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Check if two given key sequences construct same BSTs

  • Difficulty Level : Hard
  • Last Updated : 17 Aug, 2021

Given two arrays which represent two sequences of keys that are used to create BSTs. Imagine we make a Binary Search Tree (BST) from each array. We need to tell whether two BSTs will be identical or not without actually constructing the tree. 

Examples: 

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Let the input arrays be a[] and b[]

Example 1:
a[] = {2, 4, 1, 3} will construct following tree.
   2
 /  \
1    4
    /
   3
b[] = {2, 4, 3, 1} will also also construct the same tree.
   2
 /  \
1    4
    /
   3 
So the output is "True"

Example 2:
a[] = {8, 3, 6, 1, 4, 7, 10, 14, 13}
b[] = {8, 10, 14, 3, 6, 4, 1, 7, 13}

They both construct the same following BST, so output is "True"
            8
         /    \
       3       10
     /  \        \
    1     6       14
        /   \     /
       4     7   13  

1) Compare sizes of two arrays. If not same, return false. 
2) Compare first values of two arrays. If not same, return false. 
3) Create two lists from each given array such that the first list contains values smaller than first item of the corresponding array. And second list contains greater values. 
4) Recursively check the first list of first array with first list of second and same for second list.

C++




// C++ program to check if given two arrays represent
// same BST.
 
#include <bits/stdc++.h>
using namespace std;
bool sameBSTs(vector<int> aL1,
                            vector<int> aL2)
{
    // Base cases
    if (aL1.size() != aL2.size())
        return false;
    if (aL1.size() == 0)
        return true;
    if (aL1[0] != aL2[0])
        return false;
 
    // Construct two lists from each input array. The first
    // list contains values smaller than first value, i.e.,
    // left subtree. And second list contains right subtree.
    vector<int> aLLeft1 ;
    vector<int> aLRight1 ;
    vector<int> aLLeft2 ;
    vector<int> aLRight2 ;
    for (int i = 1; i < aL1.size(); i++)
    {
        if (aL1[i] < aL1[0])
            aLLeft1.push_back(aL1[i]);
        else
            aLRight1.push_back(aL1[i]);
 
        if (aL2[i] < aL2[0])
            aLLeft2.push_back(aL2[i]);
        else
            aLRight2.push_back(aL2[i]);
    }
 
    // Recursively compare left and right
    // subtrees.
    return sameBSTs(aLLeft1, aLLeft2) &&
        sameBSTs(aLRight1, aLRight2);
}
 
// Driver code
int main()
{
    vector<int> aL1;
    vector<int> aL2;
    aL1.push_back(3);
    aL1.push_back(5);
    aL1.push_back(4);
    aL1.push_back(6);
    aL1.push_back(1);
    aL1.push_back(0);
    aL1.push_back(2);
     
    aL2.push_back(3);
    aL2.push_back(1);
    aL2.push_back(5);
    aL2.push_back(2);
    aL2.push_back(4);
    aL2.push_back(6);
    aL2.push_back(0);
     
    cout << ((sameBSTs(aL1, aL2))?"true":"false")<<"\n";
    return 0;
}
 
// This code is contributed by Arnab Kundu

Java




// Java program to check if given two arrays represent
// same BST.
import java.util.ArrayList;
import java.util.Arrays;
 
public class SameBST {
    static boolean sameBSTs(ArrayList<Integer> aL1,
                            ArrayList<Integer> aL2)
    {
        // Base cases
        if (aL1.size() != aL2.size())
            return false;
        if (aL1.size() == 0)
            return true;
        if (aL1.get(0) != aL2.get(0))
            return false;
 
        // Construct two lists from each input array. The first
        // list contains values smaller than first value, i.e.,
        // left subtree. And second list contains right subtree.
        ArrayList<Integer> aLLeft1 = new ArrayList<Integer>();
        ArrayList<Integer> aLRight1 = new ArrayList<Integer>();
        ArrayList<Integer> aLLeft2 = new ArrayList<Integer>();
        ArrayList<Integer> aLRight2 = new ArrayList<Integer>();
        for (int i = 1; i < aL1.size(); i++) {
            if (aL1.get(i) < aL1.get(0))
                aLLeft1.add(aL1.get(i));
            else
                aLRight1.add(aL1.get(i));
 
            if (aL2.get(i) < aL2.get(0))
                aLLeft2.add(aL2.get(i));
            else
                aLRight2.add(aL2.get(i));
        }
 
        // Recursively compare left and right
        // subtrees.
        return sameBSTs(aLLeft1, aLLeft2) &&
               sameBSTs(aLRight1, aLRight2);
    }
 
    // Driver code
    public static void main(String[] args)
    {
        ArrayList<Integer> aL1 =
                         new ArrayList<Integer>(Arrays.
                           asList(3, 5, 4, 6, 1, 0, 2));
        ArrayList<Integer> aL2 =
                         new ArrayList<Integer>(Arrays.
                          asList(3, 1, 5, 2, 4, 6, 0));
 
