Transcript L15IncrementalProg.ppt

Examples
Example Problems,
their Algorithms, and
their C Source Code.
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Problem: Interest
Compute interest that is compounded
annually.
 Write an interactive program that allows
the user to calculate the interest
accrued in a savings account that is
compounded annually over a period of
years.
 The user must supply the principal
amount, interest rate and the number of
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
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Algorithm: Interest
Print explanation of the program
 Get principal from user.
 Get interest rate from user.
 Get number of years from user.
 For the number of years specified

o Calculate the amount in the account at the
end of the year. (amount += amount * rate)
interest accrued = amount - principal
 Print report.
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Interest : Design the Report
Interest rate : 7.0000 %
Period : 20 years
Principal at start of period : 1000.00
Interest accrued : 2869.68
Total amount at end of period : 3869.68
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Interest, programmed incrementally #1
/* Filename:
interest.c
* Author:
Sue Bogar
* Date written: 11/14//99
* Description: This program computes the interest accrued in an account
*
that compounds interest annually.
*/
#include <stdio.h>
main ( )
{
/* Print Instructions */
printf (“This program computes the interest accrued in an account that\n”);
printf (“compounds interest annually. You will need to enter the amount\n”);
printf (“of the principal, the interest rate and the number of years.\n\n”);
}
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First Output : Interest
This program computes the interest accrued in an account that
compounds interest annually. You will need to enter the amount
of the principal, the interest rate and the number of years.
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Interest, programmed incrementally #2
/* Filename:
interest.c
* Author:
Sue Bogar
* Date written: 11/14//99
* Description: This program computes the interest accrued in an account
*
that compounds interest annually.
#include <stdio.h>
main ( )
{
float principal, rate ;
int years ;
*/
/* Print Instructions */
printf (“This program computes the interest accrued in an account that\n”) ;
printf (“compounds interest annually. You will need to enter the amount\n”) ;
printf (“of the principal, the interest rate and the number of years.\n\n”) ;
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/* Get input from user */
printf (“Enter the principal amount : “) ;
scanf (“%f”, &principal) ;
printf (“Enter the interest rate as a decimal (for 7%% enter .07) : “) ;
scanf (“%f”, &rate) ;
printf (“Enter the number of years : “) ;
scanf (“%d”, &years) ;
printf (“\nprincipal = %f, rate = %f, years = %d\n”, principal, rate, years ) ;
}
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Second Output : Interest
This program computes the interest accrued in an account that
compounds interest annually. You will need to enter the amount
of the principal, the interest rate and the number of years.
Enter the principal amount : 1000.00
Enter the interest rate as a decimal (for 7% enter .07) : .07
Enter the number of years : 20
principal = 1000.000000, rate = 0.070000, years = 20
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Interest, programmed incrementally #3
/* Filename:
interest.c
* Author:
Sue Bogar
* Date written: 11/14//99
* Description: This program computes the interest accrued in an account
*
that compounds interest annually.
#include <stdio.h>
main ( )
{
float principal, rate, amount, interest ;
int years, i ;
*/
/* Print Instructions */
printf (“This program computes the interest accrued in an account that\n”);
printf (“compounds interest annually. You will need to enter the amount\n”);
printf (“of the principal, the interest rate and the number of years.\n\n”);
/* Get input from user */
printf (“Enter the principal amount : “);
scanf (“%f”, &principal);
printf (“Enter the interest rate as a decimal (for 7%% enter .07) : “) ;
scanf (“%f”, &rate);
printf (“Enter the number of years : “);
scanf (“%d”, &years);
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Interest, programmed incrementally #3
/* Save the original principal amount by varying another variable, amount */
amount = principal;
/* Calculate total amount in the account after the specified number of years */
for ( i = 0 ; i < 1 ; i++ )
{
amount += amount * rate ;
}
/* Calculate accrued interest */
interest = amount - principal ;
printf (“\nprincipal = %f, rate = %f, years = %d\n”, principal, rate, years ) ;
printf (“amount = %f, interest = %f\n”);
}
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Third Output : Interest
This program computes the interest accrued in an account that
compounds interest annually. You will need to enter the amount
of the principal, the interest rate and the number of years.
Enter the principal amount : 1000.00
Enter the interest rate as a decimal (for 7% enter .07) : .07
Enter the number of years : 20
principal = 1000.000000, rate = 0.070000, years = 20
amount = 1070.000000, interest = 70.000000
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Interest, programmed incrementally #4
/* Filename:
interest.c
* Author:
Sue Bogar
* Date written: 11/14//99
* Description: This program computes the interest accrued in an account
*
that compounds interest annually.
#include <stdio.h>
main ( )
{
float principal, rate, amount, interest ;
int years, i ;
*/
/* Print Instructions */
printf (“This program computes the interest accrued in an account that\n”);
