Week 5

1. Data Structure

1.1. Linked Lists

Singly-Linked Lists

  • Structure

      typedef struct sllist
      {
          VALUE val;
          struct sllist *next;
      }
      sllnode;
    
    • VALUE can be any type of data, char, int, etc.
  • Create a linked list.

    • sllnode* create(VALUE val);
    • Steps
      • Dynamically allocate space for a new sllnode.
      • Check to make sure we didn't run out memory.
      • Initialize the node's val field.
      • Initialize the node's next field.
      • Return a pointer to the newly created sllnode.
  • Search through a linked list to find an element.
    • bool find(sllnode* head, VALUE val);
    • Steps
      • Create a traversal pointer pointing to the list's head.
      • If the current node's val field is what we're looking for, report success.
      • If not, set the traversal pointer to the next pointer in the list and go back to step b.
      • If you've reached the end of the list, report failure.
    • The running time of this linear search will be O(n), even if our list is sorted.
  • Insert a new node into the linked list.
    • sllnode* insert(sllnode* head, VALUE val);
    • Steps
      • Dynamically allocate space for a new sllnode.
      • Check to make sure we didn't run out of memory.
      • Populate and insert the node at the beginning of the linked list.
      • Return a pointer to the new head of the linked list.
    • This would be O(1) if we didn’t want to keep the list sorted,
  • Delete an entire linked list.
    • void destroy(sllnode* head);
    • Steps
      • If you've reach a null pointer, stop.
      • Delete the rest of the list.
      • Free the current node.
    • This will take O(n) since we’ll need to find the number want to delete first.

Doubly-Linked Lists

  • A doubly-linked list, by contrast, allows us to move forward and backward through the list.

  • Structure

      typedef struct dllist
      {
          VALUE val;
          struct dllist *prev;
          struct dllist *next;        
      }
    
    • VALUE can be any type of data, char, int, etc.
  • Insert a new node into the linked list.
    • dllnode* insert(dllnode* head, VALUE val);
    • Steps
      • Dynamically allocate space for a new dllnode.
      • Check to make sure we didn't run out of memory.
      • Populate and insert the node at the beginning of the linked list.
      • Fix the prev pointer of the old head of the linked list.
      • Return a pointer to the new head of the linked list.
    • This will take running time O(n).
  • Delete a node from a linked list.
    • void delete (dllnode* target);
    • Steps
      • Fix the pointers of the surrounding nodes to "skip over" target.
      • Free target.
    • This will take running time O(1).
  • Remember, we can never break the chain when rearranging the pointers.

1.2. Stack

  • A stack is a special type of structure that can eb used to maintain data in an organized way.
  • This data structure is commonly implemented in one of two ways: as an array or as a linked list.
  • In either case, if an element needs to be removed, the most recently added element is the only element that can legally be removed.
    • Last in, first out (LIFO).
  • Operations
    • push: Add a new element to the top of the stack.
    • pop: Remove the most recently-added element from top.
  • Structure 1

    • Array-based implementatoin

        typedef struc _stack
        {
            VALUE array[CAPACITY];
            int top;
        }
        stack;
      
      • VALUE can be any type of data, char, int, etc.
      • CAPACITY is the maximum number of elements.
  • push

    • void push(stack* s, VALUE val);
    • Steps
      • Accept a pointer to the stack.
      • Accept data of type VALUE to be added to the stack.
      • Add that data to the stack at the top of the stack.
      • Change the location of the top of the stack.
  • pop

    • VALUE pop(stack* s);
    • Steps
      • Accept a pointer to the stack.
      • Change the location of the top of the stack.
      • Return the value that was removed from the stack.
  • Structure 2

    • Linked-list based implementation

      typedef struct _stack
      {
        VALUE val;
        struct _stack *next;
      }
      stack;
      
  • push

    • Steps
      • dynamically allocate a new node,
      • set its next pointer to point to the current head of the list,
      • then move the head pointer to he newly-created node.
  • pop
    • Steps
      • traverse the linked list to its second element(if it exists),
      • free the head of the list,
      • then move the head pointer to the (former) second element.

