Leaf nodes from Preorder of a Binary Search Tree (Using Recursion)

Given Preorder traversal of a Binary Search Tree. Then the task is to print leaf nodes of the Binary Search Tree from the given preorder.

Examples :

Input : preorder[] = {890, 325, 290, 530, 965};
Output : 290 530 965

Tree represented is,
      890
     /   \
  325    965
  /  \
290   530

Input :  preorder[] = { 3, 2, 4 };
Output : 2 4

In this post, a simple recursive solution is discussed. The idea is to use two min and max variables and taking i (index in input array), the index for given preorder array, and recursively creating root node and correspondingly checking if left and right are existing or not. This method returns boolean variable, and if both left and right are false it simply means that left and right are null hence it must be a leaf node so print it right there and return back true as root at that index existed.

Implementation:

C++

// Recursive C++ program  to find leaf
// nodes from given preorder traversal
#include<bits/stdc++.h>
using namespace std;

// Print the leaf node from
// the given preorder of BST.
bool isLeaf(int pre[], int &i, int n,
                        int min, int max)
{
    if (i >= n)
        return false;

    if (pre[i] > min && pre[i] < max) {
        i++;

        bool left = isLeaf(pre, i, n, min, pre[i-1]);
        bool right = isLeaf(pre, i, n, pre[i-1], max);

        if (!left && !right)
            cout << pre[i-1] << " ";

        return true;
    }
    return false;
}

void printLeaves(int preorder[],  int n)
{
    int i = 0;
    isLeaf(preorder, i, n, INT_MIN, INT_MAX);
}

// Driver code
int main()
{
    int preorder[] = { 890, 325, 290, 530, 965 };
    int n = sizeof(preorder)/sizeof(preorder[0]);
    printLeaves(preorder, n);
    return 0;
}

Java

// Recursive Java program to find leaf
// nodes from given preorder traversal
class GFG
{

    static int i = 0;

    // Print the leaf node from
    // the given preorder of BST.
    static boolean isLeaf(int pre[], int n,
            int min, int max)
    {
        if (i >= n)
        {
            return false;
        }

        if (pre[i] > min && pre[i] < max)
        {
            i++;

            boolean left = isLeaf(pre, n, min, pre[i - 1]);
            boolean right = isLeaf(pre, n, pre[i - 1], max);

            if (!left && !right)
            {
                System.out.print(pre[i - 1] + " ");
            }

            return true;
        }
        return false;
    }

    static void printLeaves(int preorder[], int n)
    {

        isLeaf(preorder, n, Integer.MIN_VALUE,
                            Integer.MAX_VALUE);
    }

    // Driver code
    public static void main(String[] args)
    {
        int preorder[] = {890, 325, 290, 530, 965};
        int n = preorder.length;
        printLeaves(preorder, n);
    }
}

// This code contributed by Rajput-Ji

Python3

# Recursive Python program to find leaf
# nodes from given preorder traversal

# Print the leaf node from
# the given preorder of BST.
def isLeaf(pre, i, n, Min, Max):
    if i[0] >= n:
        return False

    if pre[i[0]] > Min and pre[i[0]] < Max:
        i[0] += 1

        left = isLeaf(pre, i, n, Min,
                      pre[i[0] - 1])
        right = isLeaf(pre, i, n,
                       pre[i[0] - 1], Max)

        if left == False and right == False:
            print(pre[i[0] - 1], end = " ")

        return True
    return False

def printLeaves(preorder, n):
    i = [0]
    INT_MIN, INT_MAX = -999999999999, 999999999999
    isLeaf(preorder, i, n, INT_MIN, INT_MAX)

# Driver code
if __name__ == '__main__':
    preorder = [890, 325, 290, 530, 965]
    n = len(preorder)
    printLeaves(preorder, n)

# This code is contributed by PranchalK

C#

// Recursive C# program to find leaf
// nodes from given preorder traversal
using System;

class GFG
{

    static int i = 0;

    // Print the leaf node from
    // the given preorder of BST.
    static bool isLeaf(int []pre, int n,
                        int min, int max)
    {
        if (i >= n)
        {
            return false;
        }

        if (pre[i] > min && pre[i] < max)
        {
            i++;

            bool left = isLeaf(pre, n, min, pre[i - 1]);
            bool right = isLeaf(pre, n, pre[i - 1], max);

            if (!left && !right)
            {
                Console.Write(pre[i - 1] + " ");
            }

            return true;
        }
        return false;
    }

    static void printLeaves(int []preorder, int n)
    {

        isLeaf(preorder, n, int.MinValue, int.MaxValue);
    }

    // Driver code
    public static void Main(String[] args)
    {
        int []preorder = {890, 325, 290, 530, 965};
        int n = preorder.Length;
        printLeaves(preorder, n);
    }
}

// This code is contributed by princiraj1992

PHP

<?php
// Recursive PHP program to
// find leaf nodes from given
// preorder traversal

// Print the leaf node from
// the given preorder of BST.

function isLeaf($pre, &$i, $n,
                $min, $max)
{
    if ($i >= $n)
        return false;

    if ($pre[$i] > $min &&
        $pre[$i] < $max)
    {
        $i++;

        $left = isLeaf($pre, $i, $n,
                       $min, $pre[$i - 1]);
        $right = isLeaf($pre, $i, $n,
                        $pre[$i - 1], $max);

        if (!$left && !$right)
            echo $pre[$i - 1] , " ";

        return true;
    }
    return false;
}

function printLeaves($preorder, $n)
{
    $i = 0;
    isLeaf($preorder, $i, $n,
           PHP_INT_MIN, PHP_INT_MAX);
}

// Driver code
$preorder = array (890, 325, 290,
                   530, 965 );
$n = sizeof($preorder);
printLeaves($preorder, $n);

// This code is contributed by ajit
?>

Javascript

<script>

// Recursive Javascript program to find leaf
// nodes from given preorder traversal
let i = 0;

// Print the leaf node from
// the given preorder of BST.
function isLeaf(pre, n, min, max)
{
    if (i >= n)
    {
        return false;
    }

    if (pre[i] > min && pre[i] < max)
    {
        i++;

        let left = isLeaf(pre, n, min, pre[i - 1]);
        let right = isLeaf(pre, n, pre[i - 1], max);

        if (!left && !right)
        {
            document.write(pre[i - 1] + " ");
        }

        return true;
    }
    return false;
}

function printLeaves(preorder, n)
{
    isLeaf(preorder, n, Number.MIN_VALUE,
                        Number.MAX_VALUE);
}

// Driver code
let preorder = [ 890, 325, 290, 530, 965 ];
let n = preorder.length;

printLeaves(preorder, n);

// This code is contributed by divyeshrabadiya07

</script>

Output

290 530 965 

Time Complexity: O(N), As we are traversing the BST only once.
Auxiliary Space: O(h), here h is the height of the BST and the extra space is used in the recursion call stack.