9.8. Stacks¶

9.8.1. Stack Terminology and Implementation¶

The stack is a list-like structure in which elements may be inserted or removed from only one end. While this restriction makes stacks less flexible than lists, it also makes stacks both efficient (for those operations they can do) and easy to implement. Many applications require only the limited form of insert and remove operations that stacks provide. In such cases, it is more efficient to use the simpler stack data structure rather than the generic list. For example, the freelist is really a stack.

Despite their restrictions, stacks have many uses. Thus, a special vocabulary for stacks has developed. Accountants used stacks long before the invention of the computer. They called the stack a “LIFO” list, which stands for “Last-In, First-Out.” Note that one implication of the LIFO policy is that stacks remove elements in reverse order of their arrival.

The accessible element of the stack is called the top element. Elements are not said to be inserted, they are pushed onto the stack. When removed, an element is said to be popped from the stack. Here is a simple stack ADT.

Java
Java (Generic)

public interface Stack { // Stack class ADT
  // Reinitialize the stack.
  public void clear();

  // Push "it" onto the top of the stack
  public boolean push(Object it);

  // Remove and return the element at the top of the stack
  public Object pop();

  // Return a copy of the top element
  public Object topValue();

  // Return the number of elements in the stack
  public int length();
  
  // Return true if the stack is empty 
  public boolean isEmpty();
}

As with lists, there are many variations on stack implementation. The two approaches presented here are the array-based stack and the linked stack, which are analogous to array-based and linked lists, respectively.

9.8.1.1. Array-Based Stacks¶

Here is a complete implementation for the array-based stack class.

Java
Java (Generic)

class AStack implements Stack {
  private Object stackArray[];    // Array holding stack
  private static final int DEFAULT_SIZE = 10;
  private int maxSize;            // Maximum size of stack
  private int top;                // First free position at top

  // Constructors
  AStack(int size) {
    maxSize = size;
    top = 0;
    stackArray = new Object[size]; // Create stackArray
  }
  AStack() { this(DEFAULT_SIZE); }

  public void clear() { top = 0; }    // Reinitialize stack

// Push "it" onto stack
  public boolean push(Object it) {
    if (top >= maxSize) return false;
    stackArray[top++] = it;
    return true;
  }

// Remove and return top element
  public Object pop() {
    if (top == 0) return null;
    return stackArray[--top];
  }

  public Object topValue() {          // Return top element
    if (top == 0) return null;
    return stackArray[top-1];
  }

  public int length() { return top; } // Return stack size

  public boolean isEmpty() { return top == 0; } // Check if the stack is empty
}

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As with any array-based implementation, stackArray must be declared of fixed size when the stack is created.

class AStack implements Stack {
private Object stackArray[]; // Array holding stack
private static final int DEFAULT_SIZE = 10;
private int maxSize; // Maximum size of stack
private int top; // First free position at top
// Constructors
AStack(int size) {
maxSize = size;
top = 0;
stackArray = new Object[size]; // Create stackArray
}
AStack() { this(DEFAULT_SIZE); }

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The array-based stack implementation is essentially a simplified version of the array-based list. The only important design decision to be made is which end of the array should represent the top of the stack.

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One choice is to make the top be at position 0 in the array. In terms of list functions, all push and pop operations would then be on the element at position 0.

top

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Method push is easy.

public boolean push(Object it) {
if (top >= maxSize) return false;
stackArray[top++] = it;
return true;
}

top

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9.8.2. Pop¶

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Now, for the implementation of pop. top is at the first free position, which is index 4 on the array.

public Object pop() {
if (top == 0) return null;
return stackArray[--top];
}

top

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OpenDSA Data Structures and Algorithms Modules Collection

Chapter 9 Linear Structures

9.8. Stacks¶

9.8.1. Stack Terminology and Implementation¶

9.8.1.1. Array-Based Stacks¶

9.8.2. Pop¶