1. Efficiently Solving Computer Programming Problems Doncho Minkov Telerik Corporation www.telerik.com Technical Trainer

2. From Chaotic to Methodological Approach

3. 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 solution 3

5.  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 5

6.  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 6

7.  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 7

8. Visualizing and Sketching Your Ideas

9.  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 9

10.  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" 10

11. Think-up, Invent Ideas and Check Them

12.  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 12

13.  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? 13

14. Don't go Ahead before Checking Your Ideas

15.  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 15

16.  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. 16

17. Is Your Algorithm Fast Enough?

18.  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 18

19.  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! 19

20. Coding and Testing Step-by-Step

21.  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 21

22.  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 performance 22

23.  "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 23

24.  What happens to the number?  Do we need the first bit anymore?  Remove it by right shift 24 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;

25.  Testing if the correct bit is extracted and checked  Get feedback as early as possible:  The result is as expected: 25 int number = 10; int firstBit = number & 1; number >>= 1; Console.WriteLine(firstBit);Console.WriteLine(number); 0 // the first bit 5 // the number without the first bit

26.  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 26

27.  Until the number becomes equal to 0 1.Check the value of the bit 2.Right shift the number 27 while (number != 0) { int firstBit = number & 1; int firstBit = number & 1; number >>= 1; number >>= 1; Console.Write("{0} ", firstBit); Console.Write("{0} ", firstBit);}

28.  Testing with 10 28 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 = 2 10 + 2 6 + 2 4 + 2 2 + 2 1 + 2 0

29.  So far:  We can get the values of all the bits of a number  Lets count the number of ones and zeros 29 while (number != 0) { int firstBit = number & 1; number >>= 1; if (firstBit == 1) {oneCount++;}else{zeroCount++;}}

30.  Test with number 111 ( 1101111 (2) )  The result is correct 30 ones:6 zeros:1  Test with number 1234 ( 10011010010 (2) )  The result is correct ones:5 zeros:6

31.  Pass through all the numbers  Count their bits 31 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); oneCount,zeroCount);}

32.  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 inside 32 Input: 1 2345 Output: ones:1; zeros:0 ones:2; zeros:1 ones:4; zeros:1 ones:5; zeros:3 ones:7; zeros:4  The result is surprisingly incorrect:

33.  Now it is OK 33 int n = 5; for (int i = 0; i < n; i++) { int zeroCount = 0, oneCount = 0; int zeroCount = 0, oneCount = 0; int number = int.Parse(Console.ReadLine()); int number = int.Parse(Console.ReadLine()); while (number != 0) while (number != 0) { int firstBit = number & 1; int firstBit = number & 1; number >>= 1; number >>= 1; if (firstBit == 1) { oneCount++; } if (firstBit == 1) { oneCount++; } else { zeroCount++; } else { zeroCount++; } } Console.WriteLine("ones:{0}; zeros:{1}", oneCount,zeroCount); Console.WriteLine("ones:{0}; zeros:{1}", oneCount,zeroCount);}

34. Thoroughly Test Your Solution

35.  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 35

36.  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 checkable 36

37.  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 37

38.  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! 38

39.  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 39

40. 40 int n = 10000, startNumber=111; for (int i = startNumber; i < startNumber + n; i++) { int zeroCount = 0; int zeroCount = 0; int oneCount = 0; int oneCount = 0; //int number = int.Parse(Console.ReadLine()); //int number = int.Parse(Console.ReadLine()); int number = i; int number = i; int originalNumber = number; int originalNumber = number; while (number != 0) while (number != 0) { int firstBit = number & 1; int firstBit = number & 1; number >>= 1; number >>= 1; if (firstBit == 1){ oneCount++; } if (firstBit == 1){ oneCount++; } else { zeroCount++; } else { zeroCount++; } }} Replace the reading from the console with a easier type of check

41.  The result is perfect: 41 111 (10) = 1101111 (2) -> ones:6;zeros:1 … 10110 (10) = 10011101111110 (2) -> ones:10;zeros:4

42.  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 42

43. 43 // Hardcoded input data – for testing purposes int 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 …

44. Problems 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 44

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