PAT A1064 Complete Binary Search Tree GO語言題解及注意事項
1064Complete Binary Search Tree(30分)
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 integerN(≤). ThenNdistinct 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
思路:
由於是完全二叉樹,所以可以用大小為n+1的陣列儲存,其下標為[1,n],Tree[i]的左子樹是Tree[2*i](右子樹是Tree[2*i+1]),當2*i(或2*i+1)>n時,說明Tree[i]沒有左子樹(右子樹)此時陣列的順序遍歷就是完全二叉樹的層序遍歷,並且我們可以得到該樹的形狀: 而該樹又是一顆二叉搜尋數,那麼他的中序遍歷就是一個遞增數列,由此得出,只要將給定序列由小到大排序,就得到了該樹的中序遍歷序列,中序遍歷該樹並將數的中序遍歷序列插入對應節點,即可得建樹;Solution(Golang):
package main import ( "fmt" "sort" ) var ( bts = make([]int, 10010) cnt = 0 n int nums = make([]int, 10010) ) func inorder(index int) { if index > n { return } inorder(index * 2) bts[index] = nums[cnt] cnt++ inorder(index*2 + 1) } func main() { fmt.Scan(&n) for i := 0; i < n; i++ { fmt.Scan(&nums[i]) } sort.Ints(nums[0:n]) inorder(1) for i := 1; i <= n; i++ { fmt.Print(bts[i]) if i < n { fmt.Print(" ") } } }