7. Methodology of Problem Solving - C# Fundamentals

Methodology ofProblem Solving

Efficiently Solving Computer Programming Problems

Doncho Minkov

Telerik Software Academyacademy.telerik.com

Technical Trainerhttp://minkov.it/

http://csharpfundamentals.telerik.com

Table of Contents1. Problem Solving

2. Understanding the requirements

3. Analyzing the problem

4. Brainstorming

5. Using Pen and Paper

6. Checking your ideas

2

Problems SolvingFrom Chaotic to Methodological

Approach

How to Solve Problems?1. Read and analyze the problems

2. Use a sheet of paper and a pen for sketching

3. Think up, invent and try ideas

4. Break the problem into subproblems

5. Check up your ideas

6. Choose appropriate data structures

7. Think about the efficiency

8. Implement your algorithm step-by-step

9. Thoroughly test your solution4

Understanding the Requirements

Read and Analyze the Problems

Consider you are at traditional computer programming exam or contest You have 5 problems to solve in 6

hours First read carefully all problems and

try to estimate how complex each of them is Read the requirements, don't invent

them! Start solving the most easy problem

first Leave the most complex problem last

Approach the next problem when the previous is completely solved and well tested

6

Analyzing the Problems Example: we are given 3 problems:

1. Set of Numbers Count the occurrences of a number in

set of numbers

2. Students Read a set of students and print the

name of the student with the highest mark

3. Binary Representation Find the 'ones' and 'zeros' of a set of

numbers in their binary representation

7

Analyzing the Problems (2)

Read carefully the problems and think a bit

Order the problems from the easiest to the most complex:

1. Set of Numbers Whenever find the number increase a

count variable with one

2. Students Temporary student with current

highest mark

3. Binary representation If we know the 'ones', we can easily

find the zeros

8

Using a Paper and

a PenVisualizing and Sketching Your

Ideas

Use a Sheet of Paper and a Pen

Never start solving a problem without a sheet of paper and a pen You need to sketch your ideas Paper and pen is the best

visualization tool Allows your brain to think efficiently

Paper works faster than keyboard / screen

Other visualization tool could also work well

10

Paper and Pen Consider the "Binary representation" problem We can sketch it to start thinking

Some ideas immediately come, e.g. Divide by 2 and check for the

remainder Bitwise shift right and check for the

rightmost bit Bitwise shift left and check for the

leftmost bit Count only the "zeros" Count only the "ones" Count both "ones" and "zeros"

11

Invent IdeasThink-up, Invent Ideas and Check Them

Think up, Invent and Try Ideas

First take an example of the problem Sketch it on the sheet of paper

Next try to invent some idea that works for your example

Check if your idea will work for other examples Try to find a case that breaks your

idea Try challenging examples and

unusual cases If you find your idea incorrect, try to fix it or just invent a new idea

13

Invent and Try Ideas – Example

Consider the "Binary Representation" problem

Idea #1: divide by 2 and check the remainder How many times to do this? Where to check?

Idea #2: Bitwise shift and check the left/rightmost bit Left shift or right shift? How many times to repeat this? Is this fast enough?

14

Check-up Your IdeasDon't go Ahead before Checking Your

Ideas

Check-up Your Ideas Check-up your ideas with examples

It is better to find a problem before the idea is implemented

When the code is written, changing radically your ideas costs a lot of time and effort

Carefully select examples for check-up Examples should be simple enough

to be checked by hand in a minute Examples should be complex

enough to cover the most general case, not just an isolated case

16

Invent New Idea If Needed

What to do when you find your idea is not working in all cases? Try to fix your idea

Sometime a small change could fix the problem

Invent new idea and carefully check it

Iterate It is usual that your first idea is not

the best Invent ideas, check them, try

various cases, find problems, fix them, invent better idea, etc.

17

Efficiency and Performance

Is Your Algorithm Fast Enough?

