AnnouncementsHomework 3 is due this Wednesday, November 11th

Superman robot moves into the phone booth.Homework 4 will be assigned this week and will be

due next Wednesday, November 18th

First Midterm On November 21st Saturday at 9:00am (~ 100 minutes)

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

executed selectively: based on a conditioncout << "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 loopif (test) while (test){ { statement list; statement list;} }

test

Statement list

Next statement

true

false

test

Statement list

Next statement

true

false

Sum Example: why we need loops?We want to find the sum of 10 positive valuesWe can write:

int num1, num2, num3, num4, num5;int sum;cin >> num1 >> num2 >> num3 >> num4 >> num5;sum = num1 + num2 + num3 + num4 + num5;cin >> num1 >> num2 >> num3 >> num4 >> num5;sum += num1 + num2 + num3 + num4 + num5;

Sum Example (not in book)

What if we want to compute the sum of 100 values an undetermined number of values

What we need is a program to be able to read as many values as we want and then compute the sum

This is possible with loopsGood solution is to use loops.

Code is developed on board. See sum10nums.cppThis type of loops are called counting loops

number of iterations is known

Another simple exampleCalculate the sum of the integer numbers between 1 and 10

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

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

Walkthrough of the example

int sum = 0;

int i = 1;

while (i <= 10)

{

sum = sum + i;

i = i + 1;

}

cout << sum;

i<=10

sum=sum+i;i=i+1;

true

cout<<sum;

false

1i

sum 0

2

1

Walkthrough of the example

int sum = 0;

int i = 1;

while (i <= 10)

{

sum = sum + i;

i = i + 1;

}

cout << sum;

i<=10

sum=sum+i;i=i+1;

true

cout<<sum;

false

2i

sum 1

3

3

Walkthrough of the example

int sum = 0;

int i = 1;

while (i <= 10)

{

sum = sum + i;

i = i + 1;

}

cout << sum;

i<=10

sum=sum+i;i=i+1;

true

cout<<sum;

false

3i

sum 3

4

6

Walkthrough of the example

int sum = 0;

int i = 1;

while (i <= 10)

{

sum = sum + i;

i = i + 1;

}

cout << sum;

i<=10

sum=sum+i;i=i+1;

true

cout<<sum;

false

10i

sum 45

11

55

while loop syntax

<initialization> while (<test>) {

<statement1>;...<statementN>;

<update>}

while loop sum exampleSum of numbers from 1..10

int sum = 0;int i = 1;while (i <= 10){

sum = sum + i;i = i + 1;

}cout << sum;

initialization

body statements

update

test

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, but not one less or 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

for loop syntax

for (<initialization>; <test>; <update>)

{

<statement1>;...

   <statementN>;

}

Initialization, test and update parts are combinedGood for counting on an index kind of loops.

for loop syntax compared with while

<initialization>

while (<test>)

{

<statement1>;

...

<statementN>;

<update>

}

for (<initialization>;

<test>;

<update> )

{

<statement1>;...

   <statementN>;

}

for loop example

• Rewrite the same loop: sum of numbers from 1..10int sum = 0;

int i = 1;

while (i <= 10)

{

sum = sum + i;

i = i + 1;

}

int sum = 0;

for (int i=1; i <= 10; i=i+1)

{

sum = sum + i;

}

The for loopinitialization statement

executed once before the looptest expression

boolean expressionchecked each time before entering the loop body

if true execute loop body, if false terminate loop

update statementexecuted after the last statement of the loop body

several statements in initialization and update are separated by commafor(len = s.length(), k=0; k < len; k+=1)

initialization and/or test and/or update parts could be missingbut semicolons are there

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;}

Example: Print a string backwards Example: Print a string backwards ((revstring.cpprevstring.cpp))Determine the index of the last character of the string,

and then access each character backwardsHow 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 prototype?

