Problem solving using computers - Chapter 1

PROBLEM-SOLVING
USING COMPUTERS
- CHAPTER 1
PROBLEM
SOLVING
USING
COMPUTERS

INTRODUCTION
Problem-solving is transforming the description of a
problem into a solution by using our knowledge of the
problem domain and relying on our ability to select and
use appropriate problem-solving strategies, techniques,
and tools.
When we write a program, we are actually writing
instructions for the computer to solve something for us.
A COMPUTER IS A TOOL TO SOLVE A PROBLEM
PROGRAMMING IS A PROBLEM-SOLVING ACTIVITY

PROBLEM DEFINITION (Problem statement)
1
PROBLEM ANALYSIS (Identify Input, Output,
Constraints, Formulas to be used (if any)
2
COMPILATION & EXECUTION
4 CODING
3
DEBUGGING & TESTING
5
DOCUMENTATION
6
STEPS IN PROBLEM-
SOLVING
7
PROBLEM APPROACH (Algorithm, Pseudo
code, Flowchart)

A set of finite rules or
instructions to be followed in
calculations or other problem-
solving operations
ALGORITHM

Write down the steps for making peanut butter and jelly sandwich
TASK
Ingredients - Bread, Peanut butter, Jelly

Step 1: Start preparation
Step 2: Take 2 slices of bread.
Step 3: Apply peanut butter on one side of a slice.
Step 3: Apply jelly on one side of the other slice.
Step 4: Press both slices of bread together.
Step 5: Serve
CONCLUSION: Algorithm is step-wise idea of what is to be done to
get a desired output from the given input

Algorithm to add 3 numbers and print their sum
EXAMPLE
Variables - n1 | n2 | n3 | sum

START
Declare 3 integer variables n1, n2 and n3.
Take the three numbers, to be added, as
inputs in variables n1, n2, and n3 respectively.
Declare an integer variable sum to store the
resultant sum of the 3 numbers.
Add the 3 numbers and store the result in the
variable sum. (n1 + n2 + n3)
Print the value of the variable sum
END
1.
2.
3.
4.
5.
6.
7.

It should terminate after a finite time.
It should produce at least one output.
It should take zero or more input.
It should be deterministic means giving the same
output for the same input case.
Every step in the algorithm must be effective i.e.
every step should do some work.
PROPERTIES OF ALGORITHM

CHECK FOR LANGUAGE INDEPENDENCY
// C PROGRAM
#include <stdio.h>
int main()
{
int n1, n2, n3;
scanf("%d %d %d",&n1,&n2,&n3);
int sum;
sum = n1+n2+n3;
printf("%d",sum);
return 0;
}
// PYTHON PROGRAM
if __name__ == "__main__":
n1 = n2 = n3 = 0
n1 = int(input())
n2 = int(input())
n3 = int(input())
sum = 0
sum = n1+n2+n3
print(sum)
// PYTHON PROGRAM
if __name__ == "__main__":
n1 = int(input())
n2 = int(input())
n3 = int(input())
sum = n1+n2+n3
print(sum)

FLOWCHART
PSEUDO-CODE
HOW TO EXPRESS AN ALGORITHM?

FLOWCHART
A flowchart is a graphical representation of an
algorithm. Programmers often use it as a program-
planning tool to solve a problem.
It makes use of symbols that are connected among them
to indicate the flow of information and processing.
The process of drawing a flowchart for an algorithm is
known as “flowcharting”.

Draw a flowchart to add 3 numbers and print their sum
EXAMPLE
Refer the below algorithm

PSEUDO-CODE
The pseudocode is an informal way of writing a
program for better human understanding.
It is written in simple English, making the complex
program easier to understand.
Pseudocode cannot be compiled or interpreted.
It is a methodology that allows the programmer to
represent the implementation of an algorithm.

Write only one statement per line
Capitalize initial keyword
Indent to show hierarchy
End multiline structures
Keep statements language independent
It gives us the sketch of the program before actual
coding
Use the naming domain of the problem, not that of
the implementation. For instance: “Append the last
name to the first name” instead of “name = first+
last.”
Keep it simple, concise and readable.
RULES OF PSEUDO-CODE

EXAMPLE 2: WRITE THE PSEUDO CODE TO FIND THE GREATEST OF TWO NUMBERS
BEGIN
READ A,B
IF (A>B) THEN
DISPLAY a is greater
ELSE
DISPLAY b is greater
END IF
END

BRUTE FORCE ALGORITHM
Brute Force Algorithms are exactly what they sound like –
straightforward methods of solving a problem that relies on
sheer computing power and trying every possibility rather
than advanced techniques to improve efficiency.
Brute Force algorithm is a typical problem-solving
technique where the possible solution for a problem is
uncovered by checking each answer one by one, by
determining whether the result satisfies the statement of a
problem or not.
Bubble sort is one of the easiest and brute force sorting
algorithm.

