Boundary of Binary Tree in C++

Suppose we have a binary tree, we have to find the values of its boundary in anti-clockwise direction starting from root. Here boundary includes left boundary, leaves, and the right boundary in order without duplicate nodes.

• The left boundary is the path from root to the left-most node.

• The Right boundary is the path from root to the right-most node.

• When the root doesn't have left subtree or right subtree, then the root itself is left boundary or right boundary.

So, if the input is like

then the output will be [1,2,4,7,8,9,10,6,3]

To solve this, we will follow these steps −

• Define an array ret

• Define a function leftBoundary(), this will take node,

• if node is null or node is leaf, then −

  • return

• insert value of node into ret

• if left of node is present, then −

  • leftBoundary(left of node)

• Otherwise

  • leftBoundary(right of node)

• Define a function rightBoundary(), this will take node,

• if node is null or node is leaf, then −

  • return

• insert value of node into ret

• if right of node is present, then −

  • rightBoundary(left of node)

• Otherwise

  • rightBoundary(right of node)

• Define a function leaves(), this will take node,

• if node is not present, then −

  • return

• if node is leaf, then −

  • insert val of node into ret

• leaves(left of node)

• leaves(right of node)

• From the main method do the following −

• Clear the ret array

• if root is not present, then −

  • return ret

• insert val of root into ret

• leftBoundary(left of root)

• leaves(left of root);

• leaves(right of root);

• rightBoundary(right of root)

• return ret

Example

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

 Live Demo

#include <bits/stdc++.h>
using namespace std;
void print_vector(vector<auto> v){
   cout << "[";
   for(int i = 0; i<v.size(); i++){
      cout << v[i] << ", ";
   }
   cout << "]"<<endl;
}
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[0]);
   for(int i = 1; i<v.size(); i++){
      insert(&root, v[i]);
   }
   return root;
}
class Solution {
public:
   vector<int> ret;
   void leftBoundary(TreeNode* node){
      if (!node || node->val == 0 || (!node->left && !node->right))
         return;
      ret.push_back(node->val);
      if (node->left && node->left->val != 0)
         leftBoundary(node->left);
      else
         leftBoundary(node->right);
   }
   void rightBoundary(TreeNode* node){
      if (!node || node->val == 0 || (!node->left && !node->right))
         return;
      if (node->right && node->right->val != 0) {
         rightBoundary(node->right);
      }
      else {
         rightBoundary(node->left);
      }
      ret.push_back(node->val);
   }
   void leaves(TreeNode* node){
      if (!node || node->val == 0)
         return;
      if (!node->left && !node->right) {
         ret.push_back(node->val);
      }
      leaves(node->left);
      leaves(node->right);
   }
   vector<int> boundaryOfBinaryTree(TreeNode* root){
      ret.clear();
      if (!root)
         return ret;
      ret.push_back(root->val);
      leftBoundary(root->left);
      leaves(root->left);
      leaves(root->right);
      rightBoundary(root->right);
      return ret;
   }
};
main(){
   Solution ob;
   vector<int> v = {1,2,3,4,5,6,NULL,NULL,NULL,7,8,9,10};
   TreeNode *root = make_tree(v);
   print_vector(ob.boundaryOfBinaryTree(root));
}

Input

{1,2,3,4,5,6,NULL,NULL,NULL,7,8,9,10}

Output

[1, 2, 4, 7, 8, 9, 10, 6, 3, ]