        System.out.println(sameBSTs(aL1, aL2));
    }
}

Python3




# Python3 program to check if given two arrays represent
# same BST.
def sameBSTs(aL1, aL2):
     
    # Base cases
    if (len(aL1) != len(aL2)):
        return False
    if (len(aL1) == 0):
        return True
    if (aL1[0] != aL2[0]):
        return False
     
    # Construct two lists from each input array. The first
    # list contains values smaller than first value, i.e.,
    # left subtree. And second list contains right subtree.
    aLLeft1 = []
    aLRight1 = []
    aLLeft2 = []
    aLRight2 = []
    for i in range(1, len(aL1)):
        if (aL1[i] < aL1[0]):
            aLLeft1.append(aL1[i])
        else:
            aLRight1.append(aL1[i])
         
        if (aL2[i] < aL2[0]):
            aLLeft2.append(aL2[i])
        else:
            aLRight2.append(aL2[i])
     
    # Recursively compare left and right
    # subtrees.
    return sameBSTs(aLLeft1, aLLeft2) and sameBSTs(aLRight1, aLRight2)
 
# Driver code
aL1 = []
aL2 = []
aL1.append(3)
aL1.append(5)
aL1.append(4)
aL1.append(6)
aL1.append(1)
aL1.append(0)
aL1.append(2)
 
aL2.append(3)
aL2.append(1)
aL2.append(5)
aL2.append(2)
aL2.append(4)
aL2.append(6)
aL2.append(0)
 
if (sameBSTs(aL1, aL2)):
    print("true")
else:
    print("false")
 
# This code is contributed by shubhamsingh10

C#




// C# program to check if given
// two arrays represent same BST.
using System;
using System.Linq;
using System.Collections.Generic;
 
public class SameBST
{
    static bool sameBSTs(List<int> aL1,
                            List<int> aL2)
    {
        // Base cases
        if (aL1.Count != aL2.Count)
            return false;
        if (aL1.Count == 0)
            return true;
        if (aL1[0] != aL2[0])
            return false;
 
        // Construct two lists from each
        // input array. The first list contains
        // values smaller than first value, i.e.,
        // left subtree. And second list contains right subtree.
        List<int> aLLeft1 = new List<int>();
        List<int> aLRight1 = new List<int>();
        List<int> aLLeft2 = new List<int>();
        List<int> aLRight2 = new List<int>();
        for (int i = 1; i < aL1.Count; i++)
        {
            if (aL1[i] < aL1[0])
                aLLeft1.Add(aL1[i]);
            else
                aLRight1.Add(aL1[i]);
 
            if (aL2[i] < aL2[0])
                aLLeft2.Add(aL2[i]);
            else
                aLRight2.Add(aL2[i]);
        }
 
        // Recursively compare left and right
        // subtrees.
        return sameBSTs(aLLeft1, aLLeft2) &&
            sameBSTs(aLRight1, aLRight2);
    }
 
    // Driver code
    public static void Main()
    {
        int []arr1 = {3, 5, 4, 6, 1, 0, 2};
        List<int> aL1 = arr1.ToList();
        int []arr2 = {3, 1, 5, 2, 4, 6, 0};
        List<int> aL2 = arr2.ToList();
 
        Console.WriteLine(sameBSTs(aL1, aL2));
    }
}
 
/* This code contributed by PrinciRaj1992 */

Javascript




<script>
 
// javascript program to check if given two arrays represent
// same BST.
 
function sameBSTs(aL1, aL2)
{
    // Base cases
    if (aL1.length != aL2.length)
        return false;
    if (aL1.length == 0)
        return true;
    if (aL1[0] !== aL2[0])
        return false;
 
    // Construct two lists from each input array. The first
    // list contains values smaller than first value, i.e.,
    // left subtree. And second list contains right subtree.
    var aLLeft1 = [];
    var aLRight1 =[] ;
    var aLLeft2 =[];
    var aLRight2 =[];
    for (var i = 1; i < aL1.length; i++)
    {
        if (aL1[i] < aL1[0])
            aLLeft1.push(aL1[i]);
        else
            aLRight1.push(aL1[i]);
 
        if (aL2[i] < aL2[0])
            aLLeft2.push(aL2[i]);
        else
            aLRight2.push(aL2[i]);
    }
 
    // Recursively compare left and right
    // subtrees.
    if(sameBSTs(aLLeft1, aLLeft2) && sameBSTs(aLRight1, aLRight2))
    {
            return true;
    }
    return false;
}
 
// Driver code
var aL1 =[3, 5, 4, 6, 1, 0, 2] ;
var aL2 =[3, 1, 5, 2, 4, 6, 0];
 
document.write( ((sameBSTs(aL1, aL2))?"true":"false")+"<br>");
 
 
 
</script>
Output: 
true

 

Time Complexity : O(n * n)
Please refer below post for O(n) solution 
Check for Identical BSTs without building the trees
 




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