Find the minimum absolute difference in two different BST’s

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Given 2 Binary Search Trees, select one node from each tree such that their absolute difference is minimum possible. Assume each BST has at-least one node.

Examples:

Input : N₁ = 7, N₂ = 2 

BST1 :
          5 
        /   \ 
       3     7 
      / \   / \ 
     2   4 6   8
     
BST2 :
         11
           \
            13
   
Output : 3
8 is largest number in the first BST
and 11 is smallest in the second.
Thus, the final answer will be 11-8 = 3


Input : N₁ = 4, N₂ = 2
BST1 :
          3 
        /   \ 
       2     4
              \
              14
        
BST2 :
          7
           \
            13
   
Output : 1

Approach:
The idea is to use the two-pointer technique and iterating the pointers using the following steps.

Create forward iterators for both the BST’s. Let’s say that the value of nodes they are pointing at are v₁ and v₂ respectively.
Now at each step:
- Update final ans as min(ans, abs(v₁-v₂)) .
- If v₁ < v₂, move iterator of first BST else move the iterator of the second BST.
Repeat above steps till both the BST’s are pointing to a valid nodes.

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Node of Binary tree
struct node {
    int data;
    node* left;
    node* right;
    node(int data)
    {
        this->data = data;
        left = NULL;
        right = NULL;
    }
};
 
// Function to iterate to the
// next element of the BST
void next(stack<node*>& it)
{
 
    node* curr = it.top()->right;
    it.pop();
    while (curr != NULL)
        it.push(curr), curr = curr->left;
}
 
// Function to find minimum difference
int minDiff(node* root1, node* root2)
{
 
    // Iterator for two Binary Search Trees
    stack<node *> it1, it2;
 
    // Initializing first iterator
    node* curr = root1;
    while (curr != NULL)
        it1.push(curr), curr = curr->left;
 
    // Initializing second iterator
    curr = root2;
    while (curr != NULL)
        it2.push(curr), curr = curr->left;
 
    // Variable to store final answer
    int ans = INT_MAX;
 
    // Two pointer technique
    while (it1.size() and it2.size()) {
 
        // value it1 and it2 are pointing to
        int v1 = it1.top()->data;
        int v2 = it2.top()->data;
 
        // Updating final answer
        ans = min(abs(v1 - v2), ans);
 
        // Case when v1 < v2
        if (v1 < v2)
            next(it1);
        else
            next(it2);
    }
 
    // Return ans
    return ans;
}
 
// Driver code
int main()
{
    // BST-1
 
    /*    5 
        /   \ 
       3     7 
      / \   / \ 
     2   4 6   8 */
    node* root2 = new node(5);
    root2->left = new node(3);
    root2->right = new node(7);
    root2->left->left = new node(2);
    root2->left->right = new node(4);
    root2->right->left = new node(6);
    root2->right->right = new node(8);
 
    // BST-2
 
    /*  11
         \
          15
    */
    node* root1 = new node(11);
    root1->right = new node(15);
 
    cout << minDiff(root1, root2);
 
    return 0;
}

Java

// Java implementation of the approach
import java.util.*;
 
class GFG
{
 
// Node of Binary tree
static class node 
{
    int data;
    node left;
    node right;
    node(int data)
    {
        this.data = data;
        left = null;
        right = null;
    }
};
 
// Function to iterate to the
// next element of the BST
static void next(Stack<node> it)
{
    node curr = it.peek().right;
    it.pop();
    while (curr != null)
    {
        it.push(curr);
        curr = curr.left;
    }
}
 
// Function to find minimum difference
static int minDiff(node root1, node root2)
{
 
    // Iterator for two Binary Search Trees
    Stack<node> it1 = new Stack<node>();
    Stack<node> it2 = new Stack<node>();
 
    // Initializing first iterator
    node curr = root1;
    while (curr != null)
    {
        it1.push(curr);
        curr = curr.left;
    }
 
    // Initializing second iterator
    curr = root2;
    while (curr != null)
    {
        it2.push(curr);
        curr = curr.left;
    }
 
    // Variable to store final answer
    int ans = Integer.MAX_VALUE;
 
    // Two pointer technique
    while (it1.size() > 0 && it2.size() > 0) 
    {
 
        // value it1 and it2 are pointing to
        int v1 = it1.peek().data;
        int v2 = it2.peek().data;
 
        // Updating final answer
        ans = Math.min(Math.abs(v1 - v2), ans);
 
        // Case when v1 < v2
        if (v1 < v2)
            next(it1);
        else
            next(it2);
    }
 
    // Return ans
    return ans;
}
 
// Driver code
public static void main(String[] args) 
{
    // BST-1
 
    /* 5 
        / \ 
    3     7 
    / \ / \ 
    2 4 6 8 */
    node root2 = new node(5);
    root2.left = new node(3);
    root2.right = new node(7);
    root2.left.left = new node(2);
    root2.left.right = new node(4);
    root2.right.left = new node(6);
    root2.right.right = new node(8);
 
    // BST-2
 
    /* 11
        \
        15
    */
    node root1 = new node(11);
    root1.right = new node(15);
 
    System.out.println(minDiff(root1, root2));
}
}
 
// This code is contributed by 29AjayKumar

Python3

# Python3 implementation of the approach
import sys
 
# Node of the binary tree
class node:
     
    def __init__ (self, key):
         
        self.data = key
        self.left = None
        self.right = None
 
# Function to iterate to the
# next element of the BST
def next(it):
 
    curr = it[-1].right
 
    del it[-1]
    while (curr != None):
        it.append(curr)
        curr = curr.left
         
    return it
 
# Function to find minimum difference
def minDiff(root1, root2):
 
    # Iterator for two Binary Search Trees
    it1, it2 = [], []
 
    # Initializing first iterator
    curr = root1
    while (curr != None):
        it1.append(curr)
        curr = curr.left
 
