**Problem : **
Recall from that it is possible to represent arithmetic, parenthesized
expressions using a tree. If a node is an operator, such as a plus or
a division sign, each of the children must be either a number, or another
expression. In other words, the two children of an operator will be its
operands.
+
3 4
The above means (3+4).
Write a function which will take in a `tree_t` of the form:

and will evaluate the tree according to the above specification that the children of an operator will evaluate to numbers. Thetypedef struct _tree { char op; int value; struct _tree *left, *right; } tree_t;

int eval (tree_t *t) { /* Although a NULL tree is invalid, we will check for it * any way and assign it a value of 0. */ if (t == NULL) return 0; /* If there is no operator, the tree is the value in it */ if (t->op == EMPTY) return t->value; /* Otherwise, the tree evaluates to performing the operation * on the evaluation of its subtrees, the operands. */ switch (t->op) { case ADD: return eval(t->left) + eval(t->right); case SUB: return eval(t->left) - eval(t->right); case MULT: return eval(t->left) * eval(t->right); case DIV: return eval(t->left) / eval(t->right); } }

**Problem : **
Assume now that your nodes represent people and their ages and as a result
have fields for a person's name and age. Use the following definition for
`tree_t`:

Write a single function which will take in a pointer to atypedef struct _tree { int age; char *name; struct _tree *left, *right; } tree_t;

void free_tree (tree_t *t) { /* Base case */ if (t == NULL) return; /* Recursive calls */ free_tree (t->left); free_tree (t->right); /* The space for the name is dynamic and must be freed as well */ free (t->name); /* Finally free the memory for the individual node */ free (t); }

**Problem : **
A Huffman tree is a means of encoding characters, that is, a way of
assigning a certain sequence of bits to a character (ASCII is another
convention). The idea is that you can save space when storing a file if
you can find an encoding for the characters such that the file requires
fewer bits overall. We will not cover the process of building such a tree,
but we will consider the process of using one. Starting from the root
node, you keep walking along either the left or the right branch until you
reach the desired character. Moving left corresponds to a 0 bit and moving
right to a 1 bit. So, if you have to go left, right, right to get to the
character 'A', then the encoding for 'A' is 011.
How can you describe the location of all of the nodes that have characters
associated with them? The root node, for example, has no character associated
with it.

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