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

// post: return 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 program

string 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));

}

Bad loops1. for (int i = 10; i < 5; i++) { cout << "How many times do I print?"; }

2. for (int i = 10; i >= 1; i++) { cout << "How many times do I print?";}

3. int i = 1; while (i < 20) { cout << "How many times do I print?";

}

Bad loopsNever executesNever stops (infinite loops)

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

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

cin >> num; sum += num;

}

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

Infinite loopsInfinite loop is something that must be avoided

happens when the loop condition is always truesame loop body iterates forever

sometimes you see an output, sometimes you don’tpress Ctrl-C to stop

could be because of a wrong or missing update statementcould be because of a wrong condition; could be another

reason

Infinite loopsWhat 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;

}

How to fix? You can check whether num is even before starting the loop.

if (num % 2 == 0){ while (start != num) { start += 2;

cout << start << endl; }}

Other Common ProblemsEasy to iterate one more or one less timesTest each loop with the inputs that cause:

zero iterations of the loop bodyone iteration of the loop bodymaximum number of iterationsone less than the maximum number of iterations

Use the debugger and watch the variables.

Developing LoopsSome loops are easy to develop, others are notSometimes the proper loop test and body are hard to

designPractice helps, but remember:

Good design comes from experience, experience comes from bad design

Number CrunchingNumber crunching is a CS term that means a computing

operation that requires several (and sometimes complex) arithmetic operations

It was the job of early computersNumeric Analysis

classical sub-discipline of computer science

Todayimplicitly or explicitly, all operations are numeric

Now we will see some mathematical applicationsfactorial calculationprime number testing

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

long factorial(long 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, …, nSuppose we use a variable called product to hold the result,

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

Factoriallong 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 overfloweven long is not sufficient (actually there is no 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 beReally 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 itDo not forget to add bigint.cpp to your project,

BigInt is a Tapestry class Download wincode.zip file from http://cs.duke.edu/csed/tapestry

Factorial using BigInt classSee bigfact.cpp

Determining if a number is primePrime number is a natural number which has only two divisors:

1 and itselfSome 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 CryptosystemRivest, Shamir, Adlemanbased on the factorization problem of large numbershas been utilized by several security products and services

PGP (Pretty Good Privacy) – e-mail security WWW security using SSL protocol

Sophisticated mathematics used for fast prime-testing, we’ll do basic prime testingSince our algorithm is based on factorization, it will be 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 will 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 – DetailsSpecial even number check is added before the loop to

eliminate even numbers to be checked in the loopIn 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

for loop compared with while

<initialization>

while (<test>)

{

<statement1>;

...

<statementN>;

<update>

}

for (<initialization>;

<test>;

<update> )

{

<statement1>;...

   <statementN>;

}

ExampleRewrite 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; } }

Shorthand for increment/decrementLots 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;pre-incrementThese 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 post-decrement (and pre-decrement)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

<initialization>do {

<statement1>;   ...  <statementN>;

<update>} while (<condition>);

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

Try not to use break in this course Save it for later when you develop really complicated 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 then 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)

Downward-counting loopCalculate n to the power of m: nm=nxnx…xnExample: 25=2x2x2x2x2=32

int power = 1;int n, m;cin >> n >> m;for (int i = m; i <= 1; i--){

power = power * n;}

Nested loopsSometimes 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 1 line of stars

{cout << "*";

}cout << endl; // end of line 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 1 line of stars

{cout << "*";

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

line}

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

Same loop: downward-counting

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

for (j=1; j<=i; j++){ cout << "*";}cout << endl;

}

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

for (j=i; j>=1; j--)

{ cout << "*";}cout << endl;

}

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 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*iTotal 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;}

ConstantsSometimes very useful

provides self documentationre-use the same value across the programavoid accidental value changes

like variables, but their value is assigned at declaration and can never change afterwardsdeclared 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);

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

Formatting OutputWe use stream manipulator setw to specify the total number of

spaces that the next output will usesetw(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>

Examplecout << 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 cellsn 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