DSA1 | Week 3

The Card Stack Data Structure

The CARDSTACK data structure

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...after the riffle shuffle.

The CardStack Data Structure

Introducing...

< maintain an ordered stack of cards >

The Data

how many cards in the stack?

Operations & Queries

pull out the top \(k\) cards

pull out the bottom \(k\) cards

cut shuffle at \(k\) cards

typedef struct s_card {
    int cardvalue;
    
    
    
    
} t_card;

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typedef struct s_card {
    int cardvalue;
        
    struct s_card *next;
    struct s_card *prev;
    
} t_card;

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typedef struct s_cardstack {

    struct s_card *first;
    struct s_card *last;
    
} t_cardstack;

t_cardstack* cardstackInit()
{

    t_cardstack* cardstack;
    cardstack = malloc(sizeof(t_cardstack));
    
    cardstack->first = NULL;
    cardstack->last = NULL;
    
    return cardstack;

}

The initialization is pretty straightforward.

Next up...

...let us write a simple helper function

to check if our stack of cards is empty.

int isEmpty(t_cardstack *cardstack)
{
    return !cardstack->first;
}

int isEmpty(t_cardstack *cardstack)
{
    return cardstack->first;
}

int isEmpty(t_cardstack *cardstack)
{
    return !cardstack->last;
}

int isEmpty(t_cardstack *cardstack)
{
    return cardstack->last;
}

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Here is what the card stack looks like, schematically.

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pushFront(cardstack, card)

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void pushFront(t_cardstack* cardstack, int cardvalue)
{
 
    t_card *node = malloc(sizeof(t_card));
    
    node->cardvalue = cardvalue;
    
    node->prev = NULL;
    
    node->next = cardstack->first;
    
    if(cardstack->last) // the stack is NOT empty
        cardstack->first->prev = node;
    else
        cardstack->last = node;       
    
    cardstack->first = node;

}

popBack(cardstack)

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int popBack(t_cardstack *cardstack)
{
    t_card *node;
    int cardvalue;
    
    if (isEmpty(cardstack))
        return -1;
    
    node = cardstack->last;    
    cardstack->last = node->prev;
    
    if (!cardstack->last)
        cardstack->first = NULL;
    else
        cardstack->last->next = NULL;
    
    cardvalue = node->cardvalue;
    free(node);
    return cardvalue;
}

View Implementation

	Front	Back
Add	allowed	allowed
Remove	allowed	allowed

DEQUES

	Front	Back
Add	allowed	❌
Remove	allowed	❌

STACKS

	Front	Back
Add	❌	allowed
Remove	❌	allowed

STACKS

	Front	Back
Add	❌	allowed
Remove	allowed	❌

QUEUES

	Front	Back
Add	allowed	❌
Remove	❌	allowed

QUEUES

Any number of cut shuffles are done.

Five people pull out the top five cards in order.

A deck is given to someone in class.

Magic with Cards

The ones with red cards stand up.

All cards are identified.

The Card Identifier

X Y A B C

00 - ♣️ | 01 - ♠️ | 10 - ♦️ | 11 - ♥️

Five bits correspond to a card

A B C - value of the card (000 interpreted as 8)

The Sequence