Think About the Efficiency

Think about efficiency before writing the first line of code Estimate the expected running time

(e.g. using asymptotic complexity) Check the requirements

Will your algorithm be fast enough to conform with them

You don't want to implement your algorithm and find that it is slow when testing You will lose your time 19

Efficiency is not Always Required

Best solution is sometimes just not needed Read carefully your problem

statement Sometimes ugly solution could work

for your requirements and it will cost you less time

Example: if you need to sort n numbers, any algorithm will work when n ∈ [0..500]

Implement complex algorithms only when the problem really needs them!

20

ImplementationCoding and Testing Step-by-Step

Start Coding: Check List

Never start coding before you find correct idea that will meet the requirements What you will write before you

invent a correct idea to solve the problem?

Checklist to follow before start of coding: Ensure you understand well the

requirements Ensure you have invented a good

idea Ensure your idea is correct Ensure you know what data

structures to use Ensure the performance will be

sufficient

22

Coding Check List – Example

Checklist before start of coding: Ensure you understand well the

requirements Yes, counts values of bits

Ensure you have invented a correct idea Yes, the idea seems correct and is

tested

Ensure the performance will be sufficient Linear running time good

performance23

Implement yourAlgorithm Step-by-Step

"Step-by-step" approach is always better than "build all, then test" Implement a piece of your program

and test it Then implement another piece of

the program and test it Finally put together all pieces and

test it Small increments (steps) reveal errors early "Big-boom" integration takes more

time

24

Step #1 – Check The Value

Of The First Bit

What happens to the number? Do we need the first bit anymore? Remove it by right shift

25

int number=10;int firstBit = number & 1;

Now we have the value of the first bit

int number=10;int firstBit = number & 1;number >>= 1;

Step #1 – Test

Testing if the correct bit is extracted and checked Get feedback as early as possible:

The result is as expected:

26

int number = 10;int firstBit = number & 1;number >>= 1;Console.WriteLine(firstBit);Console.WriteLine(number);

0 // the first bit5 // the number without the first bit

Step #2 – Get All The Bits

Of a Number How many bits we want to check?

All for the number But how many are they Example: the number 10

10(10) = 8 + 2 = 1010(2) – 4 bits

How the find out when to stop the checking? When right shifting the zeros in the

front get more and more At some point the number will

become zero

27

Step #2 – Get All The Bits

Of a Number Until the number becomes equal to 0

1. Check the value of the bit

2. Right shift the number

28

while (number != 0){ int firstBit = number & 1; number >>= 1; Console.Write("{0} ", firstBit);}

Step #2 – Test Testing with 10

29

0 1 0 1

Testing with 1111

1 1 1 0 1 0 1 0 0 0 1

Seems correct

1111 = 1024 + 64 + 16 + 4 + 2 + 1 = 210 + 26 + 24 + 22 + 21 + 20

Step #3 – Check For The Occurrences Of Bit

Value So far: We can get the values of all the bits

of a number Lets count the number of ones and

zeros

30

while (number != 0){

int firstBit = number & 1;number >>= 1;if (firstBit == 1){

oneCount++;}else{

zeroCount++;}}

Step #3 – Test Test with number 111 (1101111(2))

The result is correct

31

ones:6 zeros:1

Test with number 1234 (10011010010(2))

The result is correct

ones:5 zeros:6

Step #4 – Count The Bits Of The Whole Set

Pass through all the numbers Count their bits

32

int zeroCount = 0, oneCount = 0, n = 5;for (int i = 0; i < n; i++){

int number = int.Parse(Console.ReadLine());while (number != 0){

int firstBit = number & 1;number >>= 1;if (firstBit == 1) { oneCount++; }else { zeroCount++; }

}Console.WriteLine("ones:{0};zeros:{1}", oneCount,zeroCount);}

Step #4 – Count The Bits Of The Whole Set

(2)

The result is surprisingly incorrect: The count of ones and zeros

appears as to stack for all the numbers of the set!

