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Minimum swap required to convert binary tree to binary search tree

Given the array representation of Complete Binary Tree i.e, if index i is the parent, index 2*i + 1 is the left child and index 2*i + 2 is the right child. The task is to find the minimum number of swap required to convert it into Binary Search Tree.

Examples:

Input : arr[] = { 5, 6, 7, 8, 9, 10, 11 }
Output : 3
Binary tree of the given array:
dig11
Swap 1: Swap node 8 with node 5.
Swap 2: Swap node 9 with node 10.
Swap 3: Swap node 10 with node 7.
dig21
So, minimum 3 swaps are required.


Input : arr[] = { 1, 2, 3 }
Output : 1
Binary tree of the given array:
dig3
After swapping node 1 with node 2.
dig41
So, only 1 swap required.



The idea is to use the fact that inorder traversal of Binary Search Tree is in increasing order of their value.
So, find the inorder traversal of the Binary Tree and store it in the array and try to sort the array. The minimum number of swap required to get the array sorted will be the answer. Please refer below post to find minimum number of swaps required to get the array sorted.

Minimum number of swaps required to sort an array

Time Complexity: O(n log n).

// C++ program for Minimum swap required
// to convert binary tree to binary search tree
#include<bits/stdc++.h>
using namespace std;
  
// Inorder Traversal of Binary Tree
void inorder(int a[], std::vector<int> &v, 
                        int n, int index)
{
    // if index is greater or equal to vector size
    if(index >= n)
        return;
    inorder(a, v, n, 2 * index + 1);
      
    // push elements in vector
    v.push_back(a[index]);
    inorder(a, v, n, 2 * index + 2);
}
  
// Function to find minimum swaps to sort an array
int minSwaps(std::vector<int> &v)
{
    std::vector<pair<int,int> > t(v.size());
    int ans = 0;
    for(int i = 0; i < v.size(); i++)
        t[i].first = v[i], t[i].second = i;
      
    sort(t.begin(), t.end());
    for(int i = 0; i < t.size(); i++)
    {
        // second element is equal to i
        if(i == t[i].second)
            continue;
        else
        {
            // swaping of elements
            swap(t[i].first, t[t[i].second].first);
            swap(t[i].second, t[t[i].second].second);
        }
          
        // Second is not equal to i
        if(i != t[i].second)
            --i;
        ans++;
    }
    return ans;
}
  
// Driver code
int main()
{
    int a[] = { 5, 6, 7, 8, 9, 10, 11 };
    int n = sizeof(a) / sizeof(a[0]);
    std::vector<int> v;
    inorder(a, v, n, 0);
    cout << minSwaps(v) << endl;
}
  
// This code is contributed by code_freak

Output:

3

Exercise: Can we extend this to normal binary tree, i.e., a binary tree represented using left and right pointers, and not necessarily complete?

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

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