# Complete Binary Tree Inserter in C++

As we know a complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible. We have to write a data structure CBTInserter that is initialized with a complete binary tree and it supports the following operations−

• CBTInserter(TreeNode root) this initializes the data structure on a given tree with head node root;

• CBTInserter.insert(int v) will used to insert a TreeNode into the tree with a value node.val = v so that the tree remains complete, and returns the value of the parent of the inserted TreeNode;

• CBTInserter.get_root() this will return the head node of the tree.

So for example, if we initialize the tree as [1,2,3,4,5,6], then insert 7 and 8, then try to get the tree, the output will be: 3, 4,[1,2,3,4,5,6,7,8], the 3 is because 7 will be inserted under 3, and 4 is because 8 will be inserted under 4.

To solve this, we will follow these steps −

• Define a queue q, and a root

• The initializer will take the full binary tree, then work as follows

• set root as given root, insert root into the q

• while true −

• if left of root is present, then insert left of root into q, otherwise break the loop

• if right of root is present, then insert right of root into q and delete front node from q, otherwise break the loop

• From the insert method, it will take the value v

• set parent := front element of q, temp := new node with value v, and insert it into q

• if left of parent is not present, then set left of parent := temp otherwise delete front element from q, and insert temp as right child of parent

• return the value of parent

• from the getRoot() method, return the root

## Example(C++)

Let us see the following implementation to get a better understanding −

Live Demo

#include <bits/stdc++.h>
using namespace std;
class TreeNode{
public:
int val;
TreeNode *left, *right;
TreeNode(int data){
val = data;
left = NULL;
right = NULL;
}
};
void insert(TreeNode **root, int val){
queue<TreeNode*> q;
q.push(*root);
while(q.size()){
TreeNode *temp = q.front();
q.pop();
if(!temp->left){
if(val != NULL)
temp->left = new TreeNode(val);
else
temp->left = new TreeNode(0);
return;
} else {
q.push(temp->left);
}
if(!temp->right){
if(val != NULL)
temp->right = new TreeNode(val);
else
temp->right = new TreeNode(0);
return;
} else {
q.push(temp->right);
}
}
}
TreeNode *make_tree(vector<int> v){
TreeNode *root = new TreeNode(v);
for(int i = 1; i<v.size(); i++){
insert(&root, v[i]);
}
return root;
}
void tree_level_trav(TreeNode*root){
if (root == NULL) return;
cout << "[";
queue<TreeNode *> q;
TreeNode *curr;
q.push(root);
q.push(NULL);
while (q.size() > 1) {
curr = q.front();
q.pop();
if (curr == NULL){
q.push(NULL);
} else {
if(curr->left)
q.push(curr->left);
if(curr->right)
q.push(curr->right);
if(curr == NULL || curr->val == 0){
cout << "null" << ", ";
} else{
cout << curr->val << ", ";
}
}
}
cout << "]"<<endl;
}
class CBTInserter {
public:
queue <TreeNode*> q;
TreeNode* root;
CBTInserter(TreeNode* root) {
this->root = root;
q.push(root);
while(1){
if(root->left){
q.push(root->left);
}
else break;
if(root->right){
q.push(root->right);
q.pop();
root = q.front();
}
else break;
}
}
int insert(int v) {
TreeNode* parent = q.front();
TreeNode* temp = new TreeNode(v);
q.push(temp);
if(!parent->left){
parent->left = temp;
} else {
q.pop();
parent->right = temp;
}
return parent->val;
}
TreeNode* get_root() {
return root;
}
};
main(){
vector<int> v = {1,2,3,4,5,6};
TreeNode *root = make_tree(v);
CBTInserter ob(root);
cout << (ob.insert(7)) << endl;
cout << (ob.insert(8)) << endl;
tree_level_trav(ob.get_root());
}

## Input

Initialize the tree as [1,2,3,4,5,6], then insert 7 and 8 into the tree, then find root

## Output

3
4
[1, 2, 3, 4, 5, 6, 7, 8, ]