Description
Binary Search Tree, abbreviated as BST, is a kind of binary tree maintains the following property:
- each node has a Key value, which can be used to compare with each other.
- For every node in the tree, every Key value in its left subtree is smaller than its own Key value.
- For every node in the tree, every Key value in its right subtree is equal to or larger than its own Key value.
Now we need to analog a BST, we only require one kind of operation: inserting.
First, we have an empty BST. Input is a sequence of numbers. We need to insert them one by one flowing the rules below:
If the inserted value is smaller than the root's value, insert it to the left subtree.
If the inserted value is larger than or equal to the value of the root's value, insert it to the right subtree.
After each input, we need to output the preorder, inorder, postorder traversal sequences.
About tree traversal, the following is from Wikipedia:
Depth-first Traversal
To traverse a non-empty binary tree in preorder, perform the following operations recursively at each node, starting with the root node:
- Visit the root.
- Traverse the left subtree.
- Traverse the right subtree.
To traverse a non-empty binary tree in inorder (symmetric), perform the following operations recursively at each node:
- Traverse the left subtree.
- Visit the root.
- Traverse the right subtree.
To traverse a non-empty binary tree in postorder, perform the following operations recursively at each node:
- Traverse the left subtree.
- Traverse the right subtree.
- Visit the root.
Look at the folowing example:
Intput is a sequence of 5 integers: 3 6 9 5 1
After each integer inserted the structure of the tree is illustrated in the flowing:
3 / \ 1 6 / \ 5 9Input
TN,(1<=NN30].
Output
Each test case, output must contain three lines: the preorder, inorder and postorder traversal sequence. The numbers in each line should be separated by a single space and you should not output anything at the end of the line! Output a blank line after each case.
Sample Input
1 5 3 6 9 5 1
Sample Output
3 1 6 5 9 1 3 5 6 9 1 5 9 6 3
Hint
#include<iostream> #include<cstdio> using namespace std; struct Node{ int key; int left; int right; }node[1010]; int n; int cnt; void insert(int root,int i) { if(node[i].key < node[root].key) { if(node[root].left == -1) node[root].left = i; else insert(node[root].left,i); } else { if(node[root].right == -1) node[root].right = i; else insert(node[root].right,i); } } void traverse1(int root) { if(root != -1) { cnt++; if(cnt < n) cout << node[root].key << " "; else cout << node[root].key << endl; traverse1(node[root].left); traverse1(node[root].right); } } void traverse2(int root) { if(root!=-1) { traverse2(node[root].left); cnt++; if(cnt < n) cout << node[root].key << " "; else cout << node[root].key << endl; traverse2(node[root].right); } } void traverse3(int root) { if(root!=-1) { traverse3(node[root].left); traverse3(node[root].right); cnt++; if(cnt < n) cout << node[root].key << " "; else cout << node[root].key << endl; } } int main() { int t; cin >> t; while(t--) { cin >> n; for(int i = 0;i < n;i++) { node[i].left = node[i].right = -1; } cin >> node[0].key; for(int i = 1;i < n;i++) { cin >> node[i].key; insert(0,i); } cnt = 0; traverse1(0); cnt = 0; traverse2(0); cnt = 0; traverse3(0); cout << endl; } return 0; } /********************************************************************** Problem: 1005 User: song_hai_lei Language: C++ Result: AC Time:44 ms Memory:2036 kb **********************************************************************/