Second Largest element in n-ary tree

Given an N-ary tree, find and return the node with second largest value in the given tree. Return NULL if no node with required value is present.

For example, in the given tree

Second largest node is 20.

A simple solution is to traverse the array twice. In the first traversal find the maximum value node. In the second traversal find the greatest element node less than the element obtained in first traversal. The time complexity of this solution is O(n).

An Efficient Solution can be to find the second largest element in a single traversal.
Below is the complete algorithm for doing this:

1) Initialize two nodes first and second to NULL as,
   first = second = NULL
2) Start traversing the tree,
   a) If the current node data say root->key is greater
      than first->key then update first and second as,
      second = first
      first = root
   b) If the current node data is in between first and 
      second, then update second to store the value
      of current node as
        second = root
3) Return the node stored in second.
// CPP program to find second largest node
// in an n-ary tree.
#include <bits/stdc++.h>
using namespace std;

// Structure of a node of an n-ary tree
struct Node {
    int key;
    vector<Node*> child;

// Utility function to create a new tree node
Node* newNode(int key)
    Node* temp = new Node;
    temp->key = key;
    return temp;

void secondLargestUtil(Node* root, Node** first,
                                  Node** second)
    if (root == NULL)

    // If first is NULL, make root equal to first
    if (!(*first))
        *first = root;

    // if root is greater than first then second
    // will become first and update first equal 
    // to root
    else if (root->key > (*first)->key) {
        *second = *first;
        *first = root;

    // If root is less than first but greater than 
    // second
    else if (!(*second) || root->key > (*second)->key)
        *second = root;

    // number of children of root
    int numChildren = root->child.size();

    // recursively calling for every child
    for (int i = 0; i < numChildren; i++)
        secondLargestUtil(root->child[i], first, second);

Node* secondLargest(Node* root)
    // second will store the second highest value
    Node* second = NULL;

    // first will store the largest value in the tree
    Node* first = NULL;

    // calling the helper function
    secondLargestUtil(root, &first, &second);

    // return the second largest element
    return second;

// Driver program
int main()
    /*   Let us create below tree
   *             5
   *         /   |  \
   *         1   2   3
   *        /   / \   \
   *       15  4   5   6

    Node* root = newNode(5);

    cout << "Second largest element is : ";
    cout << secondLargest(root) - key << endl;

    return 0;


Second largest element is : 6

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