Python first year btech Algorithmic thinking with python

Module 1
PROBLEM SOLVING STRATEGIES

Syllabus
 PROBLEM-SOLVING STRATEGIES:- Problem-solving strategies defined,
Importance of understanding multiple problem-solving strategies, Trial and Error,
Heuristics, Means-Ends Analysis, and Backtracking (Working backward).
 THE PROBLEM-SOLVING PROCESS:- Computer as a model of computation,
Understanding the problem, Formulating a model, Developing an algorithm, Writing
the program, Testing the program, and Evaluating the solution.
 ESSENTIALS OF PYTHON PROGRAMMING:- Creating and using variables in
Python, Numeric and String data types in Python, Using the math module, Using the
Python Standard Library for handling basic I/O - print, input, Python operators and
their precedence.

Problem-Solving Strategies
 The term problem solving has a slightly different meaning dependingon
the discipline.
 Definition:
 A problem-solving strategy is a plan used to find a solution or overcome
a challenge or achieve a goal.
 Solutions require sufficient resources and knowledge to attain the goal.
 Professionals such as lawyers, doctors, programmers, and consultants
are problem solvers.

Problem-Solving Strategies
 Problems can be classified into two different categories:
 ill-defined and well-defined problems.
 Ill-defined problems: issues that do not have clear goals, solution paths,
or expected solutions.
 Examples: ??
 Well-defined problems: have specific goals, clearly defined solutions, and clear
expected solutions.
 Examples: ??

Importance of Multiple Problem-Solving Strategies
 Different problems typically require you to approach them in different ways to
find the best solution.
 Understanding multiple problem-solving strategies is crucial because it equips
individuals with a diverse toolkit to tackle a variety of challenges.
 By knowing several strategies, one can quickly switch tactics when one method
does not work, increasing the chances of finding a successful solution.

Importance of Multiple Problem-Solving Strategies
 Other benefits includes:
 Adaptability
 Efficiency
 Improved Outcomes
 Skill Development.
 Common problem solving strategies include:
 Trial and Error Method
 Algorithm and Heuristic
 Means-Ends Analysis
 Backtracking

 A fundamental method of Problem solving.
 It is characterized by repeated, varied attempts which
are continued until success.
 When to avoid the trial and error method:
 When there is a clear solution
 When the cost of failure is high
 When you are working with limited resources
Trial and Error Method

 Problem: Consider the situation where you have forgotten the password to your
online account, and there is no password recovery option available. You decide
to use trial and error to regain access.
Trial and Error Method – Example 1

 Problem: Printer is not working
 Solutions:
 Try checking the ink levels, and if that doesn’t work.
 Check to make sure the paper tray isn’t jammed.
 Or may be the printer isn’t connected to a laptop.
 When using trial and error, one would continue to try different solutions until
the problem is solved.

 A farmer with a fox, a goose, and a
sack of corn needs to cross a river. The
farmer has a boat, but there is room for
only the farmer and one of his three
items. Unfortunately, both the fox and
the goose are hungry. The fox cannot
be left alone with the goose, or the fox
will eat the goose. Likewise, the goose
cannot be left alone with the sack of
corn, or the goose will eat the corn.
How does the farmer get everything
across the river?

Solution: HOW TO CROSS THE RIVER?

 Algorithms and heuristics are different approaches to solving problems.
 Algorithms are step-by-step procedures for a solution. They are guaranteed to
yield the correct solution, but may be time-consuming and require a lot of
mental effort.
 Eg:- Google use algorithms to decide which entries will appear first in your list
of results.
 In contrast, heuristics are shortcut strategies or rules-of-thumb for a solution,
but there is no guarantee for the result.
 They are estimations or shortcuts based on past experience.
 Eg:- driving in a city with frequent traffic congestion, traveling
salesperson problem, etc.
Algorithm and Heuristic