    # Initializing second iterator
    curr = root2
    while (curr != None):
        it2.append(curr)
        curr = curr.left
 
    # Variable to store final answer
    ans = sys.maxsize
 
    # Two pointer technique
    while (len(it1) > 0 and len(it2) > 0):
         
        # Value it1 and it2 are pointing to
        v1 = it1[-1].data
        v2 = it2[-1].data
 
        # Updating final answer
        ans = min(abs(v1 - v2), ans)
 
        # Case when v1 < v2
        if (v1 < v2):
            it1 = next(it1)
        else:
            it2 = next(it2)
 
    # Return ans
    return ans
 
# Driver code
if __name__ == '__main__':
     
    # BST-1
    #       5
    #     /   \
    #    3     7
    #   / \   / \
    #  2   4 6   8 
    root2 = node(5)
    root2.left = node(3)
    root2.right = node(7)
    root2.left.left = node(2)
    root2.left.right = node(4)
    root2.right.left = node(6)
    root2.right.right = node(8)
  
    # BST-2
    #    11
    #      \
    #       15
    # 
    root1 = node(11)
    root1.right = node(15)
 
    print(minDiff(root1, root2))
 
# This code is contributed by mohit kumar 29

C#

// C# implementation of the approach
using System;
using System.Collections.Generic;
 
class GFG
{
 
// Node of Binary tree
class node 
{
    public int data;
    public node left;
    public node right;
    public node(int data)
    {
        this.data = data;
        left = null;
        right = null;
    }
};
 
// Function to iterate to the
// next element of the BST
static void next(Stack<node> it)
{
    node curr = it.Peek().right;
    it.Pop();
    while (curr != null)
    {
        it.Push(curr);
        curr = curr.left;
    }
}
 
// Function to find minimum difference
static int minDiff(node root1, node root2)
{
 
    // Iterator for two Binary Search Trees
    Stack<node> it1 = new Stack<node>();
    Stack<node> it2 = new Stack<node>();
 
    // Initializing first iterator
    node curr = root1;
    while (curr != null)
    {
        it1.Push(curr);
        curr = curr.left;
    }
 
    // Initializing second iterator
    curr = root2;
    while (curr != null)
    {
        it2.Push(curr);
        curr = curr.left;
    }
 
    // Variable to store readonly answer
    int ans = int.MaxValue;
 
    // Two pointer technique
    while (it1.Count > 0 && it2.Count > 0) 
    {
 
        // value it1 and it2 are pointing to
        int v1 = it1.Peek().data;
        int v2 = it2.Peek().data;
 
        // Updating readonly answer
        ans = Math.Min(Math.Abs(v1 - v2), ans);
 
        // Case when v1 < v2
        if (v1 < v2)
            next(it1);
        else
            next(it2);
    }
 
    // Return ans
    return ans;
}
 
// Driver code
public static void Main(String[] args) 
{
    // BST-1
 
    /* 5 
        / \ 
    3     7 
    / \ / \ 
    2 4 6 8 */
    node root2 = new node(5);
    root2.left = new node(3);
    root2.right = new node(7);
    root2.left.left = new node(2);
    root2.left.right = new node(4);
    root2.right.left = new node(6);
    root2.right.right = new node(8);
 
    // BST-2
 
    /* 11
        \
        15
    */
    node root1 = new node(11);
    root1.right = new node(15);
 
    Console.WriteLine(minDiff(root1, root2));
}
}
 
// This code is contributed by Rajput-Ji

Javascript

<script>
// Javascript implementation of the approach
 
// Node of the binary tree
class node
{
    constructor(data)
    {
        this.data = data;
        this.left = null;
        this.right = null;
    }
}
 
// Function to iterate to the
// next element of the BST
function next(it)
{
    let curr = it[it.length-1].right;
    it.pop();
    while (curr != null)
    {
        it.push(curr);
        curr = curr.left;
    }
}
 
// Function to find minimum difference
function minDiff(root1,root2)
{
    // Iterator for two Binary Search Trees
    let it1 = [];
    let it2 = [];
  
    // Initializing first iterator
    let curr = root1;
    while (curr != null)
    {
        it1.push(curr);
        curr = curr.left;
    }
  
    // Initializing second iterator
    curr = root2;
    while (curr != null)
    {
        it2.push(curr);
        curr = curr.left;
    }
  
    // Variable to store final answer
    let ans = Number.MAX_VALUE;
  
    // Two pointer technique
    while (it1.length > 0 && it2.length > 0)
    {
  
        // value it1 and it2 are pointing to
        let v1 = it1[it1.length-1].data;
        let v2 = it2[it2.length-1].data;
  
        // Updating final answer
        ans = Math.min(Math.abs(v1 - v2), ans);
  
        // Case when v1 < v2
        if (v1 < v2)
            next(it1);
        else
            next(it2);
    }
  
    // Return ans
    return ans;
}
 
// Driver code
// BST-1
  
    /* 5
        / \
    3     7
    / \ / \
    2 4 6 8 */
    let root2 = new node(5);
    root2.left = new node(3);
    root2.right = new node(7);
    root2.left.left = new node(2);
    root2.left.right = new node(4);
    root2.right.left = new node(6);
    root2.right.right = new node(8);
  
    // BST-2
  
    /* 11
        \
        15
    */
    let root1 = new node(11);
    root1.right = new node(15);
  
    document.write(minDiff(root1, root2));
 
// This code is contributed by patel2127
</script>

Output:

Time complexity: O(N₁ + N₂) where N₁ and N₂ are the number of nodes of first and second BST respectively.
Space Complexity: O(H₁ + H₂) where H₁ and H₂ are the heights of first and second BST respectively.

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