Repetitive Structures

transcript

REPETITIVE STRUCTURES

CSE1222: Lecture 7 The Ohio State University 1

logExample.cpp// example of log(k) for k = 1,2,..,8. . .int main(){ cout << "log(1) = " << log(1.0) << endl; cout << "log(2) = " << log(2.0) << endl; cout << "log(3) = " << log(3.0) << endl; cout << "log(4) = " << log(4.0) << endl; cout << "log(5) = " << log(5.0) << endl; cout << "log(6) = " << log(6.0) << endl; cout << "log(7) = " << log(7.0) << endl; cout << "log(8) = " << log(8.0) << endl;

return 0;}

logExample.cpp... cout << "log(1) = " << log(1.0) << endl; cout << "log(2) = " << log(2.0) << endl; cout << "log(3) = " << log(3.0) << endl; cout << "log(4) = " << log(4.0) << endl; cout << "log(5) = " << log(5.0) << endl; cout << "log(6) = " << log(6.0) << endl; cout << "log(7) = " << log(7.0) << endl; cout << "log(8) = " << log(8.0) << endl;...

> logExample.exelog(1) = 0log(2) = 0.693147log(3) = 1.09861log(4) = 1.38629log(5) = 1.60944log(6) = 1.79176log(7) = 1.94591log(8) = 2.07944

Repetition Structures (Loops) Motivation:

If we want to repeat essentially the same code say 1000 times we should not have to write 100 lines of code!

We need a new statement to help us execute repetitive code

logWhile.cpp// example of while loop for log(k) for k = 1,2,..,8. . .int main(){ int k(0);

k = 1; while (k <= 8) { cout << "log(" << k << ") = " << log(double(k)) << endl; k++; } return 0;}

logWhile.cpp... k = 1; while (k <= 8) { cout << "log(" << k << ") = " << log(double(k)) << endl; k++; }...

> logWhile.exelog(1) = 0log(2) = 0.693147log(3) = 1.09861log(4) = 1.38629log(5) = 1.60944log(6) = 1.79176log(7) = 1.94591log(8) = 2.07944

while Loops

The while statement syntax:

while (conditional expression){ statement1; statement2; ...}

How while Loops Work1. First test the conditional expression

If it is true, then execute the statement(s)

within the loop structure is/are executed

2. After the statement(s) are executed, we try to repeat the process

If the condition is still true, then we will executethe statement(s) againThus, while the condition is true, keep repeating

3. If the condition ever evaluates to false, then stop the while statement; the program continues execution after the while statement

Control Flow of a while Loop

Statement 1

Code after loop

Code prior to loop

Return tolooping condition

Condition is true?

logWhile.cpp… while (k <= 8) { cout << "log(" << k << ") = " << log(double(k)) << endl; k++; } return 0;}

The variable k , which appears in the conditional expression, is called a loop variable

It is an important variable because its value determines whether the loop stops or keeps going

The condition is the most difficult part of writing a loop

While Examplecount = 1;while (count <= 10){

cout << count << “ “;count++; //increment count!

Output is “1 2 3 4 5 6 7 8 9 10”

The behavior of the loop is determined by the loop variable(s): Initialization of the loop variable Use in the condition determines continuation or end of the loop Update of the loop variable

Control Flow of the Example Program

coutcounter

Code after loop

counter = 1;

counter++

counter<= 10 ?

Repetition Structures 2

Motivation 2:

Allow repetition of code based on input

For example, a program should be able to output n lines of cout statements where n is a user input

logWhile2.cpp...int main(){ int n(0), k(0);

cout << "Enter number of logarithms to compute: "; cin >> n;

k = 1; while (k <= n) { cout << "log(" << k << ") = " << log(double(k)) << endl; k++; } return 0;}

logWhile2.cpp... cout << "Enter number of logarithms to compute: "; cin >> n;

k = 1; while (k <= n) { cout << "log(" << k << ") = " << log(double(k)) << endl; k++; }...