 Used in Artificial Intelligence. It involves breaking down a problem into smaller,
more manageable sub-problems to reduce the difference between the current
state and the desired goal state.
 Example: Imagine you want to plan a road trip from our college to Kashmir.
 Define the Goal (End)
 Analyze the Current State
 Identify the Differences
 Set Sub-Goals (Means)
 Implement the Plan
 Adjust as Needed (In this case based on traffic)
Means-Ends
Analysis

 When the problem to be solved is too complex to manage, break it into
manageable parts known as sub-problems. This process is known as problem
decomposition.
 Steps:
1. Understand the problem.
2. Identify the sub-problems.
3. Solving the sub-problems.
4. Combine the solution.
5. Test the combined solution.
Problem Decomposition

 The actual Tower of Hanoi problem consists of three rods sitting vertically on a
base with a number of disks of different sizes that can slide onto any rod. The
puzzle starts with the disks in a neat stack in ascending order of size on one rod,
the smallest at the top making a conical shape. The objective of the puzzle is to
move the entire stack to another rod obeying the following rules:
1. Only one disk can be moved at a time.
2. Each move consists of taking the upper disk from one of the stacks and
placing it on top of another stack or on an empty rod.
3. No larger disc may be placed on top of a smaller disk.
Tower of Hanoi paradigm

 With 3 disks, the puzzle can be solved in 7 moves. The minimal moves required
to solve a Tower of Hanoi puzzle is 2n – 1, where n is the number of disks. For
example, if there were 14 disks in the tower, the minimum amount of moves that
could be made to solve the puzzle would be 214 – 1 = 16,383 moves. There are
various ways of approaching the Tower of Hanoi or its related problems in
addition to the approaches listed above including an iterative solution, recursive
solution, non-recursive solution, a binary and Gray-code solutions, and graphical
representations. We will see Means-Ends Analysis Solution.
Tower of Hanoi paradigm

 Backtracking is like trying different paths, and when you hit a dead end, you
backtrack to the last choice and try a different route.
 Since a problem would have constraints, the solutions that fail to satisfy them
will be removed.
 It is commonly used in situations where you need to explore multiple
possibilities to solve a problem, like searching for a path in a maze or solving
puzzles like Sudoku.
Backtracking

1. Choose an initial solution.
2. Explore all possible extensions of the current solution.
3. If an extension leads to a solution, return that solution.
4. If an extension does not lead to a solution, backtrack to the previous solution
and try a different extension.
5. Repeat steps 2-4 until all possible solutions have been explored.
Backtracking – How it works?

 Finding the shortest path through a maze
 Input: A maze represented as a 2D array, where 0 represents an open space
and 1 represents a wall.
1. Start at the starting point.
2. For eachof thefourpossible directions (up, down, left, right), try
moving in that direction.
3. If moving in that direction leads to the ending point, return the path taken.
4. If moving in that direction does not lead to the ending point, backtrack to the previous
position and try a different direction.
5. Repeat steps 2-4 until the ending point is reached or all possible
paths have been explored.
Backtracking – Example

 Past Experience: Take the time to consider if you have encountered a similar
situation to your current problem in the past.
 Bring in a Facilitator: Consider inviting a facilitator to your group meeting to help
generate better solutions.
 Develop a decision matrix for evaluation: Rank your potential solutions based on
factors like timeliness, risk, manageability, expense, practicality, and effectiveness.
 Ask your peers for help: Friends, families or colleagues may have different
experiences, ideas and skills that may contribute to finding the best solution to a
problem.
 Step away from the problem: If the problem being worked on does not need an
immediate solution, consider stepping away from it for a short period of time.
Other Problem-solving Strategies

Computer as a Model of Computation

 The above model works based on input-process-output concept.
Computer as a model of computation
Von Neumann’s Computer
Architecture Model

 Definition: Problem Solving is the sequential process of analyzing information
related to a given situation and generating appropriate response options.
 Example: Calculate the average grade for all students in a class.
 Input: get all the grades … possibly by typing them in via the keyboard or
by reading them from a USB flash drive or hard disk.
 Process: add them all up and compute the average grade.
 Output: output the answer to either the monitor, to the printer, to the USB
flash drive or hard disk … or a combination of any of these devices.

