Immediate Smaller element in an N-ary Tree

Given an element x, task is to find the value of its immediate smaller element.

Example :

Input : x = 30 (for above tree)
Output : Immediate smaller element is 25

Explanation : Elements 2, 15, 20 and 25 are smaller than x i.e, 30, but 25 is the immediate smaller element and hence the answer.
Approach :

  • Let res be the resultant node.
  • Initialize the resultant Node as NULL.
  • For every Node, check if data of root is greater than res, but less than x. if yes, update res.
  • Recursively do the same for all nodes of the given Generic Tree.
  • Return res, and res->key would be the immediate smaller element.

Below is the implementation of above approach :

// C++ program to find immediate Smaller
// Element of a given element in a n-ary tree.
#include <bits/stdc++.h>
using namespace std;

// class of a node of an n-ary tree
class Node {

public:
    int key;
    vector<Node*> child;

    // constructor
    Node(int data)
    {
        key = data;
    }
};

// Function to find immediate Smaller Element
// of a given number x
void immediateSmallerElementUtil(Node* root, 
                            int x, Node** res)
{
    if (root == NULL)
        return;

    // if root is greater than res, but less
    // than x, then update res
    if (root->key < x)
        if (!(*res) || (*res)->key < root->key)
            *res = root; // Updating res

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

    // Recursive calling for every child
    for (int i = 0; i < numChildren; i++)
        immediateSmallerElementUtil(root->child[i], x, res);

    return;
}

// Function to return immediate Smaller
// Element of x in tree
Node* immediateSmallerElement(Node* root, int x)
{
    // resultant node
    Node* res = NULL;

    // calling helper function and using
    // pass by reference
    immediateSmallerElementUtil(root, x, &res);

    return res;
}

// Driver program
int main()
{
    // Creating a generic tree
    Node* root = new Node(20);
    (root->child).push_back(new Node(2));
    (root->child).push_back(new Node(34));
    (root->child).push_back(new Node(50));
    (root->child).push_back(new Node(60));
    (root->child).push_back(new Node(70));
    (root->child[0]->child).push_back(new Node(15));
    (root->child[0]->child).push_back(new Node(20));
    (root->child[1]->child).push_back(new Node(30));
    (root->child[2]->child).push_back(new Node(40));
    (root->child[2]->child).push_back(new Node(100));
    (root->child[2]->child).push_back(new Node(20));
    (root->child[0]->child[1]->child).push_back(new Node(25));
    (root->child[0]->child[1]->child).push_back(new Node(50));

    int x = 30;

    cout << "Immediate smaller element of " << x << " is ";
    cout << immediateSmallerElement(root, x)->key << endl;

    return 0;
}

Output :

Immediate smaller element of 30 is 25

Time Complexity : O(N), where N is the number of nodes in N-ary Tree.
Auxiliary Space : O(N), for recursive call(worst case when a node has N number of childs)



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