first midterm exam

CS201 – Introduction to Computing – Sabancı University 1

First Midterm Exam

November 7, 2015, Saturday 14:00 – 15:40

max 100 minutes One A4 size cheat-note allowed Closed book, closed notes, no calculators and no laptops Until the end of loops A detailed email will be sent later

Next week, a Sample Question Set will be posted on the website of the course Solutions will be posted later


Homework 3 Homework 3 is due October 21, 2015, 19:00

Robot application. Be careful where and how you create the robots

• Robot must be created only once within the main

• Examine example robot programs covered in recitations Scope rules say that each identifier can be used only in

the compound block in which it is declared• If you receive an “undeclared identifier” error for a robot

even you declare it, check where you declare and use it! Use of functions

You have to split the task into several functions Do not forget to use & for robot parameters


From Selection to Repetition The if statement and if/else statement allow a block of statements to be

executed selectively: based on a condition

cout << "Please enter a non-negative number" << endl;cin >> inputnumber; if (inputnumber < 0){ cout << inputnumber << " is negative. Wrong Input" << endl;} This piece of code does not ask another input number if the number is negative.------------------------------------------------------------------------------------------------------ The while statement repeatedly executes a block of statements while the

condition is truecout << " Please enter a non-negative number" << endl;cin >> inputnumber; while (inputnumber < 0){ cout << inputnumber << " is negative! Try again" << endl; cin >> inputnumber;}


Semantics of while loop

if (test) while (test){ { statement list; statement list;} }

test

Statement list

Next statement

true

false

test

Statement list

Next statement

true

false


Another simple example Calculate the sum of the integer numbers between 1 and 10

int sum = 0; // this program piece int num = 1; // calculates the sum

of while (num <= 10)// integers between and { // including 1 and 10 sum = sum + num; num += 1; }

Let us see how it works step by step


Easy Example (not in book)

Input 10 integer numbers and find their sum What about having

cin >> num; sum = sum + num; 10 times?

• not a good solution Good solution is to use loops.

code is developed on board. see sum10nums.cpp This type of loops are called counting loops

number of iterations is known


Another easy example (not in book)

Read a sequence of integer numbers from keyboard and find their sum. input should finish when user enters –1

• -1 is the sentinel value in this example

• not to be added to the sum Code is developed on board (see sumnums.cpp) This type of loop is called conditional loop

number of iterations is not known depends on input


Anatomy of a loop

sum = 0; count = 1;while (count <= 10){

cin >> num;sum += num;count += 1;

}

initialization

Loop test expression

Loop body

Update statement


Anatomy of a loop Initialize variables used in loop body and loop test (before the loop)

No general rule. The way of initialization and the initial values are to be determined according to the application

The loop test is evaluated before each loop iteration NOT evaluated after each statement in the loop body Current value of variables are used for the loop test before each iteration

The loop body must update some variables used in the loop test so that the loop eventually terminates If loop test is always true, loop is infinite

• Infinite loops must be avoided Basic rule of designing a loop:

Initialization, loop test and update parts should be designed carefully in order to iterate the loop as many times as needed

• neither one less nor one more. Unfortunately there is no straightforward rule of designing a bug-free

loop• you should be able to develop those parts by understanding and analyzing

the underlying problem that needs a loop


The for loop Initialization, test and update parts are combined

for (initialization; loop test expression; update){

statement list; //loop body}

initialization statement executed once before the loop

test expression boolean expression checked each time before entering the loop body

• if true execute loop body, if false terminate loop update statement

executed after the last statement of the loop body in every iteration


for loop example (similarities with while)sum = 0;

count = 1;

while (count <= 10)

{

sum = sum + count;

count = count + 1;

}

sum = 0;

for (count = 1; count <= 10; count = count+1)

{

sum = sum + count;

}


Example: Print a string backwards (revstring.cpp)

Determine the index of the last character of the string, and then access each character backwards How many times should the loop iterate ?

string s; int k; cout << "enter string: "; cin >> s; cout << s << " reversed is "; k = s.length() - 1; // index of last character in s while (k >= 0) { cout << s.substr(k,1); k -= 1; } cout << endl;

What could we use instead of s.substr(k,1) ? s.at(k)


Reverse String as a function First step, what is the function heading?

