Examples

1
Examples

• Example Problems,
• their Algorithms, and
• their C Source Code.

2
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 years .
• Without the break, the code flows into the next
  case. This is almost never what you want.

3
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
• Calculate the amount in the account at the end of
  the year. (amount amount rate)
• interest accrued amount - principal
• Print report.

4
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

5
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 ltstdio.hgt
• main ( )
• / Print Instructions /
• printf (This program computes the interest
  accrued in an account)
• printf (that compounds interest annually. You
  will need to enter the)
• printf (amount of the principal, the interest
  rate and the number of years.\n\n)

6
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.

7
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 ltstdio.hgt
• main ( )
• float principal, rate
• int years
• / Print Instructions /
• printf (This program computes the interest
  accrued in an account)
• printf (that compounds interest annually. You
  will need to enter the)
• printf (amount 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)

8
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

9
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 ltstdio.hgt
• main ( )
• float principal, rate, amount, interest
• int years, I
• / Print Instructions /
• printf (This program computes the interest
  accrued in an account)
• printf (that compounds interest annually. You
  will need to enter the)
• printf (amount 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)

10
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 lt 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)

11
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

12
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 ltstdio.hgt
• main ( )
• float principal, rate, amount, interest
• int years, I
• / Print Instructions /
• printf (This program computes the interest
  accrued in an account)
• printf (that compounds interest annually. You
  will need to enter the)
• printf (amount 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)

13
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 lt 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)

14
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

15
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 ltstdio.hgt
• main ( )
• float principal, rate, amount, interest
• int years, I
• / Print Instructions /
• printf (This program computes the interest
  accrued in an account)
• printf (that compounds interest annually. You
  will need to enter the)
• printf (amount 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)

16
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 lt 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)

17
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

18
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 ltstdio.hgt
• main ( )
• float principal, rate, amount, interest
• int years, I
• / Print Instructions /
• printf (This program computes the interest
  accrued in an account)
• printf (that compounds interest annually. You
  will need to enter the)
• printf (amount 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)

19
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 lt 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)

20
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

21
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.

22
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.

23
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 ltstdio.hgt
• main ( )
• float principal, rate, amount, interest
• int years, I
• / Print Instructions /
• printf (This program computes the interest
  accrued in an account)
• printf (that compounds interest annually. You
  will need to enter the)
• printf (amount 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 lt 0.0 principal gt 100000.0
  )

24
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 lt 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)

25
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
• Principal at start of period 1000.00
• Interest accrued 2869.68
  
• Total amount at end of period 3869.68

26
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 ltstdio.hgt
• main ( )
• float principal, rate, amount, interest
• int years, I
• / Print Instructions /
• printf (This program computes the interest
  accrued in an account)
• printf (that compounds interest annually. You
  will need to enter the)
• printf (amount of the principal, the interest
  rate and the number of years.\n\n)
• / Get valid principal amount from user /
• printf (Enter the principal amount )
• scanf (f, principal)
• while ( principal lt 0.0 principal gt 100000.0
  )

27
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 lt 0.0 rate gt 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 lt years I )
• amount amount rate

28
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)

29
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
• Principal at start of period 1000.00
• Interest accrued 2869.68
  
• Total amount at end of period 3869.68

30
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 ltstdio.hgt
• main ( )
• float principal, rate, amount, interest
• int years, I
• / Print Instructions /
• printf (This program computes the interest
  accrued in an account)
• printf (that compounds interest annually. You
  will need to enter the)
• printf (amount of the principal, the interest
  rate and the number of years.\n\n)
• / Get valid principal amount from user /
• printf (Enter the principal amount )
• scanf (f, principal)
• while ( principal lt 0.0 principal gt 100000.0
  )

31
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 lt 0.0 rate gt 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 lt 1 years gt 100 )
• printf (The number of years must be
  between 1 and 100, inclusive\n)
• printf (Enter the number of years )
• scanf (d, years)

32
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 lt 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)

33
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
• Principal at start of period 1000.00
• Interest accrued 2869.68
  
• Total amount at end of period 3869.68

34
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?

35
CombinatoricsThinking 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, well need to break the integer
  up into its individual digits, add them up and
  compare that sum to num.

36
CombinatoricsThinking through the problem

• Weve 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, well 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.

37
CombinatoricsThinking 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 digits.

38
CombinatoricsThinking through the problem

• for ( I 0 I lt 10 I)
• for ( j 0 j lt 10 j)
• for ( k 0 k lt 10 k)
• if ( I j k num )
• printf ( ddd\n, I, j, k )
• counter
• How long does this take ? 1000 ( 10 10 10 )

39
Algorithm Combinatorics

• Print explanation
• Get num from user (0 lt num lt 27)
• Validate value of num
• Vary 1 digit at a time from the digit sequence
  000 to the digit sequence 999
• If the sum of the digits is equal to num, print
  the 3 digits (or less) with no space between
  them. Dont print leading 0s.
• Increment the counter.
• Print the count

40
CombinatoricsIncremental 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
  0s) and print the count. Dont forget to
  initialize count to 0 before beginning. Get this
  running.
• Modify the code to eliminate leading 0s