Adding notes on Stacks.

Author: Clément

source/code/projects/CStack/CStack/CStack.cs

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+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+
+class CStack<T>
+{
+
+    private class Cell
+    {
+        public T Data { get; set; }
+        public Cell Next { get; set; }
+        public Cell(T data = default(T), Cell node = null)
+        {
+            Data = data;
+            Next = node;
+        }
+    }
+
+    private Cell top;
+    
+    public CStack()
+    {
+        top = null;
+    }
+    
+    public void Clear()
+    {
+        top = null;
+    }
+    public bool IsEmpty()
+    {
+        return top == null;
+    }
+    
+    public void Push(T value)
+    {
+        top = new Cell(value, top);
+    }
+    
+    public T Pop()
+    {
+        if (IsEmpty())
+            throw new ApplicationException("An empty stack cannot be popped.");
+        T removedData = top.Data;
+        top = top.Next;
+        return removedData;
+    }
+    
+    public T Peek()
+    {
+        if (IsEmpty())
+            throw new ApplicationException("An empty stack cannot be peeked.");
+        return top.Data;
+    }
+    public int Count
+    {
+        get
+        {
+            int count = 0;
+            Cell cCell = top;
+            while (cCell != null)
+            {
+                count++;
+                cCell = cCell.Next;
+            }
+            return count;
+        }
+    }
+
+    public override string ToString()
+    {
+        string returned = "";
+        if (!IsEmpty())
+        {
+            Cell cCell = top;
+            while (cCell != null)
+            {
+                if (returned.Length > 0)
+                    returned += ":";
+                returned += cCell.Data;
+                cCell = cCell.Next;
+            }
+        }
+        return returned;
+    }
+}

source/code/projects/CStack/CStack/Program.cs

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+using System;
+
+class Program
+{
+    static void Main(string[] args)
+    {
+        /* First example. */
+        CStack<int> myStack1 = new CStack<int>();
+        Console.WriteLine(myStack1);
+        myStack1.Push(1);
+        myStack1.Push(5);
+        myStack1.Push(2);
+        myStack1.Push(2);
+        myStack1.Push(1);
+        myStack1.Push(1);
+        myStack1.Push(3);
+        myStack1.Push(4);
+        myStack1.Push(5);
+        myStack1.Push(5);
+        myStack1.Push(5);
+        myStack1.Push(2);
+        myStack1.Push(2);
+        Console.WriteLine(myStack1);
+
+        /* Second example. */
+        CStack<char> myStack2 = new CStack<char>();
+        try
+        {
+            myStack2.Pop();
+        }
+        catch(Exception ex)
+        {
+            Console.WriteLine(
+              ex.Message
+            );
+        }
+        try
+        {
+            myStack2.Peek();
+        }
+        catch (Exception ex)
+        {
+            Console.WriteLine(
+              ex.Message
+            );
+        }
+
+        myStack2.Push('a');
+        myStack2.Push('z');
+        Console.WriteLine("Value at top of stack: " + myStack2.Peek());
+    }
+}

source/lectures/data/stack.md

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+---
+tags:
+- datatypes/collections
+---
+
+# The Stack collections
+
+## Introduction
+
+### Abstract Data Type
+
+Described [abstractly](./lectures/data/intro#abstract-data-types), [a stack](https://en.wikipedia.org/wiki/Stack_(abstract_data_type)) is 
+
+- a finite collection of elements,
+- in a particular order,
+- that may contain the same element multiple times.
+
+The fact that it may contain the same element multiple times makes it different from a set, the fact that it is ordered makes it different from a [multiset](https://en.wikipedia.org/wiki/Multiset).
+
+Generally, it has operations to…
+
+- … create an empty list,
+- … test for emptiness, 
+- … obtain the value of the element at "the top" of the stak ("peek"),
+- … add an element at "the top" of the stack ("push"),
+- … remove an element at "the top" of the stack ("pop").
+
+The fact that only the "top element" can be accessed is the main difference with the list abstract data type.
+Exactly like a stack of plates, stacks implement a "last in, first out" (LIFO) principle.
+
+### Difference with array 
+
+Like lists, the `Stack` class serves a similar purpose than arrays, but with a few notable differences:
+
+- Stacks do not need to have a number of elements fixed ahead of time,
+- Stacks automatically expand when elements are added,
+- Stacks automatically shrink when elements are removed.
+
+### Difference with lists
+
+However, the `Stack` class is also different from lists:
+
+- Only the top element can be read,
+- Adding and removing can only be done "on the right side", that is, at the top of the stack.
+
+## Possible Implementation
+
+Here is a possible implementation of stacks:
+
+```{download="./code/projects/CStack.zip"}
+!include code/projects/CStack/CStack/CStack.cs
+```