GCD from root to leaf path in an N-ary tree

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Given an N-ary tree and an array val[] which stores the values associated with all the nodes. Also given are a leaf node X and N integers which denotes the value of the node. The task is to find the gcd of all the numbers in the node in the path between leaf to the root.
Examples:

Input: 
            1
          /   \ 
        2      3
      /      /   \ 
     4      5     6 
                /   \
              7      8 

val[] = { -1, 6, 2, 6, 3, 4, 12, 10, 18 } 
leaf = 8 
Output: 6 

GCD(val[1], val[3], val[6], val[8]) = GCD(6, 6, 12, 18) = 6 

Input:
            1
          /   \ 
        2      3
      /      /   \ 
     4      5     6 
                /   \
              7      8 

val[] = { 6, 2, 6, 3, 4, 12, 10, 18 }
leaf = 5  
Output: 2

Approach: The problem can be solved using DFS in a tree. In the DFS function, we include an extra parameter G with the initial value as the root. Every time we visit a new node by calling DFS function recursively, we update the value of G to gcd(G, val[node]) . Once we reach the given leaf node, we print the value of gcd(G, val[leaf-node]) and break out of DFS function.
Below is the implementation of the above approach:

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
#define N 9
 
// Function to add edges in the tree
void addEgde(list<int>* adj, int u, int v)
{
    adj[u].push_back(v);
    adj[v].push_back(u);
}
 
// Function to find the GCD from root to leaf path
void DFS(int node, int parent, int G, int leaf,
         int val[], list<int>* adj)
{
    // If we reach the desired leaf
    if (node == leaf) {
        G = __gcd(G, val[node]);
        cout << G;
        return;
    }
 
    // Call DFS for children
    for (auto it : adj[node]) {
 
        if (it != parent)
            DFS(it, node, __gcd(G, val[it]), leaf, val, adj);
    }
}
 
// Driver code
int main()
{
 
    int n = 8;
    list<int>* adj = new list<int>[n + 1];
 
    addEgde(adj, 1, 2);
    addEgde(adj, 2, 4);
    addEgde(adj, 1, 3);
    addEgde(adj, 3, 5);
    addEgde(adj, 3, 6);
    addEgde(adj, 6, 7);
    addEgde(adj, 6, 8);
 
    int leaf = 5;
 
    // -1 to indicate no value in node 0
    int val[] = { -1, 6, 2, 6, 3, 4, 12, 10, 18 };
 
    // Initially GCD is the value of the root
    int G = val[1];
 
    DFS(1, -1, G, leaf, val, adj);
 
    return 0;
}

Java

// Java implementation of the approach
import java.util.*;
 
class GFG
{
static final int N = 9;
 
// Function to add edges in the tree
static void addEgde(List<Integer> []adj, int u, int v)
{
    adj[u].add(v);
    adj[v].add(u);
}
 
// Function to find the GCD from root to leaf path
static void DFS(int node, int parent, int G, int leaf,
        int val[], List<Integer> []adj)
{
    // If we reach the desired leaf
    if (node == leaf)
    {
        G = __gcd(G, val[node]);
        System.out.print(G);
        return;
    }
 
    // Call DFS for children
    for (int it : adj[node]) 
    {
 
        if (it != parent)
            DFS(it, node, __gcd(G, val[it]), leaf, val, adj);
    }
}
static int __gcd(int a, int b) 
{ 
    return b == 0? a:__gcd(b, a % b);     
}
 
// Driver code
public static void main(String[] args)
{
 
    int n = 8;
    List<Integer> []adj = new LinkedList[n + 1];
        for (int i = 0; i < n + 1; i++)
            adj[i] = new LinkedList<Integer>();
    addEgde(adj, 1, 2);
    addEgde(adj, 2, 4);
    addEgde(adj, 1, 3);
    addEgde(adj, 3, 5);
    addEgde(adj, 3, 6);
    addEgde(adj, 6, 7);
    addEgde(adj, 6, 8);
 
    int leaf = 5;
 
    // -1 to indicate no value in node 0
    int val[] = { -1, 6, 2, 6, 3, 4, 12, 10, 18 };
 
    // Initially GCD is the value of the root
    int G = val[1];
 
    DFS(1, -1, G, leaf, val, adj);
}
}
 
// This code is contributed by 29AjayKumar

Python3

# Python 3 implementation of the approach
from math import gcd
N = 9
 
# Function to add edges in the tree
def addEgde(adj, u, v):
    adj[u].append(v)
    adj[v].append(u)
 
# Function to find the GCD 
# from root to leaf path
def DFS(node, parent, G, leaf, val, adj):
     
    # If we reach the desired leaf
    if (node == leaf):
        G = gcd(G, val[node])
        print(G, end = "")
        return
 