> logWhile2.exeEnter number of logarithms to compute: 5log(1) = 0log(2) = 0.693147log(3) = 1.09861log(4) = 1.38629log(5) = 1.60944

logWhile2.cpp... cout << "Enter number of logarithms to compute: "; cin >> n;

k = 1; while (k <= n) { cout << "log(" << k << ") = " << log(double(k)) << endl; k++; }...

What happens here?

> logWhile2.exeEnter number of logarithms to compute: -3

Repetition Structures 3

If a program receives incorrect input, it can repeatedly prompt for the correct input

logWhile3.cpp// example of while loop to prompt for correct input...int main(){ double x(0.0);

cout << "Enter number: "; cin >> x;

while (x <= 0) { cout << "Input must be positive." << endl; cout << "Enter number: "; cin >> x; } cout << "log(" << x << ") = “ << log(x) << endl; return 0;}

logWhile3.cpp... cout << "Enter number: "; cin >> x;

while (x <= 0) { cout << "Input must be positive." << endl; cout << "Enter number: "; cin >> x; }

cout << "log(" << x << ") = " << log(x) << endl;...

> logWhile3.exeEnter number: -4.5Input must be positive.Enter number: 0Input must be positive.Enter number: 4.5log(4.5) = 1.50408

logWhileError.cpp// example of a while loop with a logical error. . .int main(){ int k(0);

k = 1; while (k <= 8) { cout << "log(" << k << ") = " << log(double(k)) endl; }

return 0;}

Try running this program

probability.cpp...int main(){ double p(0.0);

cout << "Enter probability player A wins 1 game: "; cin >> p;

while (p < 0.0 || p > 1.0) { cout << "Input must be in range [0:1]." << endl; cout << "Enter probability player A wins 1 game: "; cin >> p; }

cout << "Probability player A loses all 5 games = " << pow((1-p), 5.0) << endl;

return 0;}

> probability.exeEnter probability player A wins: 2Input must be in range [0:1].Enter probability player A wins: -1Input must be in range [0:1].Enter probability player A wins: 0.2Probability player A loses all 5 games = 0.32768>

...while (p < 0.0 || p > 1.0) { cout << "Input must be in range [0:1]." << endl; cout << "Enter probability player A wins 1 game: "; cin >> p; }...

temperature.cpp// print a table converting fahrenheit to celsius... int fahrenheit(0), min_fahrenheit(0), max_fahrenheit(0); int STEP_SIZE(10);

cout << "Enter min and max fahrenheit: "; cin >> min_fahrenheit >> max_fahrenheit;

fahrenheit = min_fahrenheit; // loop until fahrenheit is greater than max_fahrenheit while (fahrenheit <= max_fahrenheit) { // convert fahrenheit to celsius float celsius = (fahrenheit - 32.0) * 5.0/9.0;

cout << "farenheit = " << fahrenheit << “ celsius = " << celsius << endl;

fahrenheit += STEP_SIZE; // increment by STEP_SIZE }...

temperature.cpp... int STEP_SIZE(10);... fahrenheit = min_fahrenheit; // loop until fahrenheit is greater than max_fahrenheit while (fahrenheit <= max_fahrenheit) { // convert fahrenheit to celsius float celsius = (fahrenheit - 32.0) * 5.0/9.0;

cout << "farenheit = " << fahrenheit << “ celsius = " << celsius << endl; fahrenheit += STEP_SIZE; // increment by STEP_SIZE }...

