Algorithm Design & Basics of Python Programs

SECTION 1.1

Algorithms & Core Concepts

Understanding algorithms, IPO cycle, pseudocode, flowcharts, and trace tables

What is an Algorithm?

An algorithm is a set of steps for solving a problem in a specified order. The process of comprehending an algorithm or a program is called a dry run, which is a commonly used technique for deducing the purpose and output of an algorithm or a program.

Input-Process-Output (IPO) Cycle

The IPO cycle is a tool for problem analysis and an important structure of an algorithm or program:

Input

Data used by the program

→

Process

Method/procedure performed

→

Output

Information returned

Example: BMI Calculator
Input: Weight (kg), Height (m) → Process: BMI = Weight / Height² → Output: Body Mass Index

Pseudocode & Flowcharts

There are three common ways to express algorithms: everyday words, pseudocode, and flowcharts.

Operation	Pseudocode	Flowchart Shape
Start / End	N/A	Rounded rectangle
Process / Assignment	A ← 21	Rectangle
Input / Output	Input A, B	Parallelogram
Decision	If A = B then	Diamond
Sub-program	ProABC	Double-sided rectangle

Trace Table

A trace table helps us comprehend an algorithm in depth, trace changes in variables and states of inputs/outputs, and spot mistakes.

Pseudocode	Value of A	Value of B
A ← 2	2	N/A
B ← 5	2	5
A ← B - A	3	5
A ← A * B	15	5
B ← A - B	15	10

SECTION 1.2 & 1.3

Python Programming Basics

Variables, data types, I/O statements, operators, and expressions

Variables & Data Types

Variables are locations in computer memory for data storage. Python has 4 simple data types:

Type	Description
`int`	Integers (positive & negative)
`float`	Decimals
`bool`	True or False
`str`	Text strings

          Variable Naming Rules:

          1. Start with letter or underscore (_)
2. Only letters, numbers, underscore
3. Cannot use reserved words (e.g. print, for, if)
        

Input & Output

Output: print() displays content to the console.

print("Hello")    # Output: Hello
name = "Sam"
print("Hi", name)  # Output: Hi Sam

Input: input() receives user data as a string. Use int() or float() to convert.

name = input()
mark = int(input("Enter mark: "))

Arithmetic & Boolean Operators

Arithmetic Operators

Operation	Symbol
Addition	+
Subtraction	-
Multiplication	*
Division	/
Integer Division	//
Modulus	%
Exponent	**

Relational Operators

Meaning	Symbol
Equal to	==
Not equal to	!=
Less than	<
Greater than	>
Less/equal	<=
Greater/equal	>=

        Operator Precedence (High to Low):

        () → ** → -(neg) → *, /, //, % → +, - → comparisons → not → and → or

Boolean Operators: and, or, not are used to combine or negate Boolean expressions.

SECTION 1.4

Control Structures

Selection (if/elif/else) and Iteration (for/while loops)

Sequence

Selection

Iteration

Selection: if / elif / else

Selection control structure uses a Boolean expression as the condition for evaluation.

# if-then
if (condition):
    # "then" body

# if-then-else
if (condition):
    # "then" body
else:
    # "else" body

# if-elif-else
if (condition 1):
    # body 1
elif (condition 2):
    # body 2
else:
    # else body

Example:if mark >= 50:
    print("Pass")
    print("Promoted")
else:
    print("Fail")
    print("Repeated")

Iteration: for & while Loops

Iteration means repeatedly executing statements until the loop condition is no longer true.

for Loop

for i in range(first, last):
    # loop body

Used when the number of iterations is known.

while Loop

while (condition):
    # loop body

Used when the condition determines when to stop.

Example: Check prime numbernum = int(input("Please input a number: "))
if num > 1:
    isPrime = True
else:
    isPrime = False
for i in range(2, num):
    if num % i == 0:
        isPrime = False
if isPrime:
    print(num, "is a prime number.")
else:
    print(num, "is NOT a prime number.")

SECTION 1.5

Data Structures

1D arrays (lists), strings, and 2D arrays

1D Arrays / Python Lists

A list is a linear data structure storing data sequentially. Use the index (starting from 0) to access items.

num = [15, 10, 5, 25, 20, 30]
# Index:  0    1    2    3    4    5

Common List Algorithms:

Sum & Average

total = 0
for i in range(0, 6):
    total = total + num[i]
avg = total/6

Find Largest

largest = num[0]
for i in range(0, 6):
    if num[i] > largest:
        largest = num[i]

Linear Search

target = 25
found = False
for i in range(0, 6):
    if target == num[i]:
        found = True

Counting

bound = 20; count = 0
for i in range(0, 6):
    if num[i] > bound:
        count += 1

Strings

A string is a series of characters. Each character can be accessed by index like a list.

the_string = "Work Hard!"
# Index:   0123456789
# the_string[0] is 'W'

# Extract substring
sub_string = ""
for i in range(0, 4):
    sub_string = sub_string + the_string[i]
# sub_string = "Work"

Two-Dimensional Arrays (2D Lists)

2D arrays present data in the form of tables (rows and columns). In Python, a 2D list is a "list of lists".

list2d = [[0,1,2],[3,4,5],[6,7,8],[9,10,11]]
# Access: list2d[row][column]
# list2d[3][1] = 10

# Modify:
list2d[0] = [3,4,5]        # Replace entire row
list2d[1][2] = list2d[2][2] + 10  # Modify single item

Real-world applications: Spreadsheets, tic-tac-toe boards, minesweeper grids, Cartesian coordinate systems, bitmap images.