Sentinel node

Sentinels are used as an alternative over using NULL as the path terminator in order to get one or more of the following benefits:

• Marginally increased speed of operations
• Increased data structure robustness (arguably)

• Marginally increased algorithmic complexity and code size.
• If the data structure is accessed concurrently (which means that all nodes being accessed have to be protected at least for “read-only”), for a sentinel-based implementation the sentinel node has to be protected for “read-write” by a mutex. This extra mutex in quite a few use scenarios can cause severe performance degradation.^[1] One way to avoid it is to protect the list structure as a whole for “read-write”, whereas in the version with NULL it suffices to protect the data structure as a whole for “read-only” (if an update operation will not follow).
• The sentinel concept is not useful for the recording of the data structure on disk.

Search in a linked list

Below are two versions of a subroutine (implemented in the C programming language) for looking up a given search key in a singly linked list. The first one uses the sentinel value NULL, and the second one a (pointer to the) sentinel node Sentinel, as the end-of-list indicator. The declarations of the singly linked list data structure and the outcomes of both subroutines are the same.

struct sll_node {                          // one node of the singly linked list    struct sll_node *next;                 // end-of-list indicator or -> next node    int key;} sll, *first;

First version using NULL as an end-of-list indicator

// global initializationfirst = NULL;                              // before the first insertion (not shown)struct sll_node *Search(struct sll_node *first, int search_key) {    struct sll_node *node;    for (node = first;         node != NULL;         node = node->next)    {        if (node->key == search_key)            return node;                   // found    }    // search_key is not contained in the list:    return NULL;}

The for-loop contains two tests (yellow lines) per iteration:

• node != NULL;
• if (node->key == search_key).

Second version using a sentinel node

The globally available pointer sentinel to the deliberately prepared data structure Sentinel is used as end-of-list indicator.

// global variablesll_node Sentinel, *sentinel = &Sentinel;// global initializationsentinel->next = sentinel;first = sentinel;                          // before the first insertion (not shown)

Note that the pointer sentinel has always to be kept at the end of the list.This has to be maintained by the insert and delete functions. It is, however, about the same effort as when using a NULL pointer.

struct sll_node *SearchWithSentinelnode(struct sll_node *first, int search_key) {    struct sll_node *node;    // Prepare the “node” Sentinel for the search:    sentinel->key = search_key;    for (node = first;         node->key != search_key;         node = node->next)    {}     // Post-processing:    if (node != sentinel)        return node;                       // found    // search_key is not contained in the list:    return NULL;}

The for-loop contains only one test (yellow line) per iteration:

• node->key != search_key;.

Python implementation of a circular doubly-linked list

Linked list implementations, especially one of a circular, doubly-linked list, can be simplified remarkably using a sentinel node to demarcate the beginning and end of the list.

• The list starts out with a single node, the sentinel node which has the next and previous pointers point to itself. This condition determines if the list is empty.
• In a non-empty list, the sentinel node's next pointer gives the head of the list, and the previous pointer gives the tail of the list.

Following is a Python implementation of a circular doubly-linked list:

class Node:    def __init__(self, data, next=None, prev=None):        self.data = data        self.next = next        self.prev = prev    def __repr__(self) -> str:        return f'Node(data={self.data})'class LinkedList:    def __init__(self):        self._sentinel = Node(data=None)        self._sentinel.next = self._sentinel        self._sentinel.prev = self._sentinel    def pop_left(self) -> Node:        return self.remove_by_ref(self._sentinel.next)    def pop(self) -> Node:        return self.remove_by_ref(self._sentinel.prev)    def append_nodeleft(self, node):        self.add_node(self._sentinel, node)    def append_node(self, node):        self.add_node(self._sentinel.prev, node)    def append_left(self, data):        node = Node(data=data)        self.append_nodeleft(node)    def append(self, data):        node = Node(data=data)        self.append_node(node)    def remove_by_ref(self, node) -> Node:        if node is self._sentinel:            raise Exception('Can never remove sentinel.')        node.prev.next = node.next        node.next.prev = node.prev        node.prev = None        node.next = None        return node    def add_node(self, curnode, newnode):        newnode.next = curnode.next        newnode.prev = curnode        curnode.next.prev = newnode        curnode.next = newnode    def search(self, value):        self._sentinel.data = value        node = self._sentinel.next        while node.data != value:            node = node.next        self._sentinel.data = None        if node is self._sentinel:            return None        return node    def __iter__(self):        node = self._sentinel.next        while node is not self._sentinel:            yield node.data            node = node.next    def reviter(self):        node = self._sentinel.prev        while node is not self._sentinel:            yield node.data            node = node.prev

Notice how the add_node() method takes the node that will be displaced by the new node in the parameter curnode. For appending to the left, this is the head of a non-empty list, while for appending to right, it is the tail. But because of how the linkage is set up to refer back to the sentinel, the code just works for empty lists as well, where curnode will be the sentinel node.

Search in a binary tree

General declarations, similar to article Binary search tree:

struct bst_node {                     // one node of the binary search tree    struct bst_node *child[2];        // each: ->node  or  end-of-path indicator    int key;} ;struct bst {                          // binary search tree    struct bst_node *root;            // ->node  or  end-of-path indicator} *BST;

The globally available pointer sentinel to the single deliberately prepared data structure Sentinel = *sentinel is used to indicate the absence of a child.

// global variablebst_node Sentinel, *sentinel = &Sentinel;// global initializationSentinel.child[0] = Sentinel.child[1] = sentinel;BST->root = sentinel;                 // before the first insertion (not shown)

Note that the pointer sentinel has always to represent every leaf of the tree.This has to be maintained by the insert and delete functions. It is, however, about the same effort as when using a NULL pointer.

struct bst_node *SearchWithSentinelnode(struct bst *bst, int search_key) {    struct bst_node *node;    // Prepare the “node” Sentinel for the search:    sentinel->key = search_key;     for (node = bst->root;;) {        if (search_key == node->key)            break;        if search_key < node->key:            node = node->child[0];    // go left        else            node = node->child[1];    // go right    }     // Post-processing:    if (node != sentinel)        return node;                  // found    // search_key is not contained in the tree:    return NULL;}

Remarks

1. With the use of SearchWithSentinelnode searching loses the R/O property. This means that in applications with concurrency it has to be protected by a mutex, an effort which normally exceeds the savings of the sentinel.
2. SearchWithSentinelnode does not support the tolerance of duplicates.
3. There has to be exactly one “node” to be used as sentinel, but there may be extremely many pointers to it.

• Canary value
• Elephant in Cairo
• Guard (computer science), a boolean expression that must evaluate to true if the program execution is to continue in the branch in question
• Magic number (programming)
• Magic string
• Null object pattern
• Semipredicate problem
• Sentinel value
• Time formatting and storage bugs