Static arrays are structures whose size is fixed at compile time and.pdf
- 1. Static arrays are structures whose size is fixed at compile time and therefore cannot be extended or reduced to fit the data set. A dynamic array can be extended by doubling the size but there is overhead associated with the operation of copying old data and freeing the memory associated with the old data structure. One potential problem of using arrays for storing data is that arrays require a contiguous block of memory which may not be available, if the requested contiguous block is too large. However the advantages of using arrays are that each element in the array can be accessed very efficiently using an index. However, for applications that can be better managed without using contiguous memory we define a concept called “linked lists”. A linked list is a collection of objects linked together by references from one object to another object. By convention these objects are named as nodes. So the basic linked list is collection of nodes where each node contains one or more data fields AND a reference to the next node. The last node points to a NULL reference to indicate the end of the list. Types of Linked Lists Linked lists are widely used in many applications because of the flexibility it provides. Unlike arrays that are dynamically assigned, linked lists do not require memory from a contiguous block. This makes it very appealing to store data in a linked list, when the data set is large or device (eg: PDA) has limited memory. One of the disadvantages of linked lists is that they are not random accessed like arrays. To find information in a linked list one must start from the head of the list and traverse the list sequentially until it finds (or not find) the node. Another advantage of linked lists over arrays is that when a node is inserted or deleted, there is no need to “adjust” the array. There are few different types of linked lists. A singly linked list as described above provides access to the list from the head node. Traversal is allowed only one way and there is no going back. A doubly linked list is a list that has two references, one to the next node and another to previous node. Doubly linked list also starts from head node, but provide access both ways. That is one can traverse forward or backward from any node. A multilinked list (see figures 1 & 2) is a more general linked list with multiple links from nodes. For examples, we can define a Node that has two references, age pointer and a name pointer. With this structure it is possible to maintain a single list, where if we follow the name pointer we can traverse the list in alphabetical order of names and if we traverse the age pointer, we can traverse the list sorted by ages. This type of node organization may be useful for maintaining a customer list in a bank where same list can be traversed in any order (name, age, or any other criteria) based on the need. Designing the Node of a Linked List Linked list is a collection of linked nodes. A node is a struct with at least a data field and a reference to a node of the same type. A node is called a self-referential object, since it contains a
- 2. pointer to a variable that refers to a variable of the same type. For example, a struct Node that contains an int data field and a pointer to another node can be defined as follows. typedef struct node { int data; struct node* next; } node; node* head = NULL; Creating the first node Memory must be allocated for one node and assigned to head as follows. head = (node*) malloc(sizeof(node)); headdata = 10; headnext = NULL; Adding the second node and linking node* nextnode = malloc(sizeof(node)); nextnodedata = 12; nextnodenext = NULL; headnext = nextnode; Linked list is a data structure in which the items are ordered in a linear way. Although modern programming languages support very flexible and rich libraries that works with arrays, which use arrays to represent lists, the principles of building a linked list remain very important. The way linked lists are implemented is a ground level in order to build more complex data structures such as trees. It’s true that almost every operation we can perform on a linked list can be done with an array. It’s also true that some operations can be faster on arrays compared to linked lists. However understanding how to implement the basic operations of a linked list such as INSERT, DELETE, INSERT_AFTER, PRINT and so on is crucial in order to implement data structures as rooted trees, B-trees, red-black trees, etc. Big-O notation is a way to express the efficiency of an algorithm. If you’re going to be working with code, it is extremely important that you understand Big-O. It is, quite literally, the language we use to express efficiency. Big-O is an expression of how the execution time of a program scales with the input data. That is, as the input gets bigger, how much longer will the program take? Just a little bit? A lot longer? Suppose you have a function for which does some processing on an array of size N. If foo takes O(N) time, then, as the array grows (that is, as N increases), the number of seconds foo takes will also increase in some sort of linear fashion.