string revstring(string s) // pre: s = c0c1c2…cn-1

// post: returns cn-1…c2c1c0

Second step, how do we build a new string? Start with an empty string, "" Add one character at each iteration using

concatenation, +

rev = rev + s.substr(k,1);

Use revstring to determine if a string is a palindrome


See palindrome.cpp for full programstring revstring(string s){ // post: returns reverse of s, that is "stab" for "bats"

int k = s.length() - 1; string rev = ""; // start with empty string

while (k >= 0) { rev = rev + s.substr(k,1); k -= 1; } return rev;}

bool IsPalindrome(string word){ // post: returns true if and only word is a palindrome return word == revstring(word);}


Infinite loops Infinite loop is a loop that never stops

something that must be avoided happens when the loop condition is always true same loop body iterates indefinitely

• sometimes you see an output, sometimes you don’t• press Ctrl-C to stop

maybe the effect of a wrong or missing update statement maybe due to a wrong condition; may be due to another reason

Example: consider the following modified code from sum10nums What’s the problem in the loop below? What is missing?

• count never reaches 10, because count is not updated in the loop

sum = 0; count = 1;while (count <= 10){

cin >> num;sum += num;

}


Infinite loops

What is the problem with the code below? cannot say infinite loop, depends on input number

• For example, if num is an odd number, then the loop is infinite

cin >> num;

int start = 0; while (start != num) { start += 2; cout << start << endl; }


Developing Loops Some loops are easy to develop, others are not Sometimes the proper loop test and body are hard to design Practice helps, but remember:

Good design comes from experience, experience comes from bad design

Common loop bugs Easy to iterate one more or one less than needed Test the following cases all the time

• Zero iteration case (or whatever the minimum number of iterations)

• One iteration case (or one more than the minimum number of iterations)

• Maximum number of iterations• One less than the maximum number of iterations


Number Crunching

Number crunching is a CS term that means a computing operation that requires several (and sometimes complex) arithmetic operations

was the job of early computers Numeric Analysis

classical subdiscipline of computer science today

implicitly or explicitly, all operations are numeric Now we will see some mathematical applications

factorial calculation prime number testing


Factorial

n! = 1x2x…xn is “n factorial”; used in math, statistics

long factorial(int n) // pre: 0 <= n // post: returns n! (1 x 2 x … x n)

Similar to sum, but this time we will calculate a product within the loop. At the end we will return the final product. The loop will iterate n times, multiplying by 1, 2, …, n Suppose we use a variable called product to hold the

result, then product is n! when the loop terminates. So we will return it at the end.


Factorial

long Factorial(int num)// precondition: num >= 0// postcondition returns num! (1 x 2 x … x num){ long product = 1; int count = 0; while (count < num) { count += 1; product *= count; } return product;}

Issues Why did we use long? What happens if we use int instead? what happens if we initialize count to 1?

Let’s see fact.cpp


Factorial (Cont’d) – Using BigInt class What is the problem of the previous program?

integer overflow even long is not sufficient (actually there is not difference

between long and int for 32-bit computers like ours)• 12! is 479,001,600 so what happens with 13! ?

The type BigInt, accessible via #include "bigint.h" can be used like an int, but gets as big as you want it to be Really arbitrarily large?

• No, limited to computer memory, but computers most likely run out of time before running out of memory

Disadvantages of using BigInt compared to int?• processing speed is lower• uses up more memory

Use BigInt if you really need it Do not forget to add bigint.cpp to your project,

• BigInt is a Tapestry class, but we modified it a bit. Thus, please use the bigint.h and bigint.cpp files provided in the lecture notes rather than the one given in book's website.


