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

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++

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// 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;
}

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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

Output:

2


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Striver(underscore)79 at Codechef and codeforces D

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Improved By : SURENDRA_GANGWAR