Computer Science 1620

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Computer Science 1620

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Title: Computer Science 1620

1
Computer Science 1620

Functions

Given a number n, the factorial of n, written n!,
is computed as follows
note 0! 1
examples

n! n x (n-1) x (n-2) x x 1
3! 3 x 2 x 1 6 5! 5 x 4 x 3 x 2 x
1 120 0! 1
3

Write a program that takes a number n from the
user, and calculates the factorial of that number.

Write a program that takes a number from the
user, and calculates the factorial of that
number.

include ltiostreamgt include ltiomanipgt using
namespace std int main() int n cout ltlt
"Please enter a number" cin gtgt n double
factn 1.0 for (int i 1 i lt n i)
factn i cout ltlt fixed ltlt
setprecision(0) cout ltlt n ltlt "! " ltlt factn ltlt
endl return 0
5

Write a program that takes a number from the
user, and calculates the factorial of that
number.

Write a program that takes a number from the
user, and calculates the factorial of that
number.

Write a program that takes a number from the
user, and calculates the factorial of that
number.

Write a program that takes a number from the
user, and calculates the factorial of that
number.

Write a program that takes a number from the
user, and calculates the factorial of that
number.

Write a program that takes a number from the
user, and calculates the factorial of that
number.

Example Given a set of n objects, the number of
combinations of those objects taken r at a time
can be calculated as
ie. Given a class of 112 students, the number of
possible groups of 5 students is

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers, and displays the results.

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers, and displays the results.

include ltiostreamgt include ltiomanipgt using
namespace std int main() int n, r cout ltlt
"Please enter n and r" cin gtgt n gtgt r
double factn 1.0 for (int i 1 i lt n
i) factn i double factr 1.0
for (int i 1 i lt r i) factr
i double factnr 1.0 for
(int i 1 i lt (n-r) i) factnr
i double result factn / (factr
factnr) cout ltlt fixed ltlt setprecision(0) cout
ltlt n ltlt " choose " ltlt r ltlt " " ltlt result ltlt
endl return 0
15

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers, and displays the results.

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers, and displays the results.

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers, and displays the results.

Problem Breakdown

double factn 1.0 for (int i 1 i lt n
i) factn i double factn 1.0
for (int i 1 i lt n i) factn i
double factn 1.0 for (int i 1 i lt n
i) factn i double result factn /
(factr factnr)
Calculate n!
Calculate r!
Calculate (n-r)!
Combine results into Cnr
19

Problem Breakdown

Problem Breakdown

double factn 1.0 for (int i 1 i lt n
i) factn i double factr 1.0
for (int i 1 i lt r i) factr i
double factn 1.0 for (int i 1 i lt n
i) factn i double result factn /
(factr factnr)
Calculate n!
Calculate r!
Calculate (n-r)!
Combine results into Cnr
21

Problem Breakdown

double factn 1.0 for (int i 1 i lt n
i) factn i double factr 1.0
for (int i 1 i lt r i) factr i
double factnr 1.0 for (int i 1 i lt n-r
i) factnr i double result factn
/ (factr factnr)
Calculate n!
Calculate r!
Calculate (n-r)!
Combine results into Cnr
22

Problem Breakdown

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers.

include ltiostreamgt include ltiomanipgt using
namespace std int main() int n, r cout ltlt
"Please enter n and r" cin gtgt n gtgt r
double factn 1.0 for (int i 1 i lt n
i) factn i double factr
1.0 for (int i 1 i lt r i)
factr i double factnr 1.0 for
(int i 1 i lt n-r i) factnr i
double result factn / (factr
factnr) cout ltlt fixed ltlt setprecision(0) cout
ltlt n ltlt " choose " ltlt r ltlt " " ltlt result ltlt
endl return 0
24

Does this solve our problem?
Yes
Any problems with previous code?
duplication!!!
the calculation for factorial is the same, but
the code to calculate is repeated 3 times
the only change is the stopping condition value,
and the variable that we set.

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers.

include ltiostreamgt include ltiomanipgt using
namespace std int main() int n, r cout ltlt
"Please enter n and r" cin gtgt n gtgt r
double factn 1.0 for (int i 1 i lt n
i) factn i double factr
1.0 for (int i 1 i lt r i)
factr i double factnr 1.0 for
(int i 1 i lt n-r i) factnr i
double result factn / (factr
factnr) cout ltlt fixed ltlt setprecision(0) cout
ltlt n ltlt " choose " ltlt r ltlt " " ltlt result ltlt
endl return 0
double ltresultgt 1.0 for (int i 1 i lt
ltinputgt i) factn i
26

Imagine a "factorial machine"
one input, for a number n
one output, for the computed number n!

factorial
5
120
27

Imagine a "factorial machine"
one input, for a number n
one output, for the computed number n!

factorial
0
1
28

Imagine a "factorial machine"
one input, for a number n
one output, for the computed number n!

double result 1.0 for (int i 1 i lt x i)
result i
x
5
result
120

3 questions
where does this code go?
how do we set the input (x)?
how do we get the output (result)?

Function
a subprogram
a piece of code that can be re-used
called from other places in the program
example code to write out my name and location

cout ltlt Robert" ltlt endl cout ltlt "Lethbridge" ltlt
endl
30

Function
written outside of main
every function has a
return type
name
parameter list
you call a function by typing its name, followed
by args

include ltiostreamgt using namespace std void
whoAmI() cout ltlt Robert" ltlt endl cout ltlt
"Lethbridge" ltlt endl int main()
whoAmI() whoAmI() return 0
31
Output
include ltiