for(int i = 2; i <= N; i++) printf(" %d",tree[i]); cout << endl; return 0;}
- 1064. Complete Binary Search Tree (30)-PAT
- 1064. Complete Binary Search Tree (30)
- 【PAT】1064. Complete Binary Search Tree (30)
- 1064. Complete Binary Search Tree (30)
- 1064. Complete Binary Search Tree (30)
- 1064. Complete Binary Search Tree (30)
- 1064. Complete Binary Search Tree (30)
- 1064. Complete Binary Search Tree (30)
- 1064. Complete Binary Search Tree (30)
- 1064. Complete Binary Search Tree (30)
- 1064. Complete Binary Search Tree (30)
- 1064. Complete Binary Search Tree (30)
- 1064. Complete Binary Search Tree (30)
- PAT 1064. Complete Binary Search Tree (30)
- 1064. Complete Binary Search Tree (30)
- 1064. Complete Binary Search Tree (30)
- 1064. Complete Binary Search Tree (30)
- 1064. Complete Binary Search Tree (30)
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