Download Writing algorithms u..

Writing algorithms using the
for-statement
Programming example 1: find all divisors
of a number
• We have seen a program using a while-statement to solve
this problem.
Here, we will see that this problem can be solved more
naturally using a for-statement.
Programming example 1: find all divisors
of a number (cont.)
• Problem description:
• Write a Java program that reads in an integer n...
• and prints all its divisors
Programming example 1: find all divisors
of a number (cont.)
• A concrete example:
• Input: n = 12
• Output: 1, 2, 3, 4, 6, 12
Programming example 1: find all divisors
of a number (cont.)
• What would you do to solve this problem ?
• Problem:
• Find all divisor of the number 12
Programming example 1: find all divisors
of a number (cont.)
• I think you would have done this:
• Check if 12 is divisible by 1
• Check if 12 is divisible by 2
• ...
• Check if 12 is divisible by 12
Programming example 1: find all divisors
of a number (cont.)
• Note:
• We do not need to check numbers > 12 because
only number ≤ 12 can be divisors !
• When the remainder of the division is equal to 0, we
print out the divisor
Programming example 1: find all divisors
of a number (cont.)
• Reminder: Notation
• The notation:
for (x = 1, 2, 3, ...., 10) do
{
print x;
}
Programming example 1: find all divisors
of a number (cont.)
means:
• The variable x takes on (assumes, gets) the
value 1, 2, 3, ..., 10, one at a time
• For each individual value taken on by x, you
perform the operation "print x" once
Programming example 1: find all divisors
of a number (cont.)
•
This notation can be converted to a for-statement very
naturally:
for ( x = 1; x <= 10; x = x + 1 )
{
print x;
}
Programming example 1: find all divisors
of a number (cont.)
• Rough algorithm (pseudo code) to find all divisors:
input: n = some integer
number
for (x = 1, 2, 3, ..., n) do
{
if ( n is divisible by x ) then
print x; (because x is a divisor !)
}
Programming example 1: find all divisors
of a number (cont.)
• Structure diagram of the algorithm:
Notice it is much easier to write the algorithm using a forstatement (than a while-statement - in this example)
Programming example 1: find all divisors
of a number (cont.)
• Java program:
import java.util.Scanner;
public class Divisors01
{
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int n;
int x;
Programming example 1: find all divisors
of a number (cont.)
System.out.print("Enter a number n: ");
n = in.nextInt();
// Read in number
for ( x = 1; x <= n; x++ ) // Run x = 1, 2, ..., n
{
if ( n % x == 0 )
{ // x is a divisor of n
System.out.println(x); // Print x (because it's a divisor)
}
}
}
}
Programming example 1: find all divisors
of a number (cont.)
• Example Program: (Demo above code)
– Prog file:
http://mathcs.emory.edu/~cheung/Courses/170/Syllabus/07/Progs/
Divisors03.java
• How to run the program:
• Right click on link and save in a scratch directory
• To compile: javac Divisors03.java
• To run:
java Divisors03
Programming example 2: compute the sum
1+2+3+...+n
• Problem description:
• Write a Java program that reads in an integer n...
• and prints the sum 1+2+3+...+n
Programming example 2: compute the sum
1+2+3+...+n (cont.)
• A concrete example:
• Input: n = 5
• Output: 15 (because 1 + 2 + 3 + 4 + 5 = 15)
Programming example 2: compute the sum
1+2+3+...+n (cont.)
• What would you do to solve this problem ?
• Imagine again that you are using a calculator....
• I think you would have done this:
• Punch clear to set the total to 0.
• Press 1, then press add to add to the running total
• Press 2, then press add to add to the running total
• ...
• Press 5, then press add to add to the running total
• Show the total
Programming example 2: compute the sum
1+2+3+...+n (cont.)
• Rough algorithm (pseudo code) to compute 1 + 2 + 3 + ...
+ n:
input: n = some integer
number
sum = 0; // Clear the running total !
for ( x = 1, 2, 3, ..., n ) do
{
Add x to sum
}
Print sum;
Programming example 2: compute the sum
1+2+3+...+n (cont.)
• Sample execution (n = 5):
sum = 0;
for-statement:
add 1 to sum;
add 2 to sum;
add 3 to sum;
add 4 to sum;
add 5 to sum;
Print sum;
---> sum = 0
---> sum = 1
---> sum = 3
---> sum = 6
---> sum = 10
---> sum = 15
---> Prints 15
Programming example 2: compute the sum
1+2+3+...+n (cont.)