RECURSIVE ALGORITHM
A recursive algorithm calls itself with smaller input values
and returns the result for the current input by carrying out
basic operations on the returned value for the smaller
input.
A recursive algorithm is an algorithm that calls itself with
"smaller (or simpler)" input values, and which obtains the
result for the current input by applying simple operations
to the returned value for the smaller (or simpler) input.
Generation of factorial, Fibonacci number series are
examples of recursive algorithms.

GREEDY ALGORITHM
Greedy is an algorithmic paradigm that builds up a solution
piece by piece, always choosing the next piece that offers
the most obvious and immediate benefit. So the problems
where choosing locally optimal also leads to the global
solution being the best fit for Greedy.
For example)
Fractional Knapsack Problem

DYNAMIC ALGORITHM
Dynamic Programming is a technique in computer
programming that helps to efficiently solve a class of
problems that have overlapping subproblems and optimal
substructure properties.
The main use of dynamic programming is to solve
optimization problems. Here, optimization problems mean
that when we are trying to find out the minimum or the
maximum solution to a problem. Dynamic programming
guarantees finding the optimal solution to a problem if the
solution exists.

A top-down approach is about breaking down a system into the
subsystems that make it up. The process can be repeated to
break down subsystems into low-level elements like classes and
methods. This approach can be applied to all levels from high-
level system architecture to low-level functionality
implementation, just to remember to start from the top. It
doesn’t necessarily always be the absolute top.
Top-Down Model is followed by structural programming
languages like C, Fortran etc.
TOP DOWN APPROACH

In this design, individual parts of the system are specified in
detail. The parts are linked to form larger components, which
are in turn linked until a complete system is formed.
Object-oriented language such as C++, Python, or Java uses a
bottom-up approach where each object is identified first.
BOTTOM UP APPROACH

So simple. It's because you first defines a class and it's functions. Then you initialise
an object of that class and calls functions as per the need. Now, though process looks
like to-bottom but the execution takes place in bottom-up approach. While executing,
execution flow find object initialisation first and then it looks up for declared class
and then functions.
WHY DO OOPS FOLLOW THE BOTTOM-UP APPROACH?

class Person:
def __init__(self, name, age):
self.name = name
self.age = age
obj1 = Person("Harry", 36)
obj2 = Person("Styles", 35)
print(obj1.name)
print(obj1.age)
print("------")
print(obj2.name)
print(obj2.age)

IS PYTHON AN OBJECT-ORIENTED PROGRAMMING
LANGUAGE?

Python is both procedural and has object-oriented features, as well as some aspects of
functional programming. That is what is meant when one says that Python is a multi-
paradigm.
Python are multi-paradigm, you can write programs or libraries that are largely
procedural, object-oriented, or functional in all of these languages. It depends on
what you mean by functional. Python does have some features of a functional
language.
OOP's concepts like, Classes,Encapsulation,Polymorphism, Inheritance etc.. in Python
makes it as a object oriented programming language.
IS PYTHON AN OBJECT-ORIENTED PROGRAMMING
LANGUAGE?

TIME COMPLEXITY
SPACE COMPLEXITY
MEASURES FOR THE EFFICIENCY OF AN ALGORITHM

SWAP TWO NUMBERS - METHOD 1
(Using third variable)
x = 10
y = 50
# Swapping of two variables
# Using third variable
temp = x
x = y
y = temp
print("Value of x:", x)
print("Value of y:", y)
x = 10
y = 50
# Swapping of two variables
# without using third variable
x, y = y, x
print("Value of x:", x)
print("Value of y:", y)
SWAP TWO NUMBERS - METHOD 2
(Using comma method)

PROBLEM STATEMENT - Airport security officials have
confiscated several item of the passengers at the security check
point. All the items have been dumped into a huge box (array). Each
item possesses a certain amount of risk[0,1,2]. Here, the risk
severity of the items represent an array[] of N number of integer
values. The task here is to sort the items based on their levels of
risk in the array. The risk values range from 0 to 2.
Example :
Input :
7 -> Value of N
[1,0,2,0,1,0,2]-> Element of arr[0] to arr[N-1], while input each
element is separated by a new line.
Output :
0 0 0 1 1 2 2 -> Element after sorting based on risk severity
Explanation:
In the above example, the input is an array of size N consisting of
only 0’s, 1’s, and 2s. The output is a sorted array from 0 to 2 based
on risk severity.

n = int(input())
arr = []
for i in range(n):
arr.append(int(input()))
arr.sort()
for i in range(n):
print(arr[i], end = " ")
PSEUDOCODE -
BEGIN
READ n
INITIALIZE list arr[]
FOR i <-- 0 to n-1
APPEND elements to the list
SORT the array list arr[]
FOR i <-- 0 to n-1
PRINT elements of the array list
END

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