printf (“compounds interest annually. You will need to enter the amount\n”);
printf (“of the principal, the interest rate and the number of years.\n\n”);
/* Get input from user */
printf (“Enter the principal amount : “);
scanf (“%f”, &principal);
printf (“Enter the interest rate as a decimal (for 7%% enter .07) : “) ;
scanf (“%f”, &rate);
printf (“Enter the number of years : “);
scanf (“%d”, &years);
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Interest, programmed incrementally #4
/* Save the original principal amount by varying another variable, amount */
amount = principal;
/* Calculate total amount in the account after the specified number of years */
for ( i = 0 ; i < 2 ; i++ )
{
amount += amount * rate ;
}
/* Calculate accrued interest */
interest = amount - principal ;
printf (“\nprincipal = %f, rate = %f, years = %d\n”, principal, rate, years ) ;
printf (“amount = %f, interest = %f\n”);
}
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Fourth Output : Interest
This program computes the interest accrued in an account that
compounds interest annually. You will need to enter the amount
of the principal, the interest rate and the number of years.
Enter the principal amount : 1000.00
Enter the interest rate as a decimal (for 7% enter .07) : .07
Enter the number of years : 20
principal = 1000.000000, rate = 0.070000, years = 20
amount = 1144.900000, interest = 144.900000
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Interest, programmed incrementally #5
/* Filename:
interest.c
* Author:
Sue Bogar
* Date written: 11/14//99
* Description: This program computes the interest accrued in an account
*
that compounds interest annually.
#include <stdio.h>
main ( )
{
float principal, rate, amount, interest ;
int years, i ;
*/
/* Print Instructions */
printf (“This program computes the interest accrued in an account that\n”);
printf (“compounds interest annually. You will need to enter the amount\n”);
printf (“of the principal, the interest rate and the number of years.\n\n”);
/* Get input from user */
printf (“Enter the principal amount : “);
scanf (“%f”, &principal);
printf (“Enter the interest rate as a decimal (for 7%% enter .07) : “) ;
scanf (“%f”, &rate);
printf (“Enter the number of years : “);
scanf (“%d”, &years);
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Interest, programmed incrementally #5
/* Save the original principal amount by varying another variable, amount */
amount = principal;
/* Calculate total amount in the account after the specified number of years */
for ( i = 0 ; i < years ; i++ )
{
amount += amount * rate ;
}
/* Calculate accrued interest */
interest = amount - principal ;
printf (“\nprincipal = %f, rate = %f, years = %d\n”, principal, rate, years ) ;
printf (“amount = %f, interest = %f\n”);
}
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Fifth Output : Interest
This program computes the interest accrued in an account that
compounds interest annually. You will need to enter the amount
of the principal, the interest rate and the number of years.
Enter the principal amount : 1000.00
Enter the interest rate as a decimal (for 7% enter .07) : .07
Enter the number of years : 20
principal = 1000.000000, rate = 0.070000, years = 20
amount = 3869.680000, interest = 2869.680000
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Source code in C: Interest
/* Filename:
interest.c
* Author:
Sue Bogar
* Date written: 11/14//99
* Description: This program computes the interest accrued in an account
*
that compounds interest annually.
#include <stdio.h>
main ( )
{
float principal, rate, amount, interest ;
int years, i ;
*/
/* Print Instructions */
printf (“This program computes the interest accrued in an account that\n”);
printf (“compounds interest annually. You will need to enter the amount\n”);
printf (“of the principal, the interest rate and the number of years.\n\n”);
/* Get input from user */
printf (“Enter the principal amount : “);
scanf (“%f”, &principal);
printf (“Enter the interest rate as a decimal (for 7%% enter .07) : “) ;
scanf (“%f”, &rate);
printf (“Enter the number of years : “);
scanf (“%d”, &years);
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Source code in C: Interest
/* Save the original principal amount by varying another variable, amount */
amount = principal;
/* Calculate total amount in the account after the specified number of years */
for ( i = 0 ; i < years ; i++ )
{
amount += amount * rate ;
}
/* Calculate accrued interest */
interest = amount - principal ;
/* Print report */
printf (“Interest rate : %.4f %%\n”, 100 * rate ) ;
printf (“
Period : %d years\n\n”, years ) ;
printf (“
Principal at start of period : %9.2f”, principal );
printf (“
Interest accrued : %9.2f”, interest );
printf (“Total amount at end of period : %9.2f”, amount);
}
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Final Output : Interest
This program computes the interest accrued in an account that
compounds interest annually. You will need to enter the amount
of the principal, the interest rate and the number of years.
Enter the principal amount : 1000.00
Enter the interest rate as a decimal (for 7% enter .07) : .07
Enter the number of years : 20
Interest rate : 7.0000 %
Period : 20 years
Principal at start of period : 1000.00
Interest accrued : 2869.68
Total amount at end of period : 3869.68
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Improvements to Interest
We now have a working program that
we are convinced that is correct and
solves the problem.
 Our program is not robust, since none
of the input provided by the user is
checked for validity.
 We need to decide what is valid.

