1. Write a function in C programming language that can find and return the height of a Binary Tree.
2. Write a function in C programming language that can find and return the cost of the most expensive path from the root of a Binary Tree to a leaf.
3. Write a function in C programming language that finds if a particular Binary Tree is balanced.

More explanations are provided in the attached document.

Please find attached 450363.c containing just the function implementations. Code has been commented well, but even without that logic is quite clear as it is based on recursion. This implementation makes use of an auxiliary function min_height in determining whether a tree is balanced as per the given criteria or not.

/*
* This function finds and returns the height of a Binary Tree.
*
* The height of a binary tree is the length of the longest path from root of
* the Binary Tree to a leaf.
*
* This implementation considers that the height of a null tree is 0 and that of
* a single node tree is 1.
*/

int height (node root)
{
if (root == (node) NULL)
return 0;
else
{
...

Solution Summary

Attached solution contains just the function implementations. Code has been commented well, but even without that logic is quite clear as it is based on recursion. This implementation makes use of an auxiliary function min_height in determining whether a tree is balanced as per the given criteria or not.

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Each line of values in input file "tree2Data.txt" represents one linear binary tree, where ' _ ' represents a no value node.
Compare all trees to all other tre

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A. Write 3n − (k + 5) in prefix notation: ????.
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c. Every full binary tree with 50 leaves has ???? vertices.

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Show that if binary tree T is full at level i, then it is full at every level j smaller than i.
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Show that the depth of the complete binary tree Tn for a general n is given by
D(Tn) = [log2n].
See attached for better format.
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Using induction, give a direct proof of Propo

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a) In one paragraph, define what trees are. Be sure to mention the difference between binary and n-ary trees.
b) Represent the following hierarchical data

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