• Statement to perform the task: "add x to sum"
sum = sum + x;
Programming example 2: compute the sum
1+2+3+...+n (cont.)
• Example:
Suppose the variable sum contains 6 and x = 4
Then:
sum = sum + x;
= 6 + 4;
= 10;
---> Result, sum = 10
We have added 4 to sum !
Programming example 2: compute the sum
1+2+3+...+n (cont.)
• Structure diagram of the algorithm:
Programming example 2: compute the sum
1+2+3+...+n (cont.)
• Java program:
import java.util.Scanner;
public class Divisors01
{
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int n;
int x, sum;
Programming example 2: compute the sum
1+2+3+...+n (cont.)
System.out.print("Enter a number n: ");
n = in.nextInt();
// Read in number
sum = 0;
// Clear running total
for ( x = 1; x <= n; x++ ) // Run x = 1, 2, ..., n
{
sum = sum + x; // Add x to sum
}
System.out.println(sum); // Print final sum
}
}
Programming example 2: compute the sum
1+2+3+...+n (cont.)
• Example Program: (Demo above code)
– Prog file:
http://mathcs.emory.edu/~cheung/Courses/170/Syllabus/07/Progs/
RunningSum01.java
• How to run the program:
• Right click on link and save in a scratch directory
• To compile: javac RunningSum01.java
• To run:
java RunningSum01
Programming example 3: compute factorial
n!
• Problem description:
• Write a Java program that reads in an integer n...
• and prints the factorial n! = 1×2×3×...×n
Programming example 3: compute factorial
n! (cont.)
• A concrete example:
• Input: n = 5
• Output: 120 (because 1 × 2 × 3 × 4 × 5 = 120)
Programming example 3: compute factorial
n! (cont.)
• We can re-use the previous programming paradigm to
construct the algorithm:
• Imagine you are using a calculator....
• This is how one may compute the factorial:
Punch 1 to set the running product to 1.
(You can't use 0 as starting value for
multiplication , because the multiplying
with 0 will always produce 0)
Programming example 3: compute factorial
n! (cont.)
• Press 1, then press multiply to multiply 1 into the
running product
• Press 2, then press multiply to multiply 2 into the
running product
• ...
• Press 5, then press multiply to multiply 5 into the
running product
• Show the product
Programming example 3: compute factorial
n! (cont.)
• Rough algorithm (pseudo code) to compute n! = 1 × 2 × 3
× ... × n:
input: n = some integer
number
product = 1;
// Set running product to 1
for ( x = 1, 2, 3, ..., n ) do
{
Multiply x into product
}
Print sum;
Programming example 3: compute factorial
n! (cont.)
• Sample execution (n = 5):
product = 1;
---> product = 1
for-statement:
multiply 1 into product;
multiply 2 into product;
multiply 3 into product;
multiply 4 into product;
multiply 5 into product;
Print product;
---> product = 1
---> product = 2
---> product = 6
---> product = 24
---> product = 120
---> Prints 120
Programming example 3: compute factorial
n! (cont.)
• Statement to perform the task: "multiply x into product"
product = product *
x;
Programming example 3: compute factorial
n! (cont.)
• Example:
Suppose the variable product contains 6 and x = 4
Then:
product = product * x;
= 6 * 4;
= 24;
---> Result, product = 24
We have multiplied 4 into the product !
Programming example 3: compute factorial
n! (cont.)
• Structure diagram of the algorithm:
Programming example 3: compute factorial
n! (cont.)
• Java program:
import java.util.Scanner;
public class Factorial01
{
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int n;
int x, product;
Programming example 3: compute factorial
n! (cont.)
System.out.print("Enter a number n: ");
n = in.nextInt();
// Read in number
product = 1;
// Set init. product to 1
for ( x = 1; x <= n; x++ ) // Run x = 1, 2, ..., n
{
product = product + x; // Multiply x into product
}
System.out.println(product); // Print final product
}
}
Programming example 3: compute factorial
n! (cont.)
• Example Program: (Demo above code)
– Prog file:
http://mathcs.emory.edu/~cheung/Courses/170/Syllabus/07/Progs/
Factorial01.java
• How to run the program:
• Right click on link and save in a scratch directory
• To compile: javac Factorial01.java
• To run:
java Factorial01