# 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.

(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; ` `} ` |

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## 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

**Output:**

12

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

## Recommended Posts:

- Lowest Common Ancestor in a Binary Tree | Set 2 (Using Parent Pointer)
- Lowest Common Ancestor in a Binary Tree | Set 1
- Lowest Common Ancestor in a Binary Tree | Set 3 (Using RMQ)
- Lowest Common Ancestor in a Binary Search Tree.
- Construct Binary Tree from given Parent Array representation
- Construct Binary Tree from given Parent Array representation | Iterative Approach
- Tarjan's off-line lowest common ancestors algorithm
- Height of n-ary tree if parent array is given
- Height of a generic tree from parent array
- Find Height of Binary Tree represented by Parent array
- Minimum sub-array such that number of 1's in concatenation of binary representation of its elements is at least K
- Shortest path between two nodes in array like representation of binary tree
- Count pairs in an array which have at least one digit common
- Find K items with the lowest values
- Print common nodes on path from root (or common ancestors)

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