pat-a1064. Complete Binary Search Tree (30)

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:

101 2 3 4 5 6 7 8 9 0

Sample Output:

6 3 8 1 5 7 9 0 2 4