Question

Does this implementation of node delete works, or it my fail ?

void remove_node(node *p)
{
    node **i = &node_list;

    for (;(*i) != NULL && ((*i) != p); *i = ((*i)->next)) ;

    if (*i != NULL) 
    {
      (*i) = (*i)->next;
    }

    if (p != NULL) 
    {
      free(p);
    }
}

BTW, as far as I know, in every algorithm I saw that deletes a node from a list,
there was a variable that was supposed to keep the previous pointer. this implementation lacks this…

Answer 1

Assuming the parameter p as pArg
After for loop :-

for (;(*i) != NULL && ((*i) != p); *i = ((*i)->next)) ;

*i=pArg [if node pArg exists in linked list](case 1) or *i=NULL(case 2)

After first if:-

 if (*i != NULL) 
    {
      (*i) = (*i)->next;
    }

p=pArg->next (case 1) and no operation in (case 2)

After second if:-

if (p != NULL) 
    {
      free(p);
    }

free(pArg->next);(case 1) ; and no operation in (case 2)(if pArg really is a node in the LL)

You deleted the node pointed by pArg and not the pArg itself.

Make a little change:-

node *prevp=NULL;

for (;(*i) != NULL && ((*i) != p); *i = ((*i)->next))
{prevp=*i;} 

if (*i != NULL) 
    {
      prevp->next = (*i)->next;
    }