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UNIT – 1
ALGORITHMIC PROBLEM SOLVING
Algorithms, building blocks of algorithms (statements, state, control flow, functions), notation (pseudo code, flow chart, programming language), algorithmic problem solving, simple strategies for developing algorithms (iteration, recursion). Illustrative problems: find minimum in a list, insert a card in a list of sorted cards, guess an integer number in a range, Towers of Hanoi.
1.1 ALGORITHM
What is algorithm? An algorithm is a collection of well-defined, unambiguous and effectively computable instructions ,if execute it will return the proper output.
well-defined - The instructions given in an algorithm should be simple and defined well.
Unambiguous - The instructions should be clear,there should not be ambiguity.
effectively computable - The instructions should be written step by step ,which helps computer to understand the control flow.
PROGRAM = ALGORITHM + DATA
Algorithm is defined as “a sequence of instructions designed in such a way that if the instructions are executed in the specified sequence, the desired result will be obtained”.
It is also defined as “any problem whose solution can be expressed in a list of executable instruction”.
Set of step-by-step instructions that perform a specific task or operation
Natural language NOT programming language.
Algorithm is the sequence of steps to be performed in order to solve a problem by the
computer.
Three reasons for using algorithms are efficiency, abstraction and reusability.
Algorithms can be expressed in many different notations, including natural languages,
pseudocode, flowcharts and programming languages.
Analysis of algorithms is the theoretical study of computer program performance and
resource usage, and is often practiced abstractly without the use of specific programming language or implementation.
The practical goal of algorithm analysis is to predict the performance of different
algorithms in order to guide program design decisions.
Most algorithms do not perform the same in all cases; normally an algorithm‟s
performance varies with the data passed to it.
Typically, three cases are recognized: the best case, average case and worst case
Worst case analysis of algorithms is considered to be crucial to applications such as
games, finance and robotics.
O-notation, also known as Big O-notation, is the most common notation used to express an
algorithm‟s performance in a formal manner.
Characteristics of algorithm
1. In the algorithm each and every instruction should be precise and unambiguous.
2. The instruction in an algorithm should not be repeated infinitely.
3. Ensure that the algorithm will ultimately terminate.
4. The algorithm should be written in sequence.
5. It looks like normal English.
6. The desired result should be obtained only after the algorithm terminates.
Qualities of a good algorithm
Time - Lesser time required.
Memory - Less memory required.
Accuracy - Suitable or correct solution obtained.
Sequence - Must be sequence and some instruction may be repeated in number of times or
until particular condition is met.
Generability - Used to solve single problem and more often algorithms are designed to handle
a range of input data.
1.2 Building Blocks of Algorithms
Algorithms can be constructed from basic building blocks namely, sequence, selection and iteration.
1.2.1 Statements Statement is a single action in a computer.
In a computer statements might include some of the following actions
input data-information given to the program
process data-perform operation on a given input
output data-processed result
1.2.2 State: Transition from one process to another process under specified condition with in a time is called state.
1.2.3 Control flow:
The process of executing the individual statements in a given order is called control flow. The control can be executed in three ways
1. sequence
2. selection
3. iteration
1.2.3.1 Sequence All the instructions are executed one after another is called sequence execution. Example:
Add two numbers:
Step 1 : Start Step 2 : get a,b Step 3 : calculate c=a+b Step 4 : Display c
1.2.4 Functions
Function is a sub program which consists of block of code(set of instructions) that performs
a particular task.
For complex problems, the problem is been divided into smaller and simpler tasks during
algorithm design. Benefits of Using Functions
Reduction in line of code
code reuse
Better readability
Information hiding
Easy to debug and test
Improved maintainability
Example:
Algorithm for addition of two numbers using function Main function() Step 1: Start Step 2: Call the function add() Step 3: Stop
sub function add() Step 1: Function start Step 2: Get a, b Values Step 3: add c=a+b Step 4: Print c Step 5: Return
Examples of algorithm
Problem 1 : Find the area of a Circle of radius r.
Inputs to the algorithm: Radius r of the Circle. Expected output: Area of the Circle Algorithm:
Step 1 : Start Step 2 : Read input the Radius r of the Circle Step 3 : Area PIrr // calculation of area Step 4 : Print Area Step 5 : Stop
Problem2 : Write an algorithm to read two numbers and find their sum.
Inputs to the algorithm: First num1. Second num2. Expected output: Sum of the two numbers. Algorithm :
Step 1 : Start Step 2 : Read\input the first num1. Step 3 : Read\input the second num2. Step 4: Sum num1+num2 // calculation of sum Step 5 : Print Sum Step 6 : Stop
Problem 3 : Convert temperature Fahrenheit to Celsius Inputs to the algorithm: Temperature in Fahrenheit Expected output: Temperature in Celsius Algorithm: Step 1 : Start Step 2 : Read Temperature in Fahrenheit F Step 3 : C 5/9*(F-32) Step 4 : Print Temperature in Celsius: C Step 5 : End
Problem 4: Find the largest number between A and B Inputs to the algorithm : A, B Expected output : Largest A or B
1.3 Algorithm Notations(Expressing Algorithms)
As we know that ,an algorithm is a sequence of finite instructions,often used for calculation and data processing.