1. Understanding the problem
2. Formulating a model
3. Developing an algorithm
4. Writing the program
5. Testing the program
6. Evaluating the solution.

 Understands the problem about to be solved.
 One needs to know:
• What input data/information is available?
• In what format is the data/information?
• What is missing in the data provided?
• Does the person solving the problem have everything
needed?
• What output information needs to be produced?
• In what format should the result be: text, picture, graph?
• What are the other requirements needed for computation?
1. Understanding the problem

 Formulate a model for the problem.
 By considering the above problem, a model (or formula) is needed
for computing the average of a bunch of numbers.
 If there is no such “formula”, one must be developed.
 Assuming that the input data is a bunch of integers or real numbers 𝑥1, 𝑥2, ⋯
,
𝑥𝑛 representing a grade percentage, the following computational model
may apply:
𝐴𝑣𝑒𝑟𝑎𝑔𝑒1 = (𝑥1 + 𝑥2 + 𝑥3 + ⋯ + 𝑥𝑛)/𝑛
2. Formulating a Model

 However, the above approach will not work if the input data is a set of letter
grades like B-, C, A+, F, D-, etc.
 So, we may decide to assign an integer number to the incoming letters
as follows:
𝐴+ = 12, 𝐴 = 11, 𝐴− = 10, 𝐵+ = 9, 𝐵 = 8, etc.
 Assume these newly assigned grade numbers are 𝑦1, 𝑦2,⋯ , 𝑦𝑛, then
the following computational model may be used:
𝐴𝑣𝑒𝑟𝑎𝑔𝑒2 = (𝑦1 + 𝑦2 + 𝑦3 + ⋯ + 𝑦𝑛)/n
2. Formulating a Model

 Come up with a precise plan of what the computer is expected to do.
 Definition: Algorithm is a precise sequence of instructions for
solving a problem.
 The instructions must be understandable to a person who is trying to figure out
the steps involved.
 Two commonly used representations for an algorithm is by using
 Pseudocode
 Flowcharts
3. Develop an
Algorithm

 Consider the following example for solving the problem of a broken
lamp.
3. Develop an
Algorithm
Flowchart for a broken Lamp

Algorithm for a broken Lamp
1. IF lamp works, go to step 7.
2. Check if lamp is plugged in.
3. IF not plugged in, plug in lamp.
4. Check if bulb is burnt out.
5. IF blub is burnt, replace bulb.
6. IF lamp doesn’t work buy new lamp.
7. Quit ... problem is solved.
3. Develop an
Algorithm

Algorithm to calculate the average of grades
1. Set the sum of the grade values to 0.
2. Read all grades 𝑥1, 𝑥2, ⋯ , 𝑥𝑛.
3. for i = 1 to n, repeat the following
a. Get grade 𝑥𝑖
b. Add 𝑥𝑖 to the sum
4. Compute average to be sum/𝑛.
5. Print the average.
3. Develop an
Algorithm

 Writing a program is often called "coding" or “implementing an algorithm”.
 So the code (or source code) is actually the program itself.
 The source code would vary depending on the programming language that was
used.
 The computer requires precise instructions in order to understand what it
is being asked to do.
 Compiling is the process of converting a program into instructions that can be
understood by the computer.
 Fix all such compile-time errors before continuing on to the next step.
4. Writing the Program

 Sometime, a program may work correctly for some set of input data but not for
all.
 If the output of a program is incorrect, it is possible that the algorithm was not
properly converted into a proper program.
 Such problems with the program are known as bugs.
 Bugs are errors with a program that cause it to stop working or
produce incorrect or undesirable results.
 It is the responsibility of the programmer to fix as many bugs in a program as
present.
 To find bugs effectively, a program should be tested with many test cases.
 Debugging is the process of finding and fixing errors in program code.
5. Testing the program

