Succinct Encoding of Binary Tree in C++

Suppose we have a binary tree. As we know the succinct encoding of Binary Tree performs close to lowest possible space. The n’th Catalan number is designated by the number of structurally different binary trees with n different nodes. If the n is large, this is about 4n; thus, we require minimum about log2(4) n = 2n bits to encode it. A succinct binary tree therefore would consume 2n + O(n) bits.

So, if the input is like

then the output will be

encoded −

Structure List 1 1 1 0 0 1 0 0 1 0 1 0 0

Data List 10 20 40 50 30 70

Decoded − The tree as shown above.

To solve this, we will follow these steps −

• Define a function Encode(), this will take root, a list named struc, a list named data,
• if root is same as NULL, then −
  • insert 0 at the end of struc
  • return
• insert 1 at the end of struc
• insert value of root at the end of data
• Encode(left of root, struc, data)
• Encode(right of root, struc, data)
• Define a function Decode(), this will take a list named struc, a list named data,
• if size of struc <= 0, then −
  • return NULL
• vb := first element of struc
• delete front element from struc
• if b is same as 1, then −
  • key := first element of data
  • delete front element from data
  • root = new node with key
  • left of root := Decode(struc, data)
  • right of root := Decode(struc, data)
  • return root
• return NULL

Example (C++)

Let us see the following implementation to get 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 Encode(TreeNode *root, list<bool>&struc, list<int>&data){
   if(root == NULL){
      struc.push_back(0);
      return;
   }
   struc.push_back(1);
   data.push_back(root->val);
   Encode(root->left, struc, data);
   Encode(root->right, struc, data);
}
TreeNode *Decode(list<bool>&struc, list<int>&data){
   if(struc.size() <= 0)
   return NULL;
   bool b = struc.front();
   struc.pop_front();
   if(b == 1){
      int key = data.front();
      data.pop_front();
      TreeNode *root = new TreeNode(key);
      root->left = Decode(struc, data);
      root->right = Decode(struc, data);
      return root;
   }
   return NULL;
}
void preorder_trav(TreeNode* root){
   if(root){
      cout << "key: "<< root->val;
      if(root->left)
         cout << " | left child: "<< root->left->val;
      if(root->right)
         cout << " | right child: "<< root->right->val;
      cout << endl;
      preorder_trav(root->left);
      preorder_trav(root->right);
   }
}
main() {
   TreeNode *root = new TreeNode(10);
   root->left = new TreeNode(20);
   root->right = new TreeNode(30);
   root->left->left = new TreeNode(40);
   root->left->right = new TreeNode(50);
   root->right->right = new TreeNode(70);
   cout << "The Tree\n";
   preorder_trav(root);
   list<bool> struc;
   list<int> data;
   Encode(root, struc, data);
   cout << "\nEncoded Tree\n";
   cout << "Structure List\n";
   list<bool>::iterator si; // Structure iterator
   for(si = struc.begin(); si != struc.end(); ++si)
   cout << *si << " ";
   cout << "\nData List\n";
   list<int>::iterator di; // Data iIterator
   for(di = data.begin(); di != data.end(); ++di)
   cout << *di << " ";
   TreeNode *newroot = Decode(struc, data);
   cout << "\n\nPreorder traversal of decoded tree\n";
   preorder_trav(newroot);
}

Input

root->left = new TreeNode(20);
root->right = new TreeNode(30);
root->left->left = new TreeNode(40);
root->left->right = new TreeNode(50);
root->right->right = new TreeNode(70);

Output

The Tree
key: 10 | left child: 20 | right child: 30
key: 20 | left child: 40 | right child: 50
key: 40
key: 50
key: 30 | right child: 70
key: 70
Encoded Tree
Structure List
1 1 1 0 0 1 0 0 1 0 1 0 0
Data List
10 20 40 50 30 70
Preorder traversal of decoded tree
key: 10 | left child: 20 | right child: 30
key: 20 | left child: 40 | right child: 50
key: 40
key: 50
key: 30 | right child: 70
key: 70