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Improvements to Interest

What range of values will we allow for
the principal ?
Positive values less than or equal to
100,000.

How about the interest rate ?
Positive values less than 1.

And the numbers of years ?
Years between 1 and 100.
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Improved Interest #1
/* Filename:
interest.c
* Author:
Sue Bogar
* Date written: 11/14//99
* Description: This program computes the interest accrued in an account
*
that compounds interest annually.
#include <stdio.h>
main ( )
{
float principal, rate, amount, interest ;
int years, i ;
*/
/* Print Instructions */
printf (“This program computes the interest accrued in an account that\n”);
printf (“compounds interest annually. You will need to enter the amount\n”);
printf (“of the principal, the interest rate and the number of years.\n\n”);
/* Get principal from user */
printf (“Enter the principal amount : “);
scanf (“%f”, &principal);
/* Validate principal amount */
while ( principal < 0.0 || principal > 100000.0 )
{
printf (“The principal amount must be a value between 0 and 100000\n”) ;
printf (“Enter the principal amount : “);
scanf (“%f”, &principal);
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}
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Improved Interest #1
printf (“Enter the interest rate as a decimal (for 7%% enter .07) : “) ;
scanf (“%f”, &rate);
printf (“Enter the number of years : “);
scanf (“%d”, &years);
/* Save the original principal amount by varying another variable, amount */
amount = principal;
/* Calculate total amount in the account after the specified number of years */
for ( i = 0 ; i < years ; i++ )
{
amount += amount * rate ;
}
/* Calculate accrued interest */
interest = amount - principal ;
/* Print report */
printf (“Interest rate : %.4f %%\n”, 100 * rate ) ;
printf (“
Period : %d years\n\n”, years ) ;
printf (“
Principal at start of period : %9.2f”, principal );
printf (“
Interest accrued : %9.2f”, interest );
printf (“Total amount at end of period : %9.2f”, amount);
}
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Interest :
Testing Principal Validity Check
This program computes the interest accrued in an account that
compounds interest annually. You will need to enter the amount
of the principal, the interest rate and the number of years.
Enter the principal amount : 100000.01
The principal amount must be between 0 and 100000.
Enter the principal amount : -.01
The principal amount must be between 0 and 100000.
Enter the principal amount : 1000.00
Enter the interest rate as a decimal (for 7% enter .07) : .07
Enter the number of years : 20
Interest rate : 7.0000 %
Period : 20 years
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Principal at start of period : 1000.00
Interest accrued : 2869.68
Total amount at end of period : 3869.68
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Improved Interest #2
/* Filename:
interest.c
* Author:
Sue Bogar
* Date written: 11/14//99
* Description: This program computes the interest accrued in an account
*
that compounds interest annually.
#include <stdio.h>
main ( )
{
float principal, rate, amount, interest ;
int years, i ;
*/
/* Print Instructions */
printf (“This program computes the interest accrued in an account that\n”);
printf (“compounds interest annually. You will need to enter the amount\n”);
printf (“of the principal, the interest rate and the number of years.\n\n”);
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/* Get valid principal amount from user */
printf (“Enter the principal amount : “);
scanf (“%f”, &principal);
while ( principal < 0.0 || principal > 100000.0 )
{
printf (“The principal amount must be a value between 0 and 100000\n”) ;
printf (“Enter the principal amount : “);
scanf (“%f”, &principal);
}
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Improved Interest #2
/* Get valid interest rate from user */
printf (“Enter the interest rate as a decimal (for 7%% enter .07) : “) ;
scanf (“%f”, &rate);
while ( rate < 0.0 || rate > 1.0 )
{
printf (“The interest rate must be between 0 and 1\n”) ;
printf (“Enter the interest rate as a decimal (for 7%% enter .07) : “) ;
scanf (“%f”, &rate);
}
printf (“Enter the number of years : “);
scanf (“%d”, &years);
/* Save the original principal amount by varying another variable, amount */
amount = principal;
/* Calculate total amount in the account after the specified number of years */
