Lowest Common Ancestor in Parent Array Representation

Given a binary tree represented as parent array, find Lowest Common Ancestor between two nodes ‘m’ and ‘n’.

In the above diagram, LCA of 10 and 14 is 12 and LCA of 10 and 12 is 12.

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

(1) Make a parent array and store the parent of ith node in it. Parent of root node should be -1.
(2) Now, access all the nodes from the desired node ‘m’ till root node and mark them visited.
(3) Lastly, access all the nodes from the desired node ‘n’ till first visited node comes.
(4) This node is the lowest common ancestor

C++

// CPP program to find LCA in a tree represented 
// as parent array. 
#include <bits/stdc++.h> 
using namespace std; 
  
// Maximum value in a node 
const int MAX = 1000; 
  
// Function to find the Lowest common ancestor 
int findLCA(int n1, int n2, int parent[]) 
{ 
    // Create a visited vector and mark 
    // all nodes as not visited. 
    vector<bool> visited(MAX, false); 
  
    visited[n1] = true; 
  
    // Moving from n1 node till root and 
    // mark every accessed node as visited 
    while (parent[n1] != -1) { 
        visited[n1] = true; 
  
        // Move to the parent of node n1 
        n1 = parent[n1]; 
    } 
  
    visited[n1] = true; 
  
    // For second node finding the first 
    // node common 
    while (!visited[n2]) 
        n2 = parent[n2]; 
  
    return n2; 
} 
  
// Insert function for Binary tree 
void insertAdj(int parent[], int i, int j) 
{ 
    parent[i] = j; 
} 
  
// Driver Functiom 
int main() 
{ 
    // Maximum capacity of binary tree 
    int parent[MAX]; 
  
    // Root marked 
    parent[20] = -1; 
    insertAdj(parent, 8, 20); 
    insertAdj(parent, 22, 20); 
    insertAdj(parent, 4, 8); 
    insertAdj(parent, 12, 8); 
    insertAdj(parent, 10, 12); 
    insertAdj(parent, 14, 12); 
  
    cout << findLCA(10, 14, parent); 
  
    return 0; 
} 

Java

// Java program to find LCA in a tree represented 
// as parent array. 
import java.util.*; 
  
class GFG  
{ 
  
// Maximum value in a node 
static int MAX = 1000; 
  
// Function to find the Lowest common ancestor 
static int findLCA(int n1, int n2, int parent[]) 
{ 
    // Create a visited vector and mark 
    // all nodes as not visited. 
    boolean []visited = new boolean[MAX]; 
  
    visited[n1] = true; 
  
    // Moving from n1 node till root and 
    // mark every accessed node as visited 
    while (parent[n1] != -1) 
    { 
        visited[n1] = true; 
  
        // Move to the parent of node n1 
        n1 = parent[n1]; 
    } 
  
    visited[n1] = true; 
  
    // For second node finding the first 
    // node common 
    while (!visited[n2]) 
        n2 = parent[n2]; 
  
    return n2; 
} 
  
// Insert function for Binary tree 
static void insertAdj(int parent[], int i, int j) 
{ 
    parent[i] = j; 
} 
  
// Driver Functiom 
public static void main(String[] args) 
{ 
    // Maximum capacity of binary tree 
    int []parent = new int[MAX]; 
  
    // Root marked 
    parent[20] = -1; 
    insertAdj(parent, 8, 20); 
    insertAdj(parent, 22, 20); 
    insertAdj(parent, 4, 8); 
    insertAdj(parent, 12, 8); 
    insertAdj(parent, 10, 12); 
    insertAdj(parent, 14, 12); 
  
    System.out.println(findLCA(10, 14, parent)); 
} 
} 
  
// This code is contributed by 29AjayKumar 

Python3

# Python 3 program to find LCA in a  
# tree represented as parent array. 
  
# Maximum value in a node 
MAX = 1000
  
# Function to find the Lowest  
# common ancestor 
def findLCA(n1, n2, parent): 
      
    # Create a visited vector and mark 
    # all nodes as not visited. 
    visited = [False for i in range(MAX)] 
  
    visited[n1] = True
  
    # Moving from n1 node till root and 
    # mark every accessed node as visited 
    while (parent[n1] != -1): 
        visited[n1] = True
  
        # Move to the parent of node n1 
        n1 = parent[n1] 
  
    visited[n1] = True
  
    # For second node finding the  
    # first node common 
    while (visited[n2] == False): 
        n2 = parent[n2] 
  
    return n2 
  
# Insert function for Binary tree 
def insertAdj(parent, i, j): 
    parent[i] = j 
  
# Driver Code 
if __name__ =='__main__': 
      
    # Maximum capacity of binary tree 
    parent = [0 for i in range(MAX)] 
  
    # Root marked 
    parent[20] = -1
    insertAdj(parent, 8, 20) 
    insertAdj(parent, 22, 20) 
    insertAdj(parent, 4, 8) 
    insertAdj(parent, 12, 8) 
    insertAdj(parent, 10, 12) 
    insertAdj(parent, 14, 12) 
  
    print(findLCA(10, 14, parent)) 
      
# This code is contributed by 
# Surendra_Gangwar 

C#

// C# program to find LCA in a tree represented 
// as parent array. 
using System; 
  
class GFG  
{ 
  
// Maximum value in a node 
static int MAX = 1000; 
  
// Function to find the Lowest common ancestor 
static int findLCA(int n1, int n2, int []parent) 
{ 
    // Create a visited vector and mark 
    // all nodes as not visited. 
    Boolean []visited = new Boolean[MAX]; 
  
    visited[n1] = true; 
  
    // Moving from n1 node till root and 
    // mark every accessed node as visited 
    while (parent[n1] != -1) 
    { 
        visited[n1] = true; 
  
        // Move to the parent of node n1 
        n1 = parent[n1]; 
    } 
  
    visited[n1] = true; 
  
    // For second node finding the first 
    // node common 
    while (!visited[n2]) 
        n2 = parent[n2]; 
  
    return n2; 
} 
  
// Insert function for Binary tree 
static void insertAdj(int []parent, int i, int j) 
{ 
    parent[i] = j; 
} 
  
// Driver Code 
public static void Main(String[] args) 
{ 
    // Maximum capacity of binary tree 
    int []parent = new int[MAX]; 
  
    // Root marked 
    parent[20] = -1; 
    insertAdj(parent, 8, 20); 
    insertAdj(parent, 22, 20); 
    insertAdj(parent, 4, 8); 
    insertAdj(parent, 12, 8); 
    insertAdj(parent, 10, 12); 
    insertAdj(parent, 14, 12); 
  
    Console.WriteLine(findLCA(10, 14, parent)); 
} 
} 
  
// This code is contributed by 29AjayKumar 

Output:

Time Complexity – The time complexity of the above algorithm is O(log n) as it requires O(log n) time in searching.

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Improved By : SURENDRA_GANGWAR, 29AjayKumar

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