Algorithms can be expressed in many kinds of notation,including
1.3.1 PSEUDOCODE
Definition:-
“Pseudo” means initiation or false.
“Code” means the set of statements or instructions written in a programming language.
Pseudocode is also called as “Program Design Language [PDL]”.
Pseudocode is a Programming Analysis Tool, which is commonly used for
planning the program logic.
Pseudocode is written in normal English and cannot be understood by the computer.
Set of instructions that mimic programming language instructions
An informal high-level description of the operating principle of a computer
program. It uses the structural conventions of a programming language, but is intended for human reading rather than machine reading.
Pseudocode
Flowchart
Programming Language
Rules for writing Pseudocode
1. Write one statement per line
2. Capitalize initial keywords (READ, WRITE, IF, WHILE, UNTIL).
3. Indent to show hierarchy.
4. End multiline structure.
5. Keep statements language.
Advantages
It can be done easily in any word processor.
It can be easily modified as compared to flowchart.
Its implementation is very useful in structured design elements.
It can be written easily.
It can be read and understood easily.
Converting a pseudocode to programming language is very easy
compared with converting a flowchart to programming language.
Disadvantage
It is not visual.
We do not get a picture of the design.
There is no standardized style or format.
For a beginner, it is more difficult to follow the logic or write pseudocode as
compared to flowchart.
Pseudocode is made up of the following logic structure ,
Sequential logic
Selection logic
Iteration logic
Sequence Logic
It is used to perform instructions in a sequence,that is one after another
Thus,for sequence logic ,pseudocode instructions are written in an order in which they are to be
performed. The logic flow of pseudocode is from top to bottom.
Pseudocode to add two numbers:
START READ a,b COMPUTE c by adding a &b PRINT c STOP
Selection Logic
It is used for making decisions and for selecting the proper path out of two or more alternative
paths in program logic.
It is also known as decision logic.
Selection logic is depicted as either an IF..THEN or an IF…THEN..ELSE
Structure.
FOR i <= n, then DISPLAY i INCREMENT i END FOR END
Problem 4: Find the greater number between two numbers. BEGIN Read A, B IF A is less than B BIG = B SMALL = A ELSE BIG = A SMALL = B WRITE / DISPLAY BIG, SMALL END
Problem 5: To determine a student whether successful or fail. BEGIN READ student „s grade IF student's grade is greater than or equal to 50 Print "passed" ELSE
END
Print "failed“
1.3.2 FLOWCHARTS
Definitions: A flowchart is a schematic representation of an algorithm or a stepwise process, showing the steps as boxes of various kinds, and their order by connecting these with arrows. Flowcharts are used in designing or documenting a process or program.
A flow chart, or flow diagram, is a graphical representation of a process or system that details the sequencing of steps required to create output.
A flowchart is a picture of the separate steps of a process in sequential order. The benefits of flowcharts are as follows:
1. Communication: Flowcharts are better way of communicating the
logic of a system to all concerned.
2. Effective analysis: With the help of flowchart, problem can be analysed in more
effective way.
3. Proper documentation: Program flowcharts serve as a good program
documentation, which is needed for various purposes.
4. Efficient Coding: The flowcharts act as a guide or blueprint during the
systems analysis and program development phase.
5. Proper Debugging: The flowchart helps in debugging process.
6. Efficient Program Maintenance: The maintenance of operating program
becomes easy with the help of flowchart. It helps the programmer to put efforts more efficiently on that part
The Limitations of using flowcharts :
1. Complex logic: Sometimes, the program logic is quite complicated. In
that case, flowchart becomes complex and clumsy.
2. Alterations and Modifications: If alterations are required the flowchart
may require re-drawing completely.
3. Reproduction: As the flowchart symbols cannot be typed, reproduction
of flowchart becomes a problem.
4. The essentials of what is done can easily be lost in the technical details of how it is
done.
GUIDELINES FOR DRAWING A FLOWCHART
Flowcharts are usually drawn using some standard symbols; however, some special symbols can also be developed when required. Some standard symbols, which are frequently required for flowcharting many computer programs.
Terminator:
An oval flow chart shape indicates the start or end of the process, usually containing the word “Start” or “End”.
Terminator
These are the basic symbols used generally. Now, the basic guidelines for drawing a flowchart with the above symbols are that:
In drawing a proper flowchart, all necessary requirements should
be listed out in logical order.
The flowchart should be neat, clear and easy to follow. There should
not be any room for ambiguity in understanding the flowchart.
The flowchart is to be read left to right or top to bottom.
A process symbol can have only one flow line coming out of it.
For a decision symbol, only one flow line can enter it, but multiple
lines can leave it to denote possible answers.
The terminal symbols can only have one flow line in conjunction with them.
Flowchart is made up of the following logic structure ,
Sequential logic
Selection logic
Iteration logic
Sequence Logic
In a computer program or an algorithm, sequence involves simple steps which are to be executed one after the other. The steps are executed in the same order in which they are written.
Below is an example set of instructions to add two numbers and display the answer.
Flowchart to find factorial of given no
pre-test loop post-test
Problem 3 : Convert temperature Fahrenheit to Celsius.
Problem 4 : Flowchart for an algorithm which gets two numbers and prints sum of their value
Problem5 : Flowchart for the problem of printing even numbers between 0 and 99.