for ( i = 0 ; i < years ; i++ )
{
amount += amount * rate ;
}
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Improved Interest #2
/* Calculate accrued interest */
interest = amount - principal ;
/* Print report */
printf (“Interest rate : %.4f %%\n”, 100 * rate ) ;
printf (“
Period : %d years\n\n”, years ) ;
printf (“
Principal at start of period : %9.2f”, principal );
printf (“
Interest accrued : %9.2f”, interest );
printf (“Total amount at end of period : %9.2f”, amount);
}
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Interest :
Testing Interest Rate Validity Check
This program computes the interest accrued in an account that
compounds interest annually. You will need to enter the amount
of the principal, the interest rate and the number of years.
Enter the principal amount : 1000.00
Enter the interest rate as a decimal (for 7% enter .07) : 1.0001
The interest rate must be between 0 and 1.
Enter the interest rate as a decimal (for 7% enter .07) : -.0001
The interest rate must be between 0 and 1.
Enter the interest rate as a decimal (for 7% enter .07) : .07
Enter the number of years : 20
Interest rate : 7.0000 %
Period : 20 years
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Principal at start of period : 1000.00
Interest accrued : 2869.68
Total amount at end of period : 3869.68
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Improved Interest #3
/* Filename:
interest.c
* Author:
Sue Bogar
* Date written: 11/14//99
* Description: This program computes the interest accrued in an account
*
that compounds interest annually.
#include <stdio.h>
main ( )
{
float principal, rate, amount, interest ;
int years, i ;
*/
/* Print Instructions */
printf (“This program computes the interest accrued in an account that\n”);
printf (“compounds interest annually. You will need to enter the amount\n”);
printf (“of the principal, the interest rate and the number of years.\n\n”);
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/* Get valid principal amount from user */
printf (“Enter the principal amount : “);
scanf (“%f”, &principal);
while ( principal < 0.0 || principal > 100000.0 )
{
printf (“The principal amount must be a value between 0 and 100000\n”) ;
printf (“Enter the principal amount : “);
scanf (“%f”, &principal);
}
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Improved Interest #3
/* Get valid interest rate from user */
printf (“Enter the interest rate as a decimal (for 7%% enter .07) : “) ;
scanf (“%f”, &rate);
while ( rate < 0.0 || rate > 1.0 )
{
printf (“The interest rate must be between 0 and 1\n”) ;
printf (“Enter the interest rate as a decimal (for 7%% enter .07) : “) ;
scanf (“%f”, &rate);
}
/* Get valid number of years from user */
printf (“Enter the number of years : “);
scanf (“%d”, &years);
while ( years < 1 || years > 100 )
{
printf (“The number of years must be between 1 and 100, inclusive\n”) ;
printf (“Enter the number of years : “);
scanf (“%d”, &years);
}
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Improved Interest #3
/* Save the original principal amount by varying another variable, amount */
amount = principal;
/* Calculate total amount in the account after the specified number of years */
for ( i = 0 ; i < years ; i++ )
{
amount += amount * rate ;
}
/* Calculate accrued interest */
interest = amount - principal ;
/* Print report */
printf (“Interest rate : %.4f %%\n”, 100 * rate ) ;
printf (“
Period : %d years\n\n”, years ) ;
printf (“
Principal at start of period : %9.2f”, principal );
printf (“
Interest accrued : %9.2f”, interest );
printf (“Total amount at end of period : %9.2f”, amount);
}
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Interest :
Testing Years Validity Check
This program computes the interest accrued in an account that
compounds interest annually. You will need to enter the amount
of the principal, the interest rate and the number of years.
Enter the principal amount : 1000.00
Enter the interest rate as a decimal (for 7% enter .07) : .07
Enter the number of years : 101
The number of years must be between 1 and 100, inclusive.
Enter the number of years : 0
The number of years must be between 1 and 100, inclusive.
Enter the number of years : 20
Interest rate : 7.0000 %
Period : 20 years
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Principal at start of period : 1000.00
Interest accrued : 2869.68
Total amount at end of period : 3869.68
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Problem : Combinatorics

