Chapter 1: Introduction to Insertion Sort

Insertion sort is a practical algorithm particularly suited for sorting a limited set of elements. This method resembles how many individuals sort a hand of playing cards. We begin with an empty left hand while the cards are placed face down on a table. One by one, we pick up cards from the table and position them accurately in our left hand. To determine where a card belongs, we compare it with the cards already in hand, checking from right to left.

This section illustrates the operation of the INSERTION-SORT algorithm on the array A = <5, 2, 4, 6, 1, 3>. The indices of the array are indicated above the rectangles, while the values are displayed inside them. The iterations from (a) to (e) depict the for loop's progress (lines 1-8). In each iteration, the black rectangle shows the key from A[j], which is compared to the shaded rectangles on its left, as per the test in line 5. The shaded arrows depict values shifting one position to the right (line 6), while the black arrows indicate where the key moves to (line 8). Finally, (f) showcases the array after sorting.

Indentation is crucial for denoting block structures. For instance, the for loop commencing on line 1 includes lines 2 through 8, while the body of the while loop starting on line 5 consists of lines 6-7, excluding line 8. This indentation style is also applicable to if-else statements. Using indentation instead of traditional block indicators, such as begin and end statements, greatly minimizes clutter while enhancing clarity.

The looping constructs—while, for, and repeat-until—as well as the if-else conditional construct, maintain interpretations similar to those found in languages like C, C++, Java, Python, and Pascal. In this context, the loop counter retains its value even after exiting the loop, which differs from certain behaviors in C++, Java, and Pascal. Therefore, right after a for loop concludes, the counter reflects the value that first exceeded the loop's boundary. For example, in the for loop defined on line 1 as for j = 2 to A.length, once it terminates, j = A.length + 1 (or j = n + 1, where n = A.length). The keyword 'to' signifies an incrementing loop counter, while 'downto' indicates a decrementing one. If the counter changes by more than 1, the change is specified following the optional keyword 'by'.

Comments are denoted by the symbol "//," which indicates that the remainder of the line is for explanatory purposes.

A multiple assignment such as i = j = e assigns the value of expression e to both variables i and j; it should be understood as j = e followed by i = j.

Variables (like i, j, and key) are local to the procedure in which they are defined, and global variables will not be utilized unless explicitly mentioned.

Array elements are accessed by specifying the array name followed by the index in square brackets. For example, A[i] refers to the i-th element of the array A. The notation “...” signifies a range of values within an array. Thus, A[1..j] represents the subarray containing the elements A[1], A[2], ..., A[j].

Typically, compound data is organized into objects, which are made up of attributes. Accessing a specific attribute follows the syntax commonly found in object-oriented programming: the object name, a dot, and the attribute name. For example, we treat an array as an object, with the length attribute reflecting the number of elements it contains. To express the number of elements in array A, we write A.length. A variable representing an array or object acts as a pointer to the corresponding data. For all attributes f of an object x, assigning y = x results in y.f equaling x.f. Furthermore, if we later set x.f = 3, then both x.f and y.f will equal 3, indicating that x and y reference the same object post-assignment. Our attribute notation can also 'cascade.' For instance, if f points to an object with attribute g, x.f.g is implicitly grouped as (x.f).g. In scenarios where a pointer does not reference any object, it is assigned the special value NIL.

Parameters are passed to a procedure by value, meaning the called procedure gets its own copy of the parameters. Any changes made to a parameter do not affect the calling procedure. When objects are passed, the pointer to the object data is copied, but not the attributes themselves. For instance, if x is a parameter for a called procedure, the operation x = y within it does not affect the calling procedure. However, x.f = 3 would be visible to the calling procedure. Similarly, arrays are passed by pointer, allowing changes to individual array elements to be reflected in the calling procedure.

A return statement immediately transfers control back to the calling procedure's point of invocation. Most return statements also convey a value back to the caller. Our pseudocode diverges from many programming languages by permitting multiple values to be returned in a single statement.

The boolean operators “and” and “or” employ short-circuiting. Thus, when evaluating “x and y,” we first assess x. If x is FALSE, the overall expression cannot be TRUE, and y is not evaluated. Conversely, if x is TRUE, y must be evaluated to determine the expression's value. Similarly, in “x or y,” y is evaluated only if x is FALSE. This short-circuiting feature allows us to construct boolean expressions like “x <> NIL and x.f = y” without concerns about evaluating x.f when x is NIL.

The keyword 'error' denotes that an error occurred due to inappropriate conditions for calling the procedure. The calling procedure is responsible for managing the error, which is why we do not specify the remedial action.

In summary:

• Indentation: signifies block structures
• Looping: controls flow
• Commenting: provides additional information
• Assignment: simple or multiple
• Variables: local or global
• Access: either directly or by reference
• Data: stack, queue, graph, etc.
• Parameters: passed by copy or reference
• Return: either simple or complex
• Operators: math, binary, etc.
• Error: handling procedures

Chapter 2: Pseudocode Conventions

This video, titled "PSEUDO CODE CONVENTIONS FOR DESIGNING AN ALGORITHM," delves into essential guidelines for writing pseudocode that enhances algorithm design and clarity.

In this video, "Pseudocode convention-A guide for better algorithm design," viewers will learn strategies for improving their pseudocode practices for effective algorithm development.