Factorial using BigInt class

See bigfact.cpp


Determining if a number is prime Prime number is a natural number which has only two divisors: 1 and itself Some Cryptographic algorithms depend on prime numbers

Determining if a number is prime must be “easy” Actually factoring a number must be “hard”

• “hard” in the sense that it must be computationally infeasible to factorize in a reasonable amount of time

RSA Cryptosystem Rivest, Shamir, Adleman based on the factorization problem of large numbers has been utilized by several security products and services

• PGP (Pretty Good Privacy) – e-mail security• WWW security using SSL/TLS protocol and bany banking applications

Sophisticated mathematics used for fast prime-testing, we’ll do basic prime testing that’s reasonably fast for small numbers, but not good enough for RSA (why not?) because our algorithm is based on factorization, so it is really slow for

large numbers


Determining Primeness (continued) 1 is NOT prime, 2 is prime, 3 is prime, 5 is prime, 17 is prime, …

137, 193? We do not need to check even numbers other than 2 (2 is a

special case) To check 193, divide it by 3, 5, 7, 9, 11, 13

• Note that 14x14 = 196, so 13 largest potential factor?• we use modulus operator to check divisibility

We’ll check odd numbers as potential divisors Watch out for 2, it is a special case How far should we go to check potential divisors?

• up to and including sqrt(number) + 1• If there was a bigger factor, a smaller factor would exist. And this

smaller one must have been checked before. So we do not need to go beyond this limit.

• +1 is there to make sure that there will be no problems with precision

See primes.cpp for code


Primeness Check – Details

Special even number check is added before the loop to eliminate even numbers to be checked in the loop In order to make the code more efficient

int limit = int(sqrt(n) + 1); To assign a double value to an int, a typecast is used,

to tell the compiler that the loss of precision is intentional

• Make typecasts explicit to tell the compiler you know what you are doing

• Compiler warnings are avoided We will see typecast in more detail later


What is next with loops

Loops are useful instruments in program development Loops are statements, can be combined with other loops, with if

statements, in functions, etc. Other kinds of looping statements can make programming simpler

for loops good for counting loops

do – while loops good if the loop body must be executed at least once

nested loops loops inside other loops


Four Sections of a while loop


for loop compared with whileinitialization

while (test)

{

statement1;

...

statementN;

update;

}

for (initialization; test; update)

{

statement1;...

statementN;

}


The for loop Initialization, test and update parts are combined

for (initialization; test expression; update){

statement list; //loop body}

initialization statement executed once before the loop

test expression boolean expression checked each time before entering the loop body

• if true execute loop body, if false terminate loop update statement

executed after the last statement of the loop body in every iteration several statements in initialization and update are separated by comma initialization and/or test and/or update parts could be missing

but semicolons are there


Example Rewrite the while loop of main of primes.cpp using for

k = low; while (k <= high) { if (IsPrime(k)) { cout << k << endl; numPrimes += 1; } k += 1; }

for (k = low; k <= high; k += 1) { if (IsPrime(k)) { cout << k << endl; numPrimes += 1; } }


The for loop For loops are good for counting loops (although they can be used for

conditional loops) Number of iterations known before loop begins

• Example: sum of 10 input numbers• Example: print a string vertically

void Vertical(string s)// post: chars of s printed verticallyint len; int k;len = s.length(); k = 0; while (k < len) {

cout << s.substr(k,1) << endl; k += 1;

}

// for loop alternative 1 // for loop alternative 2int len; int k; len = s.length(); int len; int k; for(k=0; k < len; k+= 1) for(len = s.length(), k=0; k < len; k+= 1){ { cout << s.substr(k,1) << endl; cout << s.substr(k,1) << endl;} }

// for loop alternative 3int len; int k; len = s.length();k = 0;for(; k < len; k+= 1) { cout << s.substr(k,1) << endl;}


Shorthand for increment/decrement

Lots of code requires incrementing a variable by one Three methods, using = and +, using +=, and using ++

• effectively they are same num = num + 1; num += 1; num++; // post increment

It is also possible to write ++num preincrement These differ on when the increment is performed, but this

difference doesn’t matter when used as an abbreviation for the statement n += 1; in a single statement

Similarly there are postdecrement (and predecrement)

num = num - 1; num -= 1; num--;


The do-while loop Similar to while loop, but the test is after the execution of the loop body The while loop may never execute; do-while loop executes at least once

do{ loop body;} while (test ); //executes loop while the test is true

If needed, add some initialization statements to the beginning (before do)

Example; Prompt for a number between 0 and 100, loop until such a number is entered

• user should enter at least one number

do{ cout << "enter number in range [0..100] "; cin >> num;} while (num < 0 || num > 100 );

Don’t forget


Priming

Priming: reading an initial value before the loop do not get confused with prime numbers; this is something else

