g++ -O2 flag giving segmentation fault - c++

Question

The program below is a bst tree which works fine under unoptimized settings but produces a SIGSEGV under special circumstances. Since my debugging skills doesn't extend towards assembly, I can use some input to what is causing this error. Below is the full code so it can be reproduced. There is nothing fancy, a node struct is there to hold node data, a simple insert operation and a method to confirm the height of the tree.
#include <iostream>
#include <cstdlib>
using namespace std;
typedef struct avl_tree_node //node data
{
int data;
int balance{0};
avl_tree_node *left{NULL};
avl_tree_node *right{NULL};
avl_tree_node *parent{NULL};
}node;
class avl
{
private:
node *root;
int get_height(node *head) //calculates the height
{
if (head == NULL)
return -1;
int l_height = get_height(head->left);
int r_height = get_height(head->right);
if (l_height > r_height)
return l_height+1;
return r_height+1;
}
void unbalanced_insert(node *head, int item); //method definition for a simple insert
public:
avl(int data)
{
root->data = data;
root->parent = NULL;
root->left = NULL;
root->right = NULL;
}
int height() //gives the height
{
return get_height(root);
}
void unbalanced_insert(int item) //wrapper
{
unbalanced_insert(root, item);
}
};
void avl::unbalanced_insert(node *head, int item) //inserts node to the tree
{
//cout << "stepped" << endl;
if (item > head->data)
{
if (head->right == NULL)
{
head->right = (node*)malloc(sizeof(node));
head->right->data = item;
head->right->parent = head;
head->right->left = NULL;
head->right->right = NULL;
head->balance = 1;
return;
}
unbalanced_insert(head->right, item);
head->balance++;
return;
}
else
{
if (head->left == NULL)
{
head->left = (node*)malloc(sizeof(node));
head->left->data = item;
head->left->parent= head;
head->left->left = NULL;
head->left->right = NULL;
head->balance = -1;
return;
}
unbalanced_insert(head->left, item);
head->balance--;
return;
}
}
int main()
{
avl a(0);
for (int i = 1; i < 5; i++) //works until i < 4
{
a.unbalanced_insert(i);
}
cout << a.height() << endl;
return 0;
}
Under normal circumstances, I'd be happy that this works with unoptimized flags, but I have to build this with specific flags. One of such is the -O2 flag. The segmentation fault occurs between the avl a(0) object construction and the for loop inside main. The error also seems to be dependent on the boolean check of the for loop. This works fine if i < 4 and executed with: g++ avl.cpp -g -O2 -o program && ./program

Answer 1

One obvious problem, and it occurs on the very first function call in main, i.e. avl a(0):
root->data = data;
The root is uninitialized, thus the behavior is undefined.

Answer 2

I guess when instantiate the object of avl here.
avl a(0);
constructor of class as shown below is called.
avl(int data)
{
root->data = data;
root->parent = NULL;
root->left = NULL;
root->right = NULL;
}
But here I see root pointer is not allocated any memory