An array is a random access data structure, where each element can be accessed directly and in constant time. A typical illustration of random access is a book  each page of the book can be open independently of others. Random access is critical to many algorithms, for example binary search.
A linked list is a sequential access data structure, where each element can be accesed only in particular order. A typical illustration of sequential access is a roll of paper or tape  all prior material must be unrolled in order to get to data you want.
In this note we consider a subcase of sequential data structures, socalled limited access data sturctures.
A stack is a container of objects that are inserted and removed according to the lastin
firstout (LIFO) principle. In the pushdown stacks only two operations are allowed: push
the item into the stack, and pop the item out of the stack. A stack is a limited access
data structure  elements can be added and
removed from the stack only at the top. push adds an item to the top of the stack,
pop removes the item from the top. A helpful analogy is to think of a stack of books; you can remove only
the top book, also you can add a new book on the top.
A stack is a recursive data structure. Here is a structural definition of a Stack:
it consistes of a top and the rest which is a stack; 
Backtracking. This is a process when you need to access the most recent data element in a
series of elements. Think of a labyrinth or maze  how do you find a way from an entrance to an exit?
Once you reach a dead end, you must backtrack. But backtrack to where? to the previous choice point. Therefore, at each choice point you store on a stack all possible choices. Then backtracking simply means popping a next choice from the stack. 
public interface StackInterface<AnyType> { public void push(AnyType e); public AnyType pop(); public AnyType peek(); public boolean isEmpty(); }
Another implementation requirement (in addition to the above interface) is that all stack operations must run in constant time O(1). Constant time means that there is some constant k such that an operation takes k nanoseconds of computational time regardless of the stack size.
In an arraybased implementation we maintain the following fields: an array A of a default size
(≥ 1), the variable top that refers to the top
element in the stack and the capacity that refers to the array size.
The variable top changes from 1 to capacity  1 . We say that a stack is
empty when top = 1 , and the stack is full when top = capacity1 .
In a fixedsize stack abstraction, the capacity stays unchanged, therefore when top reaches capacity, the stack object throws an exception. See ArrayStack.java for a complete implementation of the stack class. In a dynamic stack abstraction when top reaches capacity, we double up the stack size. 
Linked Listbased implementation provides the best (from the efficiency point of view)
dynamic stack implementation. See ListStack.java for a complete implementation of the stack class.

A queue is a container of objects (a linear collection) that are inserted and removed according to
the firstin firstout (FIFO) principle. An excellent example of a queue is a line of students in the food court of
the UC. New additions to a line made to the back of the queue, while removal (or serving) happens in
the front. In the queue only two operations are allowed enqueue and dequeue. Enqueue
means to insert an item into the back of the queue, dequeue means removing the front item. The picture
demonstrates the FIFO access.
The difference between stacks and queues is in removing. In a stack we remove the item the most recently added; in a queue, we remove the item the least recently added.

interface QueueInterface‹AnyType> { public boolean isEmpty(); public AnyType getFront(); public AnyType dequeue(); public void enqueue(AnyType e); public void clear(); }
Each of the above basic operations must run at constant time O(1). The following picture demonstrates the idea of implementation by composition.
However, there is a free space before the front index. We shall use that space for enqueueing new items, i.e. the next entry will be stored at index 0, then 1, until front. Such a model is called a wrap around queue or a circular queue
Finally, when back reaches front, the queue is full. There are two choices to handle a full queue:a) throw an exception; b) double the array size.
The circular queue implementation is done by using the modulo operator (denoted %), which is computed by taking the remainder of division (for example, 8%5 is 3). By using the modulo operator, we can view the queue as a circular array, where the "wrapped around" can be simulated as "back % array_size". In addition to the back and front indexes, we maintain another index: cur  for counting the number of elements in a queue. Having this index simplifies a logic of implementation.
See ArrayQueue.java for a complete implementation of a circular queue.
The simplest two search techniques are known as DepthFirst Search(DFS) and BreadthFirst Search (BFS). These two searches are described by looking at how the search tree (representing all the possible paths from the start) will be traversed.
In depthfirst search we go down a path until we get to a dead end; then we backtrack or back up (by popping a stack) to get an alternative path.
In breadthfirst search we explore all the nearest possibilities by finding all possible successors and enqueue them to a queue.
We will see more on search techniques later in the course.
1 + ((2 + 3) * 4 + 5)*6
Converting from Infix to Postfix. Typically, we deal with expressions in infix notation
2 + 5
2 5 +
+2 5
70 + 150 * 1.0725
70 150 + 1.0725 *
Now, we describe how to convert from infix to postfix.
2+(4+3*2+1)/3
. We read the string by characters.
'2'  send to the output. '+'  push on the stack. '('  push on the stack. '4'  send to the output. '+'  push on the stack. '3'  send to the output. '*'  push on the stack. '2'  send to the output.
Evaluating a Postfix Expression. We describe how to parse and evaluate a postfix expression.
5 9 3 + 4 2 * * 7 + *
Stack Operations Output  push(5); 5 push(9); 5 9 push(3); 5 9 3 push(pop() + pop()) 5 12 push(4); 5 12 4 push(2); 5 12 4 2 push(pop() * pop()) 5 12 8 push(pop() * pop()) 5 96 push(7) 5 96 7 push(pop() + pop()) 5 103 push(pop() * pop()) 515
Victor S.Adamchik, CMU, 2009