Find All Duplicate Subtrees

Given a binary tree, find all duplicate subtrees. For each duplicate subtrees, we only need to return the root node of any one of them. Two trees are duplicate if they have the same structure with same node values.

Examples:

Input :
       1
      / \
     2   3
    /   / \
   4   2   4
      /
     4

Output : 
   2           
  /    and    4
 4
Explanation: Above Trees are two duplicate subtrees. 
Therefore, you need to return above trees root in the 
form of a list.

The idea is to use hashing. We store inorder traversals of subtrees in a hash. Since simple inorder traversal cannot uniquely identify a tree, we use symbols like ‘(‘ and ‘)’ to represent NULL nodes.
We pass a Unordered Map in C++ as an argument to the helper function which recursively calculates inorder string and increases its count in map. If any string gets repeated, then it will imply duplication of the subtree rooted at that node so push that node in Final result and return the vector of these nodes.

C++

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// C++ program to find averages of all levels
// in a binary tree.
#include <bits/stdc++.h>
using namespace std;
  
/* A binary tree node has data, pointer to
left child and a pointer to right child */
struct Node {
    int data;
    struct Node* left, *right;
};
  
string inorder(Node* node, unordered_map<string, int>& m)
{
    if (!node)
        return "";
  
    string str = "(";
    str += inorder(node->left, m);
    str += to_string(node->data);
    str += inorder(node->right, m);
    str += ")";
  
    // Subtree already present (Note that we use
    // unordered_map instead of unordered_set
    // because we want to print multiple duplicates
    // only once, consider example of 4 in above
    // subtree, it should be printed only once.
    if (m[str] == 1)
        cout << node->data << " ";
  
    m[str]++;
  
    return str;
}
  
// Wrapper over inorder()
void printAllDups(Node* root)
{
    unordered_map<string, int> m;
    inorder(root, m);
}
  
/* Helper function that allocates a
new node with the given data and
NULL left and right pointers. */
Node* newNode(int data)
{
    Node* temp = new Node;
    temp->data = data;
    temp->left = temp->right = NULL;
    return temp;
}
  
// Driver code
int main()
{
    Node* root = NULL;
    root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->right->left = newNode(2);
    root->right->left->left = newNode(4);
    root->right->right = newNode(4);
    printAllDups(root);
    return 0;
}

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Java

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// A java program to find all duplicate subtrees 
// in a binary tree.
import java.util.HashMap;
public class Duplicate_subtress {
  
    /* A binary tree node has data, pointer to
    left child and a pointer to right child */
    static HashMap<String, Integer> m;
    static class Node {
        int data;
        Node left;
        Node right;
        Node(int data){
            this.data = data;
            left = null;
            right = null;
        }
    }
    static String inorder(Node node)
    {
        if (node == null)
            return "";
       
        String str = "(";
        str += inorder(node.left);
        str += Integer.toString(node.data);
        str += inorder(node.right);
        str += ")";
       
        // Subtree already present (Note that we use
        // HashMap instead of HashSet
        // because we want to print multiple duplicates
        // only once, consider example of 4 in above
        // subtree, it should be printed only once.       
        if (m.get(str) != null && m.get(str)==1 )
            System.out.print( node.data + " ");
       
        if (m.containsKey(str))
            m.put(str, m.get(str) + 1);
        else
            m.put(str, 1);
          
         
        return str;
    }
       
    // Wrapper over inorder()
    static void printAllDups(Node root)
    {
        m = new HashMap<>();
        inorder(root);
    
    // Driver code
    public static void main(String args[])
    {
        Node root = null;
        root = new Node(1);
        root.left = new Node(2);
        root.right = new Node(3);
        root.left.left = new Node(4);
        root.right.left = new Node(2);
        root.right.left.left = new Node(4);
        root.right.right = new Node(4);
        printAllDups(root);
    }
}
// This code is contributed by Sumit Ghosh

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Python3

# Python3 program to find averages of
# all levels in a binary tree.

# Helper function that allocates a
# new node with the given data and
# None left and right pointers.
class newNode:
def __init__(self, data):
self.data = data
self.left = self.right = None

def inorder(node, m):
if (not node):
return “”

Str = “(”
Str += inorder(node.left, m)
Str += str(node.data)
Str += inorder(node.right, m)
Str += “)”

# Subtree already present (Note that
# we use unordered_map instead of
# unordered_set because we want to print
# multiple duplicates only once, consider
# example of 4 in above subtree, it
# should be printed only once.
if (Str in m and m[Str] == 1):
print(node.data, end = ” “)
if Str in m:
m[Str] += 1
else:
m[Str] = 1

return Str

# Wrapper over inorder()
def printAllDups(root):
m = {}
inorder(root, m)

# Driver code
if __name__ == ‘__main__’:
root = None
root = newNode(1)
root.left = newNode(2)
root.right = newNode(3)
root.left.left = newNode(4)
root.right.left = newNode(2)
root.right.left.left = newNode(4)
root.right.right = newNode(4)
printAllDups(root)

# This code is contributed by PranchalK


Output:

4 2

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