How to do a B-Tree insert:

  insert(data){
    create a new cursor
    move cursor to the entry nearest data
    if( cursor.key == keyof(data) ){
      replace cursor.data with dataof(data)
      return
    }
    childpg = NULL
    add_to_page(cursor, data+childpg)
    delete the cursor
  }

  add_to_page(cursor, data+childpg ){
    childpg->parent = cursor.page
    if( data+childpg fits on cursor.page ){
      insert data+childpg at cursor
      return
    }
    if( page==root ){
      split page+(data+childpg) into newpage1, center, newpage2
      cursor.page = &newpage1 + center + &newpage2;
      newpage1->parent = cursor.page
      newpage2->parent = cursor.page
      return
    }
    if( move_some_data_left || move_some_data_right ){
      insert data+childpg at cursor
      return
    }
    split page+(data+childpg) into page, center, newpage
    newpage->parent = page->parent
    move cursor to insertion point of center in parent page.
    add_to_page(cursor, center, (newpage));
  }

How to do a B-Tree delete:

  delete(entry){
    if( entry is not a leaf ){
      p = predecessor of entry
      // note: if entry is not a leaf then p must
      // exist and must be a leaf
      free(entry.overflowptr)
      resize entry so that is is big enough to hold p.payload
      entry.payload = p.payload
      entry.overflowptr = p.overflowptr
      p.overflowptr = NULL
      delete(p)
      return
    }
    unlink entry from its page
    refill(page containing entry)
  }

  refill(page){
    if( page is more than half full ) return
    if( page is the root and contains no entries ){
      copy the one child page into this page thus reducing
      the height of the tree by one.
      return
    }
    if( able to merge page with neighbors ){
      do the merge
      refill(parent page)
      return
    }
    borrow entrys from neighbors
  }