 Re-do some of the steps again, perhaps going as far back as step 1 again if the
expected result is not getting from the last step.
 Here the original problem needs to be reconsidered to make sure that the
answer is formatted into a proper solution to the problem.
 For example, if the result of a program is a long list of numbers, but the intent
was to identify some feature from the data, then simply producing a list of
numbers may not suffice. There may be a need to display the information in a
way that helps visualize or interpret the results with respect to the problem;
perhaps a chart or graph is needed.
6. Evaluating the Solution

 Problem: Determining the discriminant of a quadratic equation.
 Understand the problem: Here formally define the problem by specifying
the inputs and output.
 Input: The three coefficients a, b and c of the quadratic equation
 Output: The discriminant value D for the quadratic equation.
 Formulate a model for the solution: Develop a mathematical model for the
solution.
 D = b2 − 4ac
A Case Study - The Discriminant
Calculator

 Develop an algorithm: A
possible discriminant problem is given
below
1. Start
2. Read(a, b, c)
3. d = b ∗ b − 4 ∗ a ∗ c
4. Print(d)
5. Stop
algorithm (or Pseudocode) for our
Calculator

 Code the algorithm: The Python program to calculate the discriminant is as
follows
a = int(input("Enter the value of first coefficient"))
b = int(input("Enter the value of second coefficient"))
c = int(input("Enter the value of third coefficient"))
d = (b**2) - (4*a*c)
print(d)
Calculator

 Test the program: Each row denotes a set of inputs (a, b, and c) and
the expected output (d) with which the actual output is to be compared.
Calculator

Essentials of Python Programming

The Python Programming Language
 Python is an example of a high-level language.
 It is an interpreted language
 Python programs are executed by an interpreter.
 There are two ways to use the interpreter:
 Command line mode
 Script mode.

 Incommand-line mode, we type Python programs and the
interpreter prints the result
$ python
Python 3.12.4 (Sep 20 2024, 09:28:56)
Type "help", "copyright", "credits" or "license" for
more information.
>>> print (1 + 1)
2

 In script mode, we can write a program in a file and use the interpreter
to execute the contents of the file. Such a file is called a script.
 For example, we use a text editor to create a file named test.py with
the following contents:
print (1 + 1)
 To execute the program:
$ python test.py
2

Values and Data Types in Python
 A value is one of the fundamental things, like a letter or a number.
 Eg: 2, 2.5, ‘a’, “Hello”
 These values belong to different data types
 Integer, float, character, string
>>> type("Hello, World!")
<type 'str'>
>>> type(17)
<type 'int'>

Python Identifiers
 A Python identifier is a name used to identify a variable, function,
class, module or other object.
 An identifier starts with a letter A to Z or a to z or an underscore ‘_’
followed by zero or more letters, underscores and digits (0 to 9).
 Examples:
sum, name, age, _age, Age, name_1, name0

Variable
s
 A variable is a name that refers to a value
 Variables are created when they are assigned
 The variable name is case sensitive: ‘val’ is not the same as ‘Val’
 The type of the variable is determined by Python
 A variable can be reassigned to whatever, whenever
>>> message = “Welcome to Python Programming"
>>> n = 17
>>> pi = 3.14159

Variable Names
 Variable names can be arbitrarily long.
 They can contain both letters and numbers, but they have to begin with a letter.
 The underscore character ( _ ) can appear in a name.
 used in names with multiple words, such as my_name or birth_date.