Problem: enter numbers, add them up, stop when -1 entered

int sum = 0;int num;cin >> num; // prime the loopwhile (num != -1){ sum += num; cin >> num;} cout << "total = " << sum << end;

Code duplication exists here: input (and perhaps prompt) code is repeated before the loop and in the loop


Pseudo infinite solution using break To avoid repeating code, include it in the body of the loop only, use

a test to break out of the loop break statement exits (inner-most) loop

I don’t like this kind of loops (I’d prefer code duplication). Because the loop condition is not clear, hence prevents readability

DO NOT use break to break the loops

int sum = 0;int num;while (true) //seemingly infinite loop{ cin >> num; if (num == -1) { break; // get out of loop } sum += num;} cout << "total = " << sum << end;


Fence Post Problem The problem that occurs when one or more operations of the loop

body are executed one less than the others. Example: Display integers between 1 and 10 separated by comma

1,2,3,4,5,6,7,8,9,10 no comma after 10; no comma before 1.

for (n=1; n <= 10; n++)

{ cout << n << ",";

} Problem: comma after 10

for (n=1; n < 10; n++)

{ cout << n << ",";

}

cout << n; No problem, but code duplicates

Think of other solutions! (see page 175 of Tapestry)


Nested loops

Sometimes one loop occurs in another Generating 2-dimensional tabular data

• multiplication table Sorting vectors (which will be studied much later) display some geometric figures using character * (or

any other character)• display rectangles, triangles

Although other loops can be nested as well, most of the time, for loops are used in nested manner


Nested loops - Example Write a function to display a rectangle of stars (height and width are

parameters) e.g. if height is 4 and width is 7, the output should look like

****************************

for (i=1; i<= height; i++){

for (j=1; j<=width; j++) // inner loop prints one line of stars{

cout << "*";}cout << endl; // end of line marker is put to the end of each

line}

See drawfigures.cpp for the complete function and its use in main


Nested loops - Example Write a function to display a perpendicular isosceles triangle of stars

(perpendicular side length is parameter) e.g. if side length is 6 , the output should look like

*********************

for (i=1; i<= side; i++){

for (j=1; j<=i; j++) // inner loop prints one line of stars{

cout << "*";}cout << endl; // end of line marker is put to the end of each

line}

See drawfigures.cpp for the complete function and its use in main


Drawfigures – Other Considerations

What about having a function to display a line of stars (number of stars is a parameter) useful for both rectangle and triangle

void PrintLine (int numstars)// pre: numstars > 0// post: displays numstars stars in one line{

int i;for (i=1; i<= numstars; i++){ cout << "*";}cout << endl; // end of line marker is put to the end of the line

} in rectangle function, inner loop is replaced by a function call

for (i=1; i<=height; i++) {

PrintLine(width); }

use of PrintLine in triangle function is similar


Example – Multiplication Table On ith line print, i*1, i*2, i*3, ... , i*i

total number of lines is an input. Display lines starting with 1. See multiply.cpp

#include <iostream>#include <iomanip> // for setwusing namespace std;

int main(){

int i,k,numlines;const int WIDTH = 4;cin >> numlines;for (i=1; i <= numlines; i++){ for (k=1; k <= i; k++) { cout << setw(WIDTH) << i*k; } cout << endl;}

return 0;}


Constants Sometimes very useful

provide self documentation and avoid accidental value changes

re-use the same value in the entire program like variables, but their value is assigned at declaration and

can never change afterwards declared by using const before the type name (any type

is OK)const double PI = 3.14159;const string thisclass = "CS201"const int WIDTH = 4;

later you can use their valuecout << (PI*4*4) << endl;

but cannot change their valuePI = 3.14; causes a syntax error


Formatting Output

We use stream manipulator setw to specify the total number of spaces that the next output will use setw(field length)

• written in cout and affects only the next output value

not the whole cout line

• output is displayed using field length spaces in right justified manner (any empty space is on the left)

defined in header file <iomanip>, so you have to have #include <iomanip>

Example

cout << setw(9) << "cs201";• output shown is four blanks and cs201


Example using robot class (see rectangularscan.cpp) Write a program in which the robot starts at 0,0 and searches a

rectangular space that covers n*n cells n is input (in the example below, n is 8) during this journey, the robot should pick or put things on

the cells so that all visited cells occupy one thing

first midterm exam

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