> temperature.exeEnter min and max fahrenheit: 20 60farenheit = 20 celsius = -6.66667farenheit = 30 celsius = -1.11111farenheit = 40 celsius = 4.44444farenheit = 50 celsius = 10farenheit = 60 celsius = 15.5556

temperature.cpp... int STEP_SIZE(10);... fahrenheit = min_fahrenheit; // loop until fahrenheit is greater than max_fahrenheit while (fahrenheit <= max_fahrenheit) { // convert fahrenheit to celsius float celsius = (fahrenheit - 32.0) * 5.0/9.0;

> temperature.exeEnter min and max fahrenheit: 25 60farenheit = 25 celsius = -3.88889farenheit = 35 celsius = 1.66667farenheit = 45 celsius = 7.22222farenheit = 55 celsius = 12.7778

temperature2.cpp...

int STEP_SIZE(5);... fahrenheit = min_fahrenheit; while (fahrenheit <= max_fahrenheit) { float celsius = (fahrenheit - 32.0) * 5.0/9.0; cout << "farenheit = " << fahrenheit << “ celsius = " << celsius << endl; fahrenheit += STEP_SIZE; // increment by STEP_SIZE }...

> temperature2.exeEnter min and max fahrenheit: 25 60farenheit = 25 celsius = -3.88889farenheit = 30 celsius = -1.11111farenheit = 35 celsius = 1.66667farenheit = 40 celsius = 4.44444farenheit = 45 celsius = 7.22222farenheit = 50 celsius = 10farenheit = 55 celsius = 12.7778farenheit = 60 celsius = 15.5556

temperatureError.cpp// print a table converting fahrenheit to celsius... int fahrenheit(0), min_fahrenheit(0), max_fahrenheit(0); int STEP_SIZE(10);

cout << "Enter min and max fahrenheit: "; cin >> min_fahrenheit >> max_fahrenheit;

fahrenheit = min_fahrenheit; // loop until fahrenheit does not equal max_fahrenheit while (fahrenheit != max_fahrenheit) // Note != instead of <= { // convert fahrenheit to celsius float celsius = (fahrenheit - 32.0) * 5.0/9.0;

sinWhile.cpp (Error)…int main(){ double x(0.0); double increment(0.1);

cout.setf(ios::fixed); while (x != 1.0) { cout << x << ": " << sin(x) << " " << cos(x) << endl; x += increment; }

return 0;}

FOR LOOPS

logFor.cpp// example of for loop for log(k) for k = 1,2,..,8

#include <iostream>#include <cmath>using namespace std;

int main(){ for (int k = 1; k <= 8; k++) { cout << "log(" << k << ") = " << log(double(k)) << endl; }

return 0;}

logFor.cpp... for (int k = 1; k <= 8; k++) { cout << "log(" << k << ") = " << log(double(k)) << endl; }...

> logFor.exelog(1) = 0log(2) = 0.693147log(3) = 1.09861log(4) = 1.38629log(5) = 1.60944log(6) = 1.79176log(7) = 1.94591log(8) = 2.07944

for Loop Syntax

for (initialize; condition; alter)

{statement1;statement2;statement3;statement4;...

for Loop Syntax (2) Initializing list

A statement to set the starting value(s) of variables (normally a loop counter)

Expression The looping condition

Altering list Statement that is executed at the end of every loop traversal Normally determines how the counter is manipulated after each

pass through the loop

Important note: At the end of a pass through the loop, the statements in the altering list is executed BEFORE the loop expression is evaluated

How for Loops Work1. First, the initialization statements are executed

2. Then the conditional expression is tested. If it is true, then the statement(s) within the loop structure is/are executed.

3. Once the end of those statements is reached, then altering statements are executed, and the process is repeated.

4. If the expression ever evaluates to false, then the loop statement is exited, and the program continues beyond the loop.

