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Stack Overview and implementation with C.

Data Structure

A stack is a collection of items arranged in a specific order, where new items can be added or removed
only from one end, known as the top of the stack. The stack is dynamic, meaning it can change
constantly.


When adding new items to the stack, they are placed on top, causing the top of the stack to move
upward to accommodate the new highest element. This operation is called “PUSH”. Conversely, when
removing items from the stack, they are taken from the top, causing the top of the stack to move
downward to reflect the new highest element. This operation is called “POP”. Because of the way items
are inserted and deleted in a stack, it follows a “last-in, first-out” (LIFO) principle, meaning the most
recently added item is the first one to be removed. Additionally, due to the nature of the “PUSH”
the operation, a stack is sometimes referred to as a “pushdown list”.

Primitive Operations on Stack:

  • Push(s, i): This operation adds the item ‘i’ to the top of the stack ‘s’. It essentially inserts an element onto the top of the stack.
  • Pop(s): The operation pop(s) removes the element at the top of stack ‘s’ and returns it. This operation effectively retrieves and removes the topmost item from the stack.
  • Assignment with pop(s): Assigning the result of pop(s) to a variable ‘i’ involves removing the top element of stack ‘s’ and assigning its value to ‘i’. For instance, if ‘i = pop(s)’, then ‘i’ holds the value of the top element of stack ‘s’.
  • Empty(s): This operation determines whether or not the stack ‘s’ is empty. If the stack is empty, the function empty(s) returns TRUE; otherwise, it returns FALSE.
  • Stacktop(s): Returns the top element of stack ‘s’ without removing it from the stack. This operation allows you to peek at the topmost item without modifying the stack itself.
  • Note: Attempting to pop or access an item from an empty stack results in an underflow error. To avoid this error, it’s essential to ensure that the stack is not empty (i.e., empty(s) returns FALSE) before attempting the operations pop(s) or stacktop(s). This precaution prevents accessing or removing elements from a stack that doesn’t contain any items.

Stack as an ADT

A Stack, as an Abstract Data Type (ADT), is a collection of elements with two main operations: push (to
add an element to the top) and pop (to remove the top element). It follows the Last-In, First-Out (LIFO)
principle. Additional operations include peek (to view the top element without removing it) and isEmpty
(to check if the stack is empty). Stacks are commonly used in computer science for tasks like managing
function calls, expression evaluation, and undo functionality.

Representing Stacks in C – Array Implementation:

  • Structure Declaration: A stack in C is typically declared as a structure with two members: an array to hold stack elements and an integer to indicate the position of the current stack top within the array.
  • Array Size: The size of the array is declared to accommodate the maximum potential size of the stack. This allows the stack to grow and shrink within the reserved space.
  • Stack Top: The integer variable ‘top’ is used to keep track of the current position of the top of the stack. Initially, when the stack is empty, ‘top’ is usually set to -1.
  • Initialization: To initialize a stack, the ‘top’ variable is set to -1, indicating that the stack is empty. Checking for Empty
  • Stack: To determine whether the stack is empty, the condition ‘s.top == -1’ is checked.
  • Stack Elements: If ‘s.top = 4’, it means there are five elements on the stack: s.items[0], s.items[1], s.items[2], s.items[3], and s.items[4].The index ‘top’ points to the topmost element in the stack.
  • Push Operation: When a new item is pushed onto the stack, the value of ‘top’ is incremented by 1 to indicate the new top position. The new item is then inserted into the array at the index indicated by the updated ‘top’ value.
  • Pop Operation: When an element is popped from the stack, the value of ‘top’ is decremented by 1 to reflect the removal of the top element. The element at the previous top position is removed from the stack.
  • Updating Stack Top: As items are pushed onto or popped from the stack, the value of ‘top’ is adjusted accordingly to maintain the correct position of the top element.
  • Note:
  • It’s essential to manage the ‘top’ variable correctly to ensure proper stack operations.
  • Pay attention to boundary conditions to avoid underflow or overflow situations.
  • The stack operates on a First-In, Last-Out (FILO) principle, meaning the last item pushed onto the stack will be the first one popped off.

1. Implementing the POP operation in C:

The pop function is crucial in stack operations as it removes the top element from the stack. Here’s how
it’s implemented in three steps:

  • Check for Stack Underflow: First, the function checks if the stack is empty by verifying if the top index ‘top’ is equal to -1. If the stack is empty, it prints a warning message indicating underflow, signaling that there are no elements to pop. Exiting the program (using exit(1)) after encountering underflow prevents further execution, ensuring the program doesn’t attempt to access nonexistent stack elements.
  • Remove the Top Element: If the stack is not empty, the top element is removed from the stack and returned to the calling program. This removal is performed by accessing the element at the current top index ‘top’ using ‘ps->items[ps->top]’. The ‘ps’ pointer is used to access the stack structure, and ‘ps->items’ refers to the array holding stack elements. After returning the top element, the ‘top’ index is decremented using ‘ps->top–‘, effectively removing the top element from the stack.
  • Returning the Popped Element: The element removed from the stack is returned to the calling program, allowing further processing if needed.

Here’s the C code implementing the pop operation:

int pop(struct stack *ps)
{
// Check for stack underflow
if (ps->top == -1)
{
printf("\n STACK UNDERFLOW");
exit(1); // Exit program if stack underflows
}
// Remove the top element from the stack
return (ps->items[ps->top--]); // Return the popped element and decrement 'top'
}

This function efficiently implements the pop operation, ensuring proper handling of underflow situations and providing the popped element for further use in the program.

Implementing the PUSH operation in C:

In the array implementation of the stack’s push operation, when the array is full, and an attempt is
made to push another element onto the stack, overflow occurs. Here’s how the push operation is
implemented in four steps:

  • Check for Stack Overflow: The function first checks if the stack is full by comparing the top index ‘top’ with the maximum stack size minus one (STACKSIZE-1). If the stack is full, it prints a warning message indicating overflow and halts execution to prevent further pushing onto the stack.
  • Input Element Value: Next, the function takes the value of the element that is to be pushed onto the stack. This value is typically provided as an argument to the push function.
  • Increment the Stack Top: If the stack is not full, the ‘top’ index is incremented to prepare for pushing the new element onto the stack. Incrementing ‘top’ moves its position to the next available space in the stack array.
  • Enter Element into the Stack Top: Finally, the new element is inserted into the stack at the updated ‘top’ index. The value of the new element is stored in the array at the position indicated by the incremented ‘top’ index.

Here’s the C code implementing the push operation:

void push(struct stack *ps, int x)
{
// Check for stack overflow
if (ps->top == STACKSIZE - 1)
{
printf("\n STACK OVERFLOW");
exit(1); // Exit program if stack overflows
}
else
{
// Increment 'top' and insert element into the stack
++(ps->top);
ps->items[ps->top] = x;
}
}

This function effectively implements the push operation, ensuring proper handling of overflow situations and inserting elements into the stack when space is available.