Notes, summaries, assignments, exams, and problems for Computer science

Tile Sequence Validation Logic

The following function determines if a sequence of tiles is valid by checking their compatibility and adjusting their orientation if necessary.

def is_valid_sequence(seq: list[Tile]) -> bool:
    if len(seq) < 2:
        res = True
    else:
        if not are_compatible(seq[0], seq[1]):
            seq[0] = seq[0][1], seq[0][0]
        i = 1
        while i < len(seq) and are_compatible(seq[i - 1], seq[i]):
            if seq[i - 1][1] != seq[i][0]:
                seq[i] = seq[i][1], seq[i][0]
            i += 1
        res = i == len(seq)
    return res

Square-Free Number Verification

This function checks if a positive integer is square-free, meaning no prime factor has an exponent greater than one.

def

Arithmetic Progressions (AP)

Sum of terms = n[(1st term + last term)]/2

Geometric Progressions (GP)

Sum of terms = [1st term(1 - quotientⁿ)/(1 - quotient)] (Swap positions of 1 & quotient if quotient > 1)

Logarithms

• log_a(x/y) = log_ax - log_ay
• log_axⁿ = nlog_ax
• log_ab = (log_cb/log_ca)

Permutations

For a set of n objects: The total number of permutations is n!

For arranging 'r' objects from a set of 'n' objects: The number of permutations is nPr = n! / (n-r)!. (e.g., ways to arrange 3 objects from a set of 5 is 5 * 4 * 3, since there are 5 possibilities for the first object, followed by 4, then 3.)

Combinations

For selecting 'r' objects from a set of 'n' objects: The number of combinations is nCr = n! / (r! * (n-r)!). (Divide by r! since there are r! ways

Object-Oriented Programming (OOP) Fundamentals

Object-oriented programming (OOP) is a computer programming model that uses objects to represent and manipulate data.

OOP is well-suited for large, complex, and frequently updated software. Some of the main features of OOP include:

• Classes: User-defined data types that serve as a blueprint for individual objects, attributes, and methods.
• Objects: Instances of a class that are created with specific data.
• Methods: Functions that objects can perform.
• Attributes: Represent the state of an object.
• Abstraction: Exposes only the essential information of an object to the user.
• Polymorphism: Adds different meanings to a single component.
• Inheritance: Allows a class to inherit the properties and methods of another

Sure, I'll address each of the directives.

**Q-1**

(1) **Define Symmetric Matrix:**
A symmetric matrix is a square matrix that is equal to its transpose. Mathematically, a matrix \( A \) is symmetric if \( A = A^T \), where \( A^T \) denotes the transpose of \( A \). This implies that \( a_{ij} = a_{ji} \) for all elements in the matrix.

(2) **Define Tautology:**
A tautology is a statement or formula that is always true, regardless of the truth values of its component propositions. In logical terms, a tautology is a proposition that evaluates to true in every possible interpretation.

**Reh (P.T.O)**

(3) **Write down the condition for consistency of a non-homogeneous system of linear equations:**
A non-homogeneous system of linear equations \( AX =...

Program for Action Learning (PAL)

PAL, or the Program for Action Learning, is an educational approach that emphasizes practical, hands-on learning experiences. It is frequently utilized in business and organizational settings to facilitate problem-solving, teamwork, and skill development through real-world projects and challenges.

Understanding Magnitude Comparators

A magnitude comparator is a digital circuit that compares two binary numbers to determine their relative magnitudes. It identifies whether one number is:

• Greater than the other
• Less than the other
• Equal to the other

It typically consists of logic gates that analyze the binary digits of each number and generate output signals indicating the comparison result. These circuits are commonly...

Understanding Computer Fundamentals

Output Devices

Plotter

A plotter is a specialized output device that generates images on paper, similar to a printer but with a distinct approach. Plotters excel at producing large-scale drawings or images, such as construction plans or blueprints. They can be connected to the same port typically used by a printer.

Tab Stops

Tab stops simplify document formatting. By default, they are set at 0.5-inch intervals from the left margin, allowing for easy creation of elements like tables of contents or indexes without manual adjustments.

Formatting and Data Visualization

Importance of Pie Charts

Pie charts effectively illustrate relative proportions or contributions to a whole using a single data series. Their effectiveness...

CIA Triad

The CIA Triad consists of Confidentiality, Integrity, and Availability. Related concepts include Authentication, Accountability, and Auditability.

Types of Harm

• Interception
• Interruption
• Modification
• Fabrication

Web Technologies

HTML

• GET: Embeds parameters into the URL.
• POST: Sends data directly to the server; more secure.

PHP

• PUT: Used to create or replace a file at the specified URL. Sends data like POST, more suitable for uploading files.

Penetration Testing

5 Steps to Penetration Testing:

1. Reconnaissance
2. Scanning
3. Gaining Access
4. Maintaining Access
5. Clearing Tracks

Security Controls

• Prevention: Outright stopping an attack.
• Deterrence: Making an attack harder.
• Deflection: Making a target less attractive.
• Mitigation: Lessening the harm.
• Detection: Identifying