Consider a hash table \(T[0\cdots m-1]\) where quadratic probing is used to resolve collision. Recall that to resolve collision using quadratic probing when inserting a key $$e$$ in the hash table , addresses \(h(e)\), \(h(e)+1\), \(h(e)+4\), \(\cdots\), \(h(e)+i^2\) are probed until a vacant position is found or \(m/2\) trials are tested.

1. Write the corresponding declarations.
2. Write a function \(delete(T,e)\) that deletes the key \(e\) from the table and preserves the quadratic probing characteristic.

Example: after inserting \(aa\), \(bb\), \(cc\), \(dd\), the hash table is:
\begin{array}{ |c | c | c| c| c| c|c | c | c | c| c| c| } \hline
index & 0 &1 &2 &3 &4& 5& 6 &7 &8 &9 &10 \\ \hline
e& dd & & aa & bb & & & cc & & & & \\ \hline
v=H(e)& 2& &2 &2 & & &2 & & & & \\ \hline
\end{array}

After deleting \(e=bb\) at position 3, the table becomes:
\begin{array}{ |c | c | c| c| c| c|c | c | c | c| c| c| } \hline
index & 0 &1 &2 &3 &4& 5& 6 &7 &8 &9 &10 \\ \hline
e& & & aa & cc & & & dd & & & & \\ \hline
v=H(e)& & &2 &2 & & &2 & & & & \\ \hline
\end{array}

int delete(hash h, element e, int size)
{

    int i, nb ,step, pos, old;
    int	vhash = hashfunction(e,size);
    nb=1;
	step=0;
	while(nb<(size/2))
	{
	    if(h[(vhash+step*step)%size] == e) // found
	    {
	        pos=(vhash+step*step)%size;
	        while( nb<(size/2) )
	        {
	            step++;
	            if(h[(vhash+step*step)%size]!='0' && hashfunction(h[(vhash+step*step)%size],size)==vhash)
	            {
	               if(old==(vhash+step*step)%size) break;
	                h[pos] = h[(vhash+step*step)%size]; 
	                h[(vhash+step*step)%size]='0';
	               
	                old = pos;
	                pos=(vhash+step*step)%size;
	            }
	             nb++;
	        }
		    return 1;
	    }
	    step++;
	    nb++;
	}
	return 0;   
}