Related Articles

# Immediate Smaller element in an N-ary Tree

• Difficulty Level : Medium
• Last Updated : 17 May, 2018

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 ``using` `namespace` `std;`` ` `// class of a node of an n-ary tree``class` `Node {`` ` `public``:``    ``int` `key;``    ``vector 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)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

My Personal Notes arrow_drop_up