old_contents: import io, math, struct
  
  from collections import OrderedDict
  from struct      import Struct
  
  from Catalog.Identifiers import PageId, FileId, TupleId
  from Catalog.Schema      import DBSchema
  
  import Storage.FileManager
  
  class BufferPool:
    """
    A buffer pool implementation.
  
    Since the buffer pool is a cache, we do not provide any serialization methods.
  
    >>> schema = DBSchema('employee', [('id', 'int'), ('age', 'int')])
    >>> bp = BufferPool()
    >>> fm = Storage.FileManager.FileManager(bufferPool=bp)
    >>> bp.setFileManager(fm)
  
    # Check initial buffer pool size
    >>> len(bp.pool.getbuffer()) == bp.poolSize
    True
  
    """
  
    # Default to a 10 MB buffer pool.
    defaultPoolSize = 10 * (1 << 20)
  
    # Buffer pool constructor.
    #
    # REIMPLEMENT this as desired.
    #
    # Constructors keyword arguments, with defaults if not present:
    # pageSize       : the page size to be used with this buffer pool
    # poolSize       : the size of the buffer pool
    def __init__(self, **kwargs):
      self.pageSize     = kwargs.get("pageSize", io.DEFAULT_BUFFER_SIZE)
      self.poolSize     = kwargs.get("poolSize", BufferPool.defaultPoolSize)
      self.pool         = io.BytesIO(b'\x00' * self.poolSize)
  
      ####################################################################################
      # DESIGN QUESTION: what other data structures do we need to keep in the buffer pool?
      self.freeList     = [] 
      # Buffer Pool Frames
      # Dictionary : offset -> pin number
      self.frames       = {x : 0 for x in range(0, self.pageSize * self.numPages(), self.pageSize)};
      # Buffer Pool replacement queue ( Least Recently Used )
      self.replaceQ     = []
  
  
    def setFileManager(self, fileMgr):
      self.fileMgr = fileMgr
  
    # Basic statistics
  
    def numPages(self):
      return math.floor(self.poolSize / self.pageSize)
  
    def numFreePages(self):
      raise 
  
    def size(self):
      return self.poolSize
  
    def freeSpace(self):
      return self.numFreePages() * self.pageSize
  
    def usedSpace(self):
      return self.size() - self.freeSpace()
  
  
    # Buffer pool operations
  
    def hasPage(self, pageId):
      raise NotImplementedError
    
    def getPage(self, pageId):
      raise NotImplementedError
  
    # Removes a page from the page map, returning it to the free 
    # page list without flushing the page to the disk.
    def discardPage(self, pageId):
      raise NotImplementedError
  
    def flushPage(self, pageId):
      raise NotImplementedError
  
    # Evict using LRU policy. 
    # We implement LRU through the use of an OrderedDict, and by moving pages
    # to the end of the ordering every time it is accessed through getPage()
    def evictPage(self):
      raise NotImplementedError
  
  
  if __name__ == "__main__":
      import doctest
      doctest.testmod()
  
new_contents: import io, math, struct
  
  from collections import OrderedDict
  from struct      import Struct
  
  from Catalog.Identifiers import PageId, FileId, TupleId
  from Catalog.Schema      import DBSchema
  
  import Storage.FileManager
  
  class BufferPool:
    """
    A buffer pool implementation.
  
    Since the buffer pool is a cache, we do not provide any serialization methods.
  
    >>> schema = DBSchema('employee', [('id', 'int'), ('age', 'int')])
    >>> bp = BufferPool()
    >>> fm = Storage.FileManager.FileManager(bufferPool=bp)
    >>> bp.setFileManager(fm)
  
    # Check initial buffer pool size
    >>> len(bp.pool.getbuffer()) == bp.poolSize
    True
  
    """
  
    # Default to a 10 MB buffer pool.
    defaultPoolSize = 10 * (1 << 20)
  
    # Buffer pool constructor.
    #
    # REIMPLEMENT this as desired.
    #
    # Constructors keyword arguments, with defaults if not present:
    # pageSize       : the page size to be used with this buffer pool
    # poolSize       : the size of the buffer pool
    def __init__(self, **kwargs):
      self.pageSize     = kwargs.get("pageSize", io.DEFAULT_BUFFER_SIZE)
      self.poolSize     = kwargs.get("poolSize", BufferPool.defaultPoolSize)
      self.pool         = io.BytesIO(b'\x00' * self.poolSize)
  
      ####################################################################################
      # DESIGN QUESTION: what other data structures do we need to keep in the buffer pool?
      
      # Buffer Pool Frames
      # Dictionary : offset -> (pId, pin number)
      # ? We can keep a backward mapping as well
      self.frames       = {x : (None, 0) for x in range(0, self.pageSize * self.numPages(), self.pageSize)};
      self.backward     = dict();
      
      # Use a queue to store freeList
      self.freeList     = self.frames.keys();
      
      # Buffer Pool replacement queue ( Least Recently Used )
      self.replaceQ     = []
  
  
    def setFileManager(self, fileMgr):
      self.fileMgr = fileMgr
  
    # Basic statistics
  
    def numPages(self):
      return math.floor(self.poolSize / self.pageSize)
  
    def numFreePages(self):
      return len( self.freeList ); 
  
    def size(self):
      return self.poolSize
  
    def freeSpace(self):
      return self.numFreePages() * self.pageSize
  
    def usedSpace(self):
      return self.size() - self.freeSpace()
  
  
    # Buffer pool operations
  
    def hasPage(self, pageId):
      raise NotImplementedError
    
    def getPage(self, pageId):
      raise NotImplementedError
  
    # Removes a page from the page map, returning it to the free 
    # page list without flushing the page to the disk.
    def discardPage(self, pageId):
      raise NotImplementedError
  
    def flushPage(self, pageId):
      raise NotImplementedError
  
    # Evict using LRU policy. 
    # We implement LRU through the use of an OrderedDict, and by moving pages
    # to the end of the ordering every time it is accessed through getPage()
    def evictPage(self):
      raise NotImplementedError
  
  
  if __name__ == "__main__":
      import doctest
      doctest.testmod()
  
subject: Complete the architecture structure