PAT-1064 Complete Binary Search Tree(完全二叉树)
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
题目大意:给出一个构成完全二叉树(除了最后一层的右边可能缺少部分节点,其余层均达到最大节点数)的序列,要求输出该完全二叉树的层次遍历。
主要思想:根据完全二叉树的特性可以用一个数组很方便的表示出来,将根节点的索引设为1,之后每个索引为i的节点,其左节点为2i,右节点为2i+1,然后对于输入的序列进行排序后按照中序遍历依次填入二叉树数组,这样完全二叉树就构造成功了,而最后一步的层次遍历输出其实就是对数组的顺序输出。
#include <cstdio>
#include <algorithm>
int n; //节点个数
int index = 0; //序列数组的索引
int a[1005]; //输入的序列数组
int node[1005]; //完全二叉树数组
using namespace std;
void travel(int i) {
if (i > n) return;
travel(2*i);
node[i] = a[index++];
travel(2*i+1);
}
int main(void) {
int i;
scanf("%d", &n);
for (i = 0; i < n; i++) {
scanf("%d", &a[i]);
}
sort(a, a+n);
travel(1); //中序遍历构造完全二叉树
//层次遍历输出
for (i = 1; i < n; i++)
printf("%d ", node[i]);
printf("%d\n", node[i]);
return 0;
}
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