Control Flow of a for Loop

Statement 1

Code after loop

InitializeStatement;

Return tolooping condition

Altering statement;

Code prior to loop

Condition is true?

for Loop Example for (int k = 1; k <= 8; k++) { cout << "log(" << k << ") = " << log(double(k)) << endl; }

// the while-loop equivalent: int k(0); . . . k = 1; while (k <= 8) { cout << "log(" << k << ") = " << log(double(k)) << endl; k++; }

for Loop Example2// Compute n logarithms:

for (int k = 1; k <= n; k++) { cout << "log(" << k << ") = " << log(double(k)) << endl; }

// the while-loop equivalent: int k(0); . . . k = 1; while (k <= n) { cout << "log(" << k << ") = " << log(double(k)) << endl; k++; }

(Too) Clever for Loop Example double x(0.0); cout << “Enter Number: “; for (cin >> x; x <= 0; cin >> x) // a while loop is better { cout << "Input must be positive." << endl; cout << "Enter number: "; }

// the while-loop equivalent: double x(0.0); cout << “Enter number: “; cin >> x; while (x <= 0) { cout << "Input must be positive." << endl; cout << "Enter number: "; cin >> x; } cout << "log(" << x << ") = " << log(x) << endl;

for Loops for loops and while loops are

interchangeable

A for loop is a pre-test loop

Whether to use a while or a for loop is a question of style and readability

Use for loops to count from a to bUse while loops to iterate until some condition is

satisfied

for Loop Example4 for (int k = 1; k <= 8; k++) { cout << "log(" << k << ") = " << log(double(k)) << endl; } cout << k << endl; // SYNTAX ERROR

// Variable k can be declared before the for-loop int k(0); for (k = 1; k <= 8; k++) { cout << "log(" << k << ") = " << log(double(k)) << endl; } cout << k << endl; // What is the value of k?

Using Nested Loops A loop inside of another loop Extremely useful and very common

for (int i = 1; i <= 5; i++){ cout << “i is now “ << i << endl;

//inner (nested) loop for (int j = 1; j <= 4; j++) {

cout << “j is now “ << j << endl; }

} //What is the output?

cout“i is now..”

Code after loop

int i = 1;

int j = 1;

cout“j is now..”

i <= 5?

j <= 4?

Nested for loops: square.cpp// print a square of x's... int length(0);

cout << "Enter square edge length: "; cin >> length;

for (int row = 1; row <= length; row++) { // print length x's for (int col = 1; col <= length; col++) { cout << "x"; } cout << endl; // print newline to finish row }...

Nested for loops: square.cpp... for (int row = 1; row <= length; row++) { // print length x's for (int col = 1; col <= length; col++) { cout << "x"; } cout << endl; // print newline to finish row }...

> square.exeEnter square edge length: 6xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Nested for loops: diagonal.cpp// print a diagonal of x's... int length(0);

cout << "Enter diagonal length: "; cin >> length;

for (int row = 1; row <= length; row++) { // print (row-1) spaces for (int col = 1; col <= row-1; col++) { cout << " "; } cout << "x" << endl; // print x on diagonal }...

Nested for loops: diagonal.cpp... for (int row = 1; row <= length; row++) { // print (row-1) spaces for (int col = 1; col <= row-1; col++) { cout << " "; } cout << "x" << endl; // print x on diagonal }...

> diagonal.exeEnter diagonal length: 6x x x x x x

squareError.cpp// version of square.cpp with errors... int length(0);

cout << "Enter square edge length: "; cin >> length;

for (int row = 1; row <= length; row++); { // print length x's for (int col = 1; col <= length; col++); { cout << "x"; } cout << endl; // print newline to finish row }...

do-while loops A do-while loop checks the condition at the

end of the loop

Example: char c(‘n’); do {

... //rest of the program cout << “Do you wish to continue: “;

cin >> c; } while (c == ‘y’ || c == ‘Y’);

See text for more details.

Conclusion on Loops

Loops are generally used for repetition of a section of code

There are three basic types:while, for, and do-whilewhile and for are pretest (entrance

controlled)do-while is posttest (exit controlled)

Common Programming Errors (1)

Use == when comparing for equivalence in while, for, and do-while statements!

