{"cells":[{"cell_type":"markdown","metadata":{},"source":"Linked Lists\n============\n\n"},{"cell_type":"markdown","metadata":{},"source":["## Agenda\n\n"]},{"cell_type":"markdown","metadata":{},"source":["1.  The `LinkedList` and `Node` classes\n2.  Implementing `append`\n3.  Implementing deletion\n4.  Bidirectional links\n5.  Run-time analysis\n6.  Closing remarks\n\n"]},{"cell_type":"markdown","metadata":{},"source":["## 1.  The `LinkedList` and `Node` classes\n\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["class LinkedList:\n    class Node:\n        def __init__(self, val, next=None):\n            self.val = val\n            self.next = next\n\n    def __init__(self):\n        self.head = None\n        self.count = 0\n\n    def prepend(self, value):\n        pass\n\n    def __len__(self):\n        return self.count\n\n    def __iter__(self):\n        n = self.head\n        while n:\n            yield n.val\n            n = n.next\n\n    def __repr__(self):\n        return '[' + ', '.join(x for x in self) + ']'"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["lst = LinkedList()\nfor i in range(10):\n    lst.prepend(i)\nlst"]},{"cell_type":"markdown","metadata":{},"source":["## 1.  Implementing `append`\n\n"]},{"cell_type":"markdown","metadata":{},"source":["### Option 1\n\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["class LinkedList (LinkedList): # note: using inheritance to extend prior definition\n    def append(self, value):\n        pass"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["lst = LinkedList()\nfor i in range(10):\n    lst.append(i)\nlst"]},{"cell_type":"markdown","metadata":{},"source":["### Option 2\n\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["class LinkedList (LinkedList):\n    def __init__(self):\n        self.head = self.tail = None\n        self.count = 0\n\n    def prepend(self, value):\n        pass\n\n    def append(self, value):\n        pass"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["lst = LinkedList()\nfor i in range(10):\n    lst.append(i)\nlst"]},{"cell_type":"markdown","metadata":{},"source":["## 1.  Implementing deletion\n\n"]},{"cell_type":"markdown","metadata":{},"source":["### Deleting the head\n\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["class LinkedList (LinkedList):\n    def del_head(self):\n        assert(len(self) > 0)\n        pass"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["lst = LinkedList()\nfor i in range(10):\n    lst.append(i)\nlst.del_head()\nlst.del_head()\nlst"]},{"cell_type":"markdown","metadata":{},"source":["### Deleting the tail\n\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["class LinkedList (LinkedList):\n    def del_tail(self):\n        assert(len(self) > 0)\n        pass"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["lst = LinkedList()\nfor i in range(10):\n    lst.append(i)\nlst.del_tail()\nlst.del_tail()\nlst"]},{"cell_type":"markdown","metadata":{},"source":["## 1.  Bidirectional links (Doubly-linked list) & Sentinel head\n\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["class LinkedList:\n    class Node:\n        def __init__(self, val, prior=None, next=None):\n            self.val = val\n            self.prior = prior\n            self.next  = next\n\n    def __init__(self):\n        self.count = 0\n\n    def prepend(self, value):\n        self.count += 1\n\n    def append(self, value):\n        self.count += 1\n\n    def __getitem__(self, idx):\n        pass\n\n    def __len__(self):\n        return self.count\n\n    def __iter__(self):\n        n = self.head.next\n        while n is not self.head:\n            yield n.val\n            n = n.next\n\n    def __repr__(self):\n        return '[' + ', '.join(str(x) for x in self) + ']'"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["lst = LinkedList()\nfor i in range(10):\n    lst.prepend(i)\nfor i in range(10):\n    lst.append(i)\nlst"]},{"cell_type":"markdown","metadata":{},"source":["## 1.  Incorporating a \"cursor\"\n\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["class LinkedList:\n    class Node:\n        def __init__(self, val, prior=None, next=None):\n            self.val = val\n            self.prior = prior\n            self.next  = next\n\n    def __init__(self):\n        self.head = self.cursor = LinkedList.Node(None)\n        self.head.prior = self.head.next = self.head\n        self.count = 0\n\n    def append(self, value):\n        n = LinkedList.Node(value, prior=self.head.prior, next=self.head)\n        n.prior.next = n.next.prior = n\n        self.count += 1\n\n    def cursor_set(self, idx):\n        pass\n\n    def cursor_insert(self, x):\n        pass\n\n    def cursor_delete(self):\n        pass\n\n    def __len__(self):\n        return self.count\n\n    def __iter__(self):\n        n = self.head.next\n        while n is not self.head:\n            yield n.val\n            n = n.next\n\n    def __repr__(self):\n        return '[' + ', '.join(str(x) for x in self) + ']'"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["lst = LinkedList()\nfor i in range(10):\n    lst.append(i)\nlst"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["lst.cursor_set(4)\nfor x in 'abcd':\n    lst.cursor_insert(x)\nlst"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["lst.cursor_set(8)\nfor _ in range(4):\n    lst.cursor_delete()"]},{"cell_type":"markdown","metadata":{},"source":["## 1.  Run-time analysis\n\n"]},{"cell_type":"markdown","metadata":{},"source":["Run-time complexities for circular, doubly-linked list of $N$ elements:\n\n-   indexing (position-based access) = $O(?)$\n-   search (unsorted) = $O(?)$\n-   search (sorted) = $O(?)$ — binary search isn't possible!\n-   prepend = $O(?)$\n-   append = $O(?)$\n-   indexing = $O(?)$\n-   insertion at arbitrary position: indexing = $O(?)$ + insertion = $O(?)$\n-   deletion of arbitrary element: indexing = $O(?)$ + deletion = $O(?)$\n\n"]}],"metadata":{"org":null,"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.5.2"}},"nbformat":4,"nbformat_minor":0}