pat-a1064. Complete Binary Search Tree (30)

xiaoxiao2021-02-28  111

乍看一下30分还以为会写很多代码。这个题关键在于使用什么样的结构存储树。完全二叉树用数组直接存储,下标代表左右子女的位置。将题目的数字排序可以得到前序遍历,然后递归建树。数组里面的顺序就是层次遍历

#include<cstdio> #include<algorithm> using namespace std; int tree[1010]; int nu[1010]; int p=0,n; void creat(int root){ if(root*2<=n) creat(root*2); tree[root]=nu[p++]; if(root*2+1<=n) creat(root*2+1); } int main(){ scanf("%d",&n); for(int i=0;i<n;++i) scanf("%d",nu+i); sort(nu,nu+n); creat(1); printf("%d",tree[1]); for(int i=2;i<=n;++i) printf(" %d",tree[i]); return 0; }

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
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