(Same as using == in if-statements)

Precision problem: double x, y;. . . “while (x != y)” may always be true even

though mathematically x should equal y

Common Programming Errors (1)For each statement, what is the output?

for (int i = 1; i < 7; i++) { cout << i << endl; }

for (int i = 1; i <= 7; i++) { cout << i << endl; }

for (int i = 0; i <= 7; i++){ cout << i << endl; }

for (int i = 0; i < 7; i++)

{ cout << i << endl; }

Common Programming Errors (1)For each statement, what is the output?

for (int i = 1; i < 7; i++) { cout << i; }

for (int i = 1; i < 7; i++){

cout << “Row “ << i;for (int j = 1; j < 4; j++){ cout << “ Col “ << j << endl; }

Common Programming Errors (2) Do not place a semicolon at the

end of a for statement:int i;for (i = 1; i <= 10; i++);{ cout << “i = “ << i << endl; }

What does this output?

Common Programming Errors (3) Use semicolons, not commas, to separate

items in a for statement:for (i=0, i<10, i++) //invalidfor (i=0; i<10; i++) //valid

Do not forget the semicolon at the end of the while statement in a do-while loopdo {

...} while(x > 0);

LOOP PROGRAMMING

TECHNIQUES

Interactive Input with a loopint main(){

double x(0.0), total(0.0), average(0.0);const int NUM_INPUTS(4);

total = 0.0;for (int i = 0; i < NUM_INPUTS; i++){

// ask user for a numbercout << "Enter a number: ";cin >> x;

total = total + x;}

average = total / NUM_INPUTS;cout << "The average of the entered values is: "

<< average << endl;}

Selection within a Loopint main(){

double x(0.0), postot(0.0), negtot(0.0);const int NUM_INPUTS(5);

// NOTE: postot and negtot initialized to 0.for (int i = 1; i <= NUM_INPUTS; i++){

cout << "Enter a number: ";cin >> x;

// Selection: Separate positive from negative inputs.if (x > 0)

{ postot = postot + x; }else

{ negtot = negtot + x; }}

cout << "The positive total is " << postot << endl;cout << "The negative total is " << negtot << endl;

return(0);}

Selection within a Loop (2)int main(){

double x(0.0), postot(0.0), negtot(0.0);

// NOTE: postot and negtot initialized to 0.while (x != 0.0){

// Selection: Separate positive from negative inputs.if (x > 0)

{ postot = postot + x; }else

{ negtot = negtot + x; }

cout << "The positive total is " << postot << endl;cout << "The negative total is " << negtot << endl;

Evaluating Functions of One Variable// Calculates several values for y = 10x² + 3x

- 2int main(){

int x(0), y(0), xmin(0), xmax(0);

cout << "Minimum and maximum x values: ";cin >> xmin >> xmax;

for (x = xmin; x <= xmax; x++){

y = 10 * pow(x, 2) + 3 * x – 2; cout << "x = " << x

<< " f(x) = " << y << endl; }

Prompting for Correct Inputint main(){

const int MAX_AGE(125);int age(0);

cout << “Enter your age (1-“ << MAX_AGE << “):”;cin >> age;

while (age <= 0 || age > MAX_AGE){

cout << “Invalid input. Try again.” << endl;

cout << “Enter your age (1-“ << MAX_AGE << “):”;cin >> age;

Summation: Sum of Cubes...int main(){

long sum(0);int n(0);

cout << “Enter number of terms in the summation: “;cin >> n;

for (int i = 1; i <= n; i++) {

sum += i*i*i; }

cout << “1^3 + 2^3 + 3^3 + ... + “ << n << “^3 = “ << sum << endl;

return 0;}

Summation Over Two Variables Input: n

Compute

Summation Over Two Variables Compute

Table of (i-j) (where j ≤ i):

(i-j) j=0 j=1 j=2 j=3 ...

i=0 0 ...

i=1 1 0 ...

i=2 2 1 0 ...

i=3 3 2 1 0 ...

... ... ... ... ... ...