We defined the counters outside the iteration of the set loop

Put them inside33

Input: 12345

Output: ones:1; zeros:0ones:2; zeros:1ones:4; zeros:1ones:5; zeros:3ones:7; zeros:4

The result is surprisingly incorrect:

Step #4 – Fixing the Bug

Now it is OK34

int n = 5;for (int i = 0; i < n; i++){ int zeroCount = 0, oneCount = 0; int number = int.Parse(Console.ReadLine()); while (number != 0) { int firstBit = number & 1; number >>= 1; if (firstBit == 1) { oneCount++; } else { zeroCount++; } } Console.WriteLine("ones:{0}; zeros:{1}", oneCount,zeroCount);}

TestingThoroughly Test Your Solution

Thoroughly Test your Solution

Wise software engineers say that: Inventing a good idea and

implementing it is half of the solution

Testing is the second half of the solution

Always test thoroughly your solution Invest in testing One 100% solved problem is better

than 2 or 3 partially solved Testing existing problem takes less

time than solving another problem from scratch

36

How to Test? Testing could not certify absence of defects It just reduces the defects rate Well tested solutions are more

likely to be correct Start testing with a good representative of the general case Not a small isolated case Large and complex test, but

Small enough to be easily checkable37

How to Test? (2) Test the border cases

E.g. if n ∈ [0..500] try n=0 , n=1, n=2, n=499, n=500

If a bug is found, repeat all tests after fixing it to avoid regressions

Run a load test How to be sure that your algorithm

is fast enough to meet the requirements?

Use copy-pasting to generate large test data 38

Read the Problem Statement

Read carefully the problem statement Does your solution print exactly

what is expected? Does your output follow the

requested format? Did you remove your debug

printouts? Be sure to solve the requested problem, not the problem you think is requested! Example: "Write a program to print

the number of permutations on n elements" means to print a single number, not a set of permutations!

39

Testing – Example Test with a set of 10 numbers

Serious error found change the algorithm

Change the algorithm The counters never reset to zero

Test whether the new algorithm works Test with 1 number Test with 2 numbers Test with 0 numbers Load test with 52 000 numbers

40

Test With 10000 Numbers – Example

41

int n = 10000, startNumber=111;

for (int i = startNumber; i < startNumber + n; i++){ int zeroCount = 0; int oneCount = 0; //int number = int.Parse(Console.ReadLine()); int number = i; int originalNumber = number; while (number != 0) { int firstBit = number & 1; number >>= 1; if (firstBit == 1){ oneCount++; } else { zeroCount++; } }}

Replace the reading from the console with a easier

type of check

Test With 10000 Numbers – Example (2)

The result is perfect:

42

111(10) = 1101111(2) -> ones:6;zeros:1

…

10110(10) = 10011101111110(2) -> ones:10;zeros:4

Testing Tips You are given the task of the binary representation

The program must read from the console Integer numbers N and B N integer numbers

While writing and testing the program Don't read from the console First hardcode the numbers Later make it

When you are sure it works

43

Hard-Coded Input – Example

44

// Hardcoded input data – for testing purposesint n = 5;int num1 = 11;int num2 = 127;int num3 = 0;int num4 = 255;int num5 = 24;

// Read the input from the console//int n = int.Parse(Console.ReadLine());//for (int i=0; i<n; i++)//{// int num = int.Parse(Console.ReadLine());// // Process the number …// // …//}

// Now count the bits for these n numbers …

SummaryProblems solving needs methodology:

Understanding and analyzing problems

Using a sheet of paper and a pen for sketching

Thinking up, inventing and trying ideas

Decomposing problems into subproblems

Selecting appropriate data structures

Thinking about the efficiency and performance

Implementing step-by-step Testing the nominal case, border

cases and efficiency

45

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Methodology ofProblem Solving

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