We write a few more methods.
Node * Tree_Successor(Node* root)
{
 Assert (root != null);
if (root->right)
  {return Tree_Minimum(root->right);}
Node* x = root;
// find the lowest ancestor of x whose left child is also an ancestor of x
Node* y = root->parent;
while ( y && x == y->right)
  {
      x = y;
      y = y->parent;
   }
return y;
}
Node* Tree_Minimum(Node* root)
{
Node *x = root;
while (x && x->left)
       x = x->left;
 return x;
}

Node* Tree_Predecessor(Node* root)
{
Assert (root != null);
if (root->left)
{return Tree_Maximum(root->left);}
Node* x= root;
Node* y =   root->parent;
while (y && x == y->left)
{
 x = y;
 y = y -> parent;
}
return y;
}

File - System organization
There are primarily two design considerations:
1) exposure of file system to user via definitions of file, attributes operations
2) overlay of logical filesystem on top of physical file system via data structures and algorithms
The file system stack consists of
application programs
logical file system
file-organization module
basic file system
I/O control
devices
a typical open file table will have
index, file_name, permissions, access dates, and pointer to disk block.
A file is represented by an inode (short for index node) in Unix. The in ode contains the user and group identifiers of the file, last file modification and access, count of number of hard links, and the type of the file.In addition, the inode contains 15 pointers to the disk blocks containing the data contents of the file. Inodes also contain pointers that point to direct blocks. There can be pointers to single indirect and double indirect as well as triple indirect blocks. File structures are inherited by the child process after a fork so several processes may share the same offset location for a file.