Combinatorics is the art of enumerating
combinations and permutations.

Find and count all positive integers with
three digits or less whose digits add up
to a number specified by the user.

What constraints should we put on the
sum of the digits?
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Combinatorics
Thinking through the problem
The smallest number is 0, so the input
should be 0 or greater.
 The largest number is 999, so the input
should be 27 (9 + 9 + 9) or less.
 We could have a single for loop that
goes through the integers from 0 to 999.
 For each integer, we’ll need to break the
integer up into its individual digits, add
them up and compare that sum to num.

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Combinatorics
Thinking through the problem




We’ve already learned the trick used to separate an
integer into its digits. It involved using integer division
and modulus within a loop. Each iteration of the loop
stripped one digit off of the integer.
So within the for loop, we’ll need to have another loop
that separates the integer into its digits, sums them,
compares the sum to num and prints and counts the
integer if they are equal.
This approach will solve the problem, but it takes a lot
of work at each step and will take a long time.
How many steps ?
1000 * 3
There must be a quicker and easier way.
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Combinatorics
Thinking through the problem
Instead of working with the integers 0
through 999, we could work with each of
the digits instead.
 We could vary just one of the digits at a
time using nested for loops, like this :
0 0 0, 0 0 1, … 0 0 9, 0 1 0, … 9 9 9
 This will eliminate the need to split the
integer into its digits.
 Each for loop will control one of the
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digits.

Combinatorics
Thinking through the problem
for ( i = 0 ; i < 10 ; i++)
{
for ( j = 0 ; j < 10 ; j++)
{
for ( k = 0 ; k < 10 ; k++)
{
if ( i + j + k == num )
{
printf ( “%d%d%d\n”, i, j, k ) ;
counter++ ;
}
}
}
}
How long does this take ? 1000 ( 10 * 10 * 10 )
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Algorithm : Combinatorics
Print explanation
 Get num from user
 Validate value of num (0 <= num <= 27)
 Vary 1 digit at a time from the digit
sequence 000 to the digit sequence 999

o If the sum of the digits is equal to num,
print the 3 digits (or less) with no space
between them. Don’t print leading 0’s.
o Increment the counter.
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
Print the count
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Combinatorics
Incremental Programming
Write the explanation, get it running
 Get num from user and validate it, get
this running.
 Write the nested for loops that will print
all three digits when they sum to num.
(has leading 0’s) and print the count.
Don’t forget to initialize count to 0
before beginning. Get this running.
 Modify the code to eliminate leading 0’s

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