Height of n-ary tree if parent array is given

Introduction

In the domain of computer science and data structures, trees are fundamental designs that assume a vital part in different algorithms and applications. Among the different sorts of trees, n-ary trees hold unique importance because of their capacity to address various leveled associations with multiple children per node. Deciding the level of a n-ary tree is a typical issue experienced in algorithmic situations. In this article, we will dig into understanding how to register the level of a n-ary tree when just the parent exhibit is given, with an emphasis on execution in the C programming language.

Understanding n-ary Trees

Before diving into the complexities of height calculation, it's basic to understand what n-ary trees are. Not at all like binary trees where every node can have all things considered two children, n-ary trees permit nodes to have various children, frequently signified by the parameter 'n'. These trees are portrayed by their various leveled structure, where every node addresses a data component, and its children address further developments or relationships.

Height of an n-ary Tree

The height of a tree is characterized as the length of the longest way from the root node to any leaf node. With regards to a n-ary tree, deciding its height turns into a marginally unique undertaking contrasted with binary trees because of the presence of multiple children per node.

Approach to Calculate Height

When given the parent array representation of an n-ary tree, we can utilize a depth-first traversal approach to compute the height effectively. Here is a step-by-step clarification of the approach:

Initialize Depth Array: Create an array to store the depth of every node in the tree. At first, all depths are set to Zero.

Traverse Parent Array: Repeat through the parent array, and for every node, calculate its depth based on the depth of its parent node.

Update Maximum Depth: Monitor the most extreme depth encountered during traversal, which ultimately addresses the height of the tree.

Code

#include <stdio.h>
#include <stdlib.h>
#define MAX_NODES 1000 
int parent[MAX_NODES]; 
int depth[MAX_NODES];  
int find_height(int n) {
    int max_depth = 0;
    for (int i = 0; i < n; i++) {
        int p = parent[i]; 
        depth[i] = (p == -1) ? 1 : depth[p] + 1;
        if (depth[i] > max_depth)
            max_depth = depth[i];
    }
    return max_depth;
}
int main() {
    int n; 
    printf("Enter the number of nodes in the tree: ");
    scanf("%d", &n);
    printf("Enter the parent array (enter -1 for root node):\n");
    for (int i = 0; i < n; i++) {
        scanf("%d", &parent[i]);
    }
    int height = find_height(n);
    printf("Height of the n-ary tree: %d\n", height);
    return 0;
}

Output:

Height of n-ary tree if parent array is given

Code Explanation

Initialization

Start by incorporating the fundamental header files, explicitly "stdlib.h" for memory assignment and "stdio.h" for input and output activities. Define the constant MAX_NODES to address the most extreme number of nodes in the tree.
There are two defined arrays: parent and depth. The depth array is used to hold the depth of each node in the tree, whereas the parent array contains the parent array representation of the tree.

The function find_height

This function calculates the n-ary tree's height.
To get the depth of each node, iteratively traverses the parent array.
It calculates each node's depth by comparing it to that of its parent node.
If the current node is a root node, its depth is updated to 1. Otherwise, it is updated to the depth of its parent node plus 1.
It records the deepest point reached, which is ultimately equivalent to the tree's height.
The function returns the greatest depth (height) of the tree.

Main function

The program execution starts at the main function.
The user is prompted to enter n, which is the number of nodes in the tree.
The user is then prompted to enter the tree's parent array representation.
It uses the find_height function to calculate the n-ary tree's height after receiving the input.
Lastly, it prints the tree's height to the console.

User Input and Output

The user must enter the number of nodes in the tree.
Next, the user enters the tree's parent array representation.
The parent array that is supplied is used by the software to calculate the tree's height.
The user is shown the computed height.

Conclusion

We successfully computed the tree's height by utilizing dynamic programming techniques in conjunction with a depth-first traversal methodology. The given C implementation provides a clear knowledge of the underlying principles and acts as a real illustration of this procedure. Any developer or computer scientist will find it useful to know how to calculate the height of n-ary trees since it is a necessary ability for solving a variety of algorithmic difficulties.

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