Variable Names – invalid syntax
>>> 76trombones = "big parade"
SyntaxError: invalid syntax
>>> more$ = 1000
>>> class = "Computer Science
101"

Keywords
 Keywords define the language's rules and structure, and they cannot be used as
variable names.
 Python has 29 keywords:

Statements
 A statement is an instruction that the Python interpreter can execute.
 Egs:- print statement and assignment statement.
print (“We are S1 CSE
Students……”) age = 19
h = “Hello…”
price = 25.5

Evaluating Expressions
 An expression is a combination of values, variables, and operators.
>>> 1 + 1
2
>>> Sum = a + b

The math Module
 A module is a file consisting of Python code.
 It can define functions, classes, and variables which can be used in
other programs.
 Math module consists of all the built-in functions to perform
mathematical operations.
 To use a mathematical function in a program, first import the math
module using the import keyword.
 Example:
import math
print(math.pi)
print(math.sqr
t(16))

 math.sqrt(x)
 math.exp(x)
 math.pi
 math.log(x) #log(x) is
base e
 For example:
>>> math.sqrt(2) / 2.0
0.707106781187
The math Module

Composition
 Python functions can be composed.
 We can use one expression as part of another.
 Example:
>>> x = math.cos(angle + math.pi/2)
>>> x = math.exp(math.log(10.0))

Input/Output Functions
 To print a message or value to screen, use:
 print() – It prints something on the screen
 To read values from the keyboard, use:
 input() – It reads the input and returns a string.
 int(input()) – Reads the input and returns an
integer.
 Example:
name = input(“Enter Name”);
age = int(input(“Enter Age”));
print(“Hello ”, name)

name = input(“Enter Name”);
print("Enter name")
name = input()
Print(name)

Example Programs
 Simple desktop calculator using Python. Only the five basic
arithmetic operators.
 Write a program to find the value of (a + b)2
 Write a program to evaluate the expression n(n - 1)/2

Operators in Python
 Operators are special symbols that represent computations like addition and
multiplication.
 The values the operator uses are called operands.
Examples:
20+32, hour-1, hour*60+minute,minute/60,5**2,
(5+9)*(15-7)
• When a variable name appears in the place of an operand, it is replaced with
its value before the operation is performed.

 Python language supports the following types of
operators.
1. Arithmetic Operators
2. Comparison (Relational) Operators
3. Assignment Operators
4. Logical Operators
5. Bitwise Operators
6. Membership Operators
7. Identity Operators.
Operators in Python

1. Arithmetic
Operators Floor division is also called
integer division
Example:
>>> 7.0//2
3.0
>>> 7//2
3

2. Assignment
Operator
• ‘=’ is the assignment operator. The assignment statement creates new variables
and gives them values.
• Examples:
>>> a = 10
>>> a = b = 5
>>> a, b, c = 1, 2.5, "ram"
• Python supports the
following six additional
assignment operators

3. Comparison Operator
• The result of a comparison is either
True or False.
• Examples:
>>> i, j, k = 3, 4, 7
>>> i > j
False
>>> (j + k)
True
> (i + 5)
• Comparison operators support chaining.
For example, x < y <= z is equivalent to
x < y and y <= z.

4. Logical Operators
• Python includes three Boolean (logical) operators: and , or , and not.
• The and operator and or operator expect two operands, which are hence called
binary operators.
• The and operator returns True if and only if both of its operands are True, and
returns False otherwise.
• The or operator returns False if and only if both of its operands are False, and
returns True otherwise.
• The not operator expects a single operand and is hence called a unary operator.
• It returns the logical negation of the operand, that is, True, if the
operand is False, and False if the
operand is True.

4. Logical Operators – Truth Table
Truth tables for logical or and
logical and operators.
Truth tables for
logical not operator.
Python interprets all non-zero values as True and zero as False

4. Logical Operators - Example
>>> 7 and 1
1
>>> -2 or 0
-2
>>> -100 and 0
0
>>> True and False
False
>>> False or True
True
>>> False or False
False
>>> not True
False

5. Bitwise Operators
• Bitwise operators take the binary representation of the operands and work on
their bits, one bit at a time.
• The bits of the operand(s) are compared starting with the rightmost bit (least
significant bit), then moving towards the left and ending with the leftmost
(most significant) bit.
• The result of the comparison will depend on the compared bits and the
operation being performed.
• Bitwise operators can be divided into three general categories:
• One’s complement, Logical bitwise, and Bitwise shift

