PAT - 甲级 - 1064. Complete Binary Search Tree (30)(完全二叉搜索树层次遍历)
2017-11-09 14:05
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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:
Sample Output:
给定条件:
1.给定n个节点
2.这n个节点是属于一颗二叉搜索树的节点,并且这棵树是完全二叉树
要求:
1.这棵树的层次遍历结果
求解:
1.因为是二叉搜索树,所以将n个节点排序后可得到该二叉树中序遍历的结果
2.如果根节点的编号为x,那么它的左子树根节点是2*x,右子树根节点是2*x+1 (x!=0),编号顺序即层次遍历顺序
3.根据中序遍历结果,更新层次遍历中的节点信息
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
给定条件:
1.给定n个节点
2.这n个节点是属于一颗二叉搜索树的节点,并且这棵树是完全二叉树
要求:
1.这棵树的层次遍历结果
求解:
1.因为是二叉搜索树,所以将n个节点排序后可得到该二叉树中序遍历的结果
2.如果根节点的编号为x,那么它的左子树根节点是2*x,右子树根节点是2*x+1 (x!=0),编号顺序即层次遍历顺序
3.根据中序遍历结果,更新层次遍历中的节点信息
#include<cstdio> #include<algorithm> using namespace std; int n, id; int a[1005]; int ans[1005]; void dfs(int index){ if(index > n) return ; dfs(index*2); ans[index] = a[id++]; dfs(index*2+1); } int main(){ while(scanf("%d",&n) != EOF){ id = 1; for(int i = 1; i <= n; i++){ scanf("%d",&a[i]); } sort(a+1,a+n+1); dfs(1); for(int i = 1; i <= n; i++){ if(i!=1) printf(" "); printf("%d", ans[i]); } } return 0; }
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