1.3. Queues

  • data structure, same as stack.
  • only different:
    • First in, first out (FIFO).
  • Operations
    • Enqueue: Add a new element to the end of the queue.
    • Dequeue: Remove the oldest element from the front of the queue.
  • Structure 1

    • Array-based implementation

      typedef struct _queue
      {
        VALUE array[CAPACITY];
        int front;
        int size;
      }
      queue;
      
  • enqueue
    • void enqueue(queue* q, VALUE data);
    • Steps
      • Accept a pointer to the queue.
      • Accept data of type VALUE to be added to the queue.
      • Add that data to the queue at the end of the queue.
      • Change the size of the queue.
  • dequeue

    • VALUE dequeue(queue* q);
    • Steps
      • Accept a pointer to the queue.
      • Change the location of the front of the queue.
      • Decrease the size of the queue.
      • Return the value that was removed from the queue.
  • Structure 2

    • Linked list-based implementation

      typedef struct _queue
      {
        VALUE val;
        struct _queue *prev;
        struct _queue *next;        
      }
      queue;
      
  • enqueue
    • void enqueue(queue* q, VALUE data);
    • Steps
      • Dynamically allocate a new node.
      • Set its next pointer to NULL, set its prev pointer to the tail.
      • Set the tail's next pointer to the new node.
      • Move the tail pointer to the newly-created node.
  • dequeue
    • VALUE dequeue(queue* q);
    • Steps
      • Traverse the linked list to its second element(if it exists);
      • Free the head of the list;
      • Move the head pointer to the (former) second element;
      • Make that node's prev pointer point to NULL.

1.4. Binary Search Tree

    • Each node can only have a maximum of 2 children,
    • we can simply add new nodes by allocating memory for them and changing pointers to point to them.
  • Structure

      typedef struct node
      {
          int n;
          struct node *left;
          struct node *right;
      }
      node;
    
  • use recursion to search:

      bool search(int n, node* tree)
      {
          if (tree == NULL)
          {
              return false;
          }
          else if (n < tree->n)
          {
              return search(n, tree->left);
          }
          else if (n > tree->n)
          {
              return search(n, tree->right);
          }
          else
          {
              return true;
          }
      }
    

1.5. Hash Tables

  • A hash table amounts to a combination of two things:

    • First, a hash function, which returns an nonnegative integer value called a hash code.

        hash = hashfunc(key)
        index = hash % array_size
      
    • Second, an array capable of storing data of the type we with to place into the data structure.

  • most hash table designs employ an imperfect hash function, which might cause hash collisions where the hash function generates the same index for more than one key. Such collisions must be accommodated in some way.

Collision resolution

  • Linear probing
    • It is subject to a problem called clustering. Once there's a miss, two adjacent cells will contain data, making it more likely in the future that the cluster will grow.
  • Separate chaining
    • Each bucket is independent, and has linked list of entries with the same index.
      • The time for hash table operations is the time to find the bucket (which is constant) plus the time for the list operation.

1.6. Tries

typedef struct _trie
{
    char name[45];
    struct _trie* paths[45];
}
trie;
  • the struct of dictionary.

      typedef struct Node
      {
          struct Node *children[INDICES_SIZE];
          bool is_word;
      }
      Node;
    
  • the key program of load dictionary.

      if (currentNode->children[indexNo] == NULL) 
      {
          // calloc = malloc + memset
          // calloc() zero-initializes the buffer, 
          // malloc() leaves the memory uninitialized. 
          // currentNode->children equals (*currentNode).children
          currentNode->children[indexNo] = calloc(1, sizeof(Node));
          currentNode->children[indexNo]->is_word = false;
      } 
      currentNode = currentNode->children[indexNo];
    
  • Tries combine structures and pointers together to store data.

  • Each array contains pointers to the next layer of arrays.
  • The data to be searched for in the trie is now a roadmap.
  • A trie has running time of O(1), since we just need to look up words based on the letters in them, and that’s not affected by the number of other words in the trie. Inserting and removing a word, too, is also a constant time operation.

1.7. Some Syntax of Pointers Supplement

int x = 0;
int *px;
px = &x; // Stores the address of x in px
printf("%d\n", *px); // => Prints 0, the value of x
(*px)++; // Increment the value px is pointing to by 1

struct rectangle {
  int width;
  int height;
};

void function_1()
{
  struct rectangle my_rec;

  // Access struct members with .
  my_rec.width = 10;
  my_rec.height = 20;

  // You can declare pointers to structs
  struct rectangle *my_rec_ptr = &my_rec;

  // Use dereferencing to set struct pointer members...
  (*my_rec_ptr).width = 30;

  // ... or even better: prefer the -> shorthand for the sake of readability
  my_rec_ptr->height = 10; // Same as (*my_rec_ptr).height = 10;
}

2. Refers

https://en.wikipedia.org/wiki/Hash_table http://docs.cs50.net/2016/fall/notes/5/week5.html https://learnxinyminutes.com/docs/c/

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