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Calculate depth of a full Binary tree from Preorder
  • Difficulty Level : Medium
  • Last Updated : 05 Mar, 2021

Given preorder of a binary tree, calculate its depth(or height) [starting from depth 0]. The preorder is given as a string with two possible characters. 

  1. ‘l’ denotes the leaf
  2. ‘n’ denotes internal node

The given tree can be seen as a full binary tree where every node has 0 or two children. The two children of a node can ‘n’ or ‘l’ or mix of both.
Examples :  

Input  : nlnll
Output : 2
Explanation :

Input  : nlnnlll
Output : 3

 

Preorder of the binary tree is given so traverse 
Also, we would be given a string of char (formed of ‘n’ and ‘l’), so there is no need to implement tree also.
The recursion function would be: 
1) Base Case: return 0; when tree[i] = ‘l’ or i >= strlen(tree) 
2) find_depth( tree[i++] ) //left subtree 
3) find_depth( tree[i++] ) //right subtree
Where i is the index of the string tree. 



C++




// C++ program to find height of full binary tree
// using preorder
#include <bits/stdc++.h>
using namespace std;
 
// function to return max of left subtree height
// or right subtree height
int findDepthRec(char tree[], int n, int& index)
{
    if (index >= n || tree[index] == 'l')
        return 0;
 
    // calc height of left subtree (In preorder
    // left subtree is processed before right)
    index++;
    int left = findDepthRec(tree, n, index);
 
    // calc height of right subtree
    index++;
    int right = findDepthRec(tree, n, index);
 
    return max(left, right) + 1;
}
 
// Wrapper over findDepthRec()
int findDepth(char tree[], int n)
{
    int index = 0;
    findDepthRec(tree, n, index);
}
 
// Driver program
int main()
{
    // Your C++ Code
    char tree[] = "nlnnlll";
    int n = strlen(tree);
 
    cout << findDepth(tree, n) << endl;
 
    return 0;
}


Java




// Java program to find height
// of full binary tree using
// preorder
import java .io.*;
 
class GFG
{
    // function to return max
    // of left subtree height
    // or right subtree height
    static int findDepthRec(String tree,
                            int n, int index)
    {
        if (index >= n ||
            tree.charAt(index) == 'l')
            return 0;
 
        // calc height of left subtree
        // (In preorder left subtree
        // is processed before right)
        index++;
        int left = findDepthRec(tree,
                                n, index);
 
        // calc height of
        // right subtree
        index++;
        int right = findDepthRec(tree, n, index);
 
        return Math.max(left, right) + 1;
    }
 
    // Wrapper over findDepthRec()
    static int findDepth(String tree,
                         int n)
    {
        int index = 0;
        return (findDepthRec(tree,
                             n, index));
    }
 
    // Driver Code
    static public void main(String[] args)
    {
        String tree = "nlnnlll";
        int n = tree.length();
        System.out.println(findDepth(tree, n));
    }
}
 
// This code is contributed
// by anuj_67.


Python3




#Python program to find height of full binary tree
# using preorder
     
# function to return max of left subtree height
# or right subtree height
def findDepthRec(tree, n, index) :
 
    if (index[0] >= n or tree[index[0]] == 'l'):
        return 0
 
    # calc height of left subtree (In preorder
    # left subtree is processed before right)
    index[0] += 1
    left = findDepthRec(tree, n, index)
 
    # calc height of right subtree
    index[0] += 1
    right = findDepthRec(tree, n, index)
    return (max(left, right) + 1)
 
# Wrapper over findDepthRec()
def findDepth(tree, n) :
 
    index = [0]
    return findDepthRec(tree, n, index)
 
         
# Driver program to test above functions
if __name__ == '__main__':
    tree= "nlnnlll"
    n = len(tree)
 
    print(findDepth(tree, n))
 
# This code is contributed by SHUBHAMSINGH10


C#




// C# program to find height of
// full binary tree using preorder
using System;
 
class GFG {
 
    // function to return max of left subtree
    // height or right subtree height
    static int findDepthRec(char[] tree, int n, int index)
    {
        if (index >= n || tree[index] == 'l')
            return 0;
 
        // calc height of left subtree (In preorder
        // left subtree is processed before right)
        index++;
        int left = findDepthRec(tree, n, index);
 
        // calc height of right subtree
        index++;
        int right = findDepthRec(tree, n, index);
 
        return Math.Max(left, right) + 1;
    }
 
    // Wrapper over findDepthRec()
    static int findDepth(char[] tree, int n)
    {
        int index = 0;
        return (findDepthRec(tree, n, index));
    }
 
    // Driver program
    static public void Main()
    {
        char[] tree = "nlnnlll".ToCharArray();
        int n = tree.Length;
        Console.WriteLine(findDepth(tree, n));
    }
}
 
// This code is contributed by vt_m.


Output: 

3

Time Complexity: O(N)

Auxiliary Space: O(1)

This article is contributed by Shubham Gupta. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 

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