    # Call DFS for children
    for it in adj[node]:
        if (it != parent):
            DFS(it, node, gcd(G, val[it]),
                          leaf, val, adj)
 
# Driver code
if __name__ == '__main__':
    n = 8
    adj = [[0 for i in range(n + 1)] 
              for j in range(n + 1)]
  
    addEgde(adj, 1, 2)
    addEgde(adj, 2, 4)
    addEgde(adj, 1, 3)
    addEgde(adj, 3, 5)
    addEgde(adj, 3, 6)
    addEgde(adj, 6, 7)
    addEgde(adj, 6, 8)
 
    leaf = 5
 
    # -1 to indicate no value in node 0
    val = [-1, 6, 2, 6, 3, 4, 12, 10, 18]
 
    # Initially GCD is the value of the root
    G = val[1]
 
    DFS(1, -1, G, leaf, val, adj)
 
# This code is contributed by
# Surendra_Gangwar

C#

// C# implementation of the approach
using System;
using System.Collections.Generic;
 
class GFG
{
static readonly int N = 9;
  
// Function to add edges in the tree
static void addEgde(List<int> []adj, int u, int v)
{
    adj[u].Add(v);
    adj[v].Add(u);
}
  
// Function to find the GCD from root to leaf path
static void DFS(int node, int parent, int G, int leaf,
        int []val, List<int> []adj)
{
    // If we reach the desired leaf
    if (node == leaf)
    {
        G = __gcd(G, val[node]);
        Console.Write(G);
        return;
    }
  
    // Call DFS for children
    foreach (int it in adj[node]) 
    {
  
        if (it != parent)
            DFS(it, node, __gcd(G, val[it]), leaf, val, adj);
    }
}
static int __gcd(int a, int b) 
{ 
    return b == 0? a:__gcd(b, a % b);     
}
  
// Driver code
public static void Main(String[] args)
{
  
    int n = 8;
    List<int> []adj = new List<int>[n + 1];
        for (int i = 0; i < n + 1; i++)
            adj[i] = new List<int>();
    addEgde(adj, 1, 2);
    addEgde(adj, 2, 4);
    addEgde(adj, 1, 3);
    addEgde(adj, 3, 5);
    addEgde(adj, 3, 6);
    addEgde(adj, 6, 7);
    addEgde(adj, 6, 8);
  
    int leaf = 5;
  
    // -1 to indicate no value in node 0
    int []val = { -1, 6, 2, 6, 3, 4, 12, 10, 18 };
  
    // Initially GCD is the value of the root
    int G = val[1];
  
    DFS(1, -1, G, leaf, val, adj);
}
}
 
// This code is contributed by PrinciRaj1992

Javascript

<script>
 
// JavaScript implementation of the approach
 
let N = 9;
 
// Function to add edges in the tree
function addEgde(adj,u,v)
{
    adj[u].push(v);
    adj[v].push(u);
}
 
// Function to find the GCD from root to leaf path
function DFS(node,parent,G,leaf,val,adj)
{
    // If we reach the desired leaf
    if (node == leaf)
    {
        G = __gcd(G, val[node]);
        document.write(G);
        return;
    }
   
    // Call DFS for children
    for (let it of adj[node]) 
    {
   
        if (it != parent)
            DFS(it, node, __gcd(G, val[it]), leaf, val, adj);
    }
}
 
// Driver code
function __gcd(a,b)
{
    return b == 0? a:__gcd(b, a % b);    
}
 
let n = 8;
let adj = new Array(n + 1);
for (let i = 0; i < n + 1; i++)
    adj[i] = [];
addEgde(adj, 1, 2);
addEgde(adj, 2, 4);
addEgde(adj, 1, 3);
addEgde(adj, 3, 5);
addEgde(adj, 3, 6);
addEgde(adj, 6, 7);
addEgde(adj, 6, 8);
 
let leaf = 5;
 
// -1 to indicate no value in node 0
let val = [ -1, 6, 2, 6, 3, 4, 12, 10, 18 ];
 
// Initially GCD is the value of the root
let G = val[1];
 
DFS(1, -1, G, leaf, val, adj);
 
 
// This code is contributed by rag2127
 
</script>

Output:

Time Complexity: O(NlogN), as we are traversing the graph using DFS (recursion). Where N is the number of nodes in the graph.

Auxiliary Space: O(N), as we are using extra space for the recursive stack. Where N is the number of nodes in the graph.

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