- 3. The first decision in planning the linked-list implementation of the Queue class is which end of the list will correspond to the front of the queue. Recall that items need to be added to the rear of the queue, and removed from the front of the queue. Therefore, we should make our choice based on whether it is easier to add/remove a node from the front/end of a linked list. If we keep pointers to both the first and last nodes of the list, we can add a node at either end in constant time. However, while we can remove the first node in the list in constant time, removing the last node requires first locating the previous node, which takes time proportional to the length of the list. Therefore, we should choose to make the end of the list be the rear of the queue, and the front of the list be the front of the queue. Other than saving space, the first advantage I can see for singly linked lists over doubly linked lists is to avoid having to update two links instead of one when you modify the list, when adding an element for example. Of course, one might say that you can always ignore the second link, but in that case, it is no longer doubly linked, but only an unused field.What might also be seen as an advantage is that singly linked list are necessarily consistent, though possibly wrong when there are bugs in the program. Doubly linked lists can end-up having inconsistent links forward and backward. But it is debatable which of the two cases, if any, is an advantage. update: I had tried to see some impact on garbage collection, but found none. Actually, there is one when storage reclamation is done by reference counting, as reference counting is defeated by loops, and doubly linked lists contain loops. Singly linked list escape the problem. Of course, there are ways around it for doubly linked lists, such as the use of weak pointers, or programmable reference counting as part of data abstraction. Solution Static arrays are structures whose size is fixed at compile time and therefore cannot be extended or reduced to fit the data set. A dynamic array can be extended by doubling the size but there is overhead associated with the operation of copying old data and freeing the memory associated with the old data structure. One potential problem of using arrays for storing data is that arrays require a contiguous block of memory which may not be available, if the requested contiguous block is too large. However the advantages of using arrays are that each element in the array can be accessed very efficiently using an index. However, for applications that can be better managed without using contiguous memory we define a concept called “linked lists”. A linked list is a collection of objects linked together by references from one object to another object. By convention these objects are named as nodes. So the basic linked list is collection of
- 4. nodes where each node contains one or more data fields AND a reference to the next node. The last node points to a NULL reference to indicate the end of the list. Types of Linked Lists Linked lists are widely used in many applications because of the flexibility it provides. Unlike arrays that are dynamically assigned, linked lists do not require memory from a contiguous block. This makes it very appealing to store data in a linked list, when the data set is large or device (eg: PDA) has limited memory. One of the disadvantages of linked lists is that they are not random accessed like arrays. To find information in a linked list one must start from the head of the list and traverse the list sequentially until it finds (or not find) the node. Another advantage of linked lists over arrays is that when a node is inserted or deleted, there is no need to “adjust” the array. There are few different types of linked lists. A singly linked list as described above provides access to the list from the head node. Traversal is allowed only one way and there is no going back. A doubly linked list is a list that has two references, one to the next node and another to previous node. Doubly linked list also starts from head node, but provide access both ways. That is one can traverse forward or backward from any node. A multilinked list (see figures 1 & 2) is a more general linked list with multiple links from nodes. For examples, we can define a Node that has two references, age pointer and a name pointer. With this structure it is possible to maintain a single list, where if we follow the name pointer we can traverse the list in alphabetical order of names and if we traverse the age pointer, we can traverse the list sorted by ages. This type of node organization may be useful for maintaining a customer list in a bank where same list can be traversed in any order (name, age, or any other criteria) based on the need. Designing the Node of a Linked List Linked list is a collection of linked nodes. A node is a struct with at least a data field and a reference to a node of the same type. A node is called a self-referential object, since it contains a pointer to a variable that refers to a variable of the same type. For example, a struct Node that contains an int data field and a pointer to another node can be defined as follows. typedef struct node { int data; struct node* next; } node; node* head = NULL; Creating the first node Memory must be allocated for one node and assigned to head as follows. head = (node*) malloc(sizeof(node)); headdata = 10;
- 5. headnext = NULL; Adding the second node and linking node* nextnode = malloc(sizeof(node)); nextnodedata = 12; nextnodenext = NULL; headnext = nextnode; Linked list is a data structure in which the items are ordered in a linear way. Although modern programming languages support very flexible and rich libraries that works with arrays, which use arrays to represent lists, the principles of building a linked list remain very important. The way linked lists are implemented is a ground level in order to build more complex data structures such as trees. It’s true that almost every operation we can perform on a linked list can be done with an array. It’s also true that some operations can be faster on arrays compared to linked lists. However understanding how to implement the basic operations of a linked list such as INSERT, DELETE, INSERT_AFTER, PRINT and so on is crucial in order to implement data structures as rooted trees, B-trees, red-black trees, etc. Big-O notation is a way to express the efficiency of an algorithm. If you’re going to be working with code, it is extremely important that you understand Big-O. It is, quite literally, the language we use to express efficiency. Big-O is an expression of how the execution time of a program scales with the input data. That is, as the input gets bigger, how much longer will the program take? Just a little bit? A lot longer? Suppose you have a function for which does some processing on an array of size N. If foo takes O(N) time, then, as the array grows (that is, as N increases), the number of seconds foo takes will also increase in some sort of linear fashion. The first decision in planning the linked-list implementation of the Queue class is which end of the list will correspond to the front of the queue. Recall that items need to be added to the rear of the queue, and removed from the front of the queue. Therefore, we should make our choice based on whether it is easier to add/remove a node from the front/end of a linked list. If we keep pointers to both the first and last nodes of the list, we can add a node at either end in constant time. However, while we can remove the first node in the list in constant time, removing the last node requires first locating the previous node, which takes time proportional to the length of the list. Therefore, we should choose to make the end of the list be the rear of the queue, and the front of the list be the front of the queue. Other than saving space, the first advantage I can see for singly linked lists over doubly linked lists is to avoid having to update two links instead of one when you modify the list, when adding
- 6. an element for example. Of course, one might say that you can always ignore the second link, but in that case, it is no longer doubly linked, but only an unused field.What might also be seen as an advantage is that singly linked list are necessarily consistent, though possibly wrong when there are bugs in the program. Doubly linked lists can end-up having inconsistent links forward and backward. But it is debatable which of the two cases, if any, is an advantage. update: I had tried to see some impact on garbage collection, but found none. Actually, there is one when storage reclamation is done by reference counting, as reference counting is defeated by loops, and doubly linked lists contain loops. Singly linked list escape the problem. Of course, there are ways around it for doubly linked lists, such as the use of weak pointers, or programmable reference counting as part of data abstraction.