5.1 One’s complement Operation
-7
>>> ~8
-9
• One’s complement is denoted by the symbol ∼.
• It operates by changing all zeroes to ones and ones to zeroes in the
binary representation of the operand.
>>> ~6
8 = 1000
∼8 = 0111 (Which is the 2’s
complement of -9)
= -9

5.2 Logical Bitwise
• There are three logical bitwise operators: bitwise and (&), bitwise exclusive or
(𝖠), and bitwise or ( | ).
• A bitwise and expression will return 1 if both the operand bits are 1.Otherwise,
it will return 0.
• A bitwise or expression will return 1 if at least one of the operand bits is 1.
Otherwise, it will return 0.
• A bitwise exclusive or expression will return 1 if the bits are not alike (one bit
is 0 and the other is 1). Otherwise, it will return 0.

5.2 Logical Bitwise
>>> a = 5
>>> b = 6
>>> a & b
4
>>> a | b
7
>>> a ^ b
3

5.3 Bitwise Shift Operators
• The two bitwise shift operators are shift left (<<) and shift right (>>).
• The expression x << n shifts each bit of the binary representation of x to the
left, n times. Each time we shift the bits left, the vacant bit position at the right
end is filled with a zero.
• The expression x >> n shifts each bit of the binary representation of x to the
right, n times. Each time we shift the bits right, the vacant bit position at the
left end is filled with a zero.

5.3 Bitwise Shift Operators
>>> 120 >> 2
30
>>> 10 << 3
80
120 = 0111 1000
Right shifting once − 0011 1100
Right shifting twice − 0001 1110
120 >> 2 = 30
10 = 0000 1010
Left shifting once − 0001 0100
Left shifting twice − 0010 1000
Left shifting thrice − 0101 0000
10 << 3 = 80

6. Membership Operators
• These operators test for the membership of a data item in a sequence, such as a
string.
• Two membership operators are used in Python.
• in – Evaluates to True if it finds the item in the specified sequence
and False otherwise.
• not in – Evaluates to True if it does not find the item in the specified
sequence and False otherwise.

6. Membership Operators - Example
>>> ‘E' in ‘HELLO'
True
>>> ‘e' in ‘HELLO'
False
>>> 'a' not in ‘Welcome'
True

6. Identity Operators
• is and is not are the identity operators in Python. They are used to
check if two values (or variables) are located in the same part of the memory.
• x is y evaluates to True if and only if x and y are the same object.
• x is not y yields the inverse truth value.

 When more than one operator appears in an expression, the order of evaluation
depends on the rules of precedence.
 The acronym PEMDAS is a useful way to remember the order of operations.
2 * (3-1) is 4
(1+1)**(5-2) is 8
2**1+1 is 3, and not 4
3*1**3 is 3, and not 27
2*3-1 is 5, not 4
2/3-1 is -1, not 1
 Note: Multiplication and Division have the same precedence. In this case it will Left
to Right associativity.
Precedence of Operators

String Operations
branch = “ CSE”
semester = “S1”
s = “ Students...”
greeting = “Hello ” + semester + branch + s
print (greeting)
O/P:
Hello S1 CSE Students...
Or we can use
greeting = “Hello ” , semester , branch , s

String Operations
“Hello” * 3 is “HelloHelloHello".
• One of the operands has to be a string; the other has
to be an integer.

Comments
 To add notes to your programs to explain in natural language what the program
is doing.
 Comments are marked with the # symbol.
 Eg:
# compute the percentage of marks obtained
percentage = (m1 + m2 + m3) * 100 / 300
– Everything from the # to the end of the line is
ignored

Indentation
 Python uses indentation to highlight the blocks of code.
 Whitespace is used for indentation in Python.
 All statements with the same distance to the right belong to the same block of
code.
 If a block has to be more deeply nested, it is simply indented further to the
right.

Indentation - Example
# Python program showing indentation
site = 'gfg'
if site == 'gfg':
print(‘Welcome S1 Students...')
else:
print(‘Hai……’)
print('All set
!')

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