Summation Over Two Variables

Input: n

Compute Algorithm:

1. sum ← 0;

2. for i ← 0 to n do

3. for j ← 0 to i do

4. sum ← sum + (i-j);

Algorithm

From “Programming and Problem Solving with C++” By Nell Dale:

An algorithm is “a step-by-step procedure for solving a problem”.

Summation Over Two Variables

Input: n

Compute Algorithm:

1. sum ← 0;

3. for j ← 0 to i do

4. sum ← sum + (i-j);

Summation over two variables...int main(){ long sum(0); // Initialize sum to zero int n(0);

cout << "Enter max value of i: "; cin >> n;

for (int i = 0; i <= n; i++) { for (int j = 0; j <= i; j++) { sum = sum + (i-j); } }

cout << "sum_{i=0}^n sum_{j=0}^i (i-j) = " << sum << endl;

return 0;}

Printing a table using nested loops

Input: n

Output: Table of 1/(i-j)2 for i = 1,...,n and j = 1,...,n.

Don’t print anything when i = j. Why?

Printing a table using nested loops

Input: n

Output: Table of 1/(i-j)2 for i = 1,...,n and j = 1,...,n.

Algorithm:

2. for j ← 1 to n do

3. if (i ≠ j) print 1/(i-j)2

4. else print "******"

5. print newline; (Why?)

Printing a table using nested loops...int main(){ int numRows(0); int diff(0);

cout << "Enter number of table rows: "; cin >> numRows;

cout.setf(ios::fixed); // fixed precision output

Printing a table using nested loops...for (int i = 1; i <= numRows; i++) { for (int j = 1; j <= numRows; j++) { if (i != j) { diff = i-j; cout << " " << 1.0/(diff*diff); } else { cout << " ****** "; } } cout << endl; // end row }...

> printTable.exeEnter number of table rows: 6 ****** 1.000000 0.250000 0.111111 0.062500 0.040000 1.000000 ****** 1.000000 0.250000 0.111111 0.062500 0.250000 1.000000 ****** 1.000000 0.250000 0.111111 0.111111 0.250000 1.000000 ****** 1.000000 0.250000 0.062500 0.111111 0.250000 1.000000 ****** 1.000000 0.040000 0.062500 0.111111 0.250000 1.000000 ****** >

for (int i = 1; i <= numRows; i++){ for (int j = 1; j <= numRows; j++) { if (i != j) { diff = i-j; cout << " " << 1.0/(diff*diff); } else { cout << " ****** "; } } cout << endl; // end row }

Problem: Print primes

Print prime numbers between 2 and n.

Print prime numbers

Input: n

Output: Prime numbers between 2 and n.

Algorithm:

1. for k ← 2 to n do

2. flag_composite ← false;

3. for j ← 2 to k-1 do

4. if (k mod j = 0) then

5. flag_composite ← true;

6. if (flag_composite = false) print k.

prime.cpp...int main(){ int n(0); bool flag_composite(false);

cout << "Enter n: "; cin >> n;...

prime.cpp... cout << "Prime numbers:" << endl; for (int k = 2; k <= n; k++) { flag_composite = false; for (int j = 2; j < k; j++) { if (k%j == 0) // if (k mod j == 0) { flag_composite = true; } }

if (!flag_composite) { cout << k << endl; // k is prime } }...

> prime.exeEnter n: 20235711131719

for (int k = 2; k <= n; k++) { flag_composite = false; for (int j = 2; j < k; j++) { if (k%j == 0) // if (k mod j == 0) { flag_composite = true; } }

if (!flag_composite) { cout << k << endl; } // k is prime }

Types of Loops

More loopsPretest Loops check the looping condition

first, then begins execution○ while ○ for

Posttest Loops begins execution first, then checks looping condition○ do-while

Summary while loops:

Repeat until some condition is fulfilled;Pretest loop.

for loops:Used for counting;3 parts: for (initialize; condition; alter){...}

Pretest loop. do-while loops:

Example: “Do you wish to continue?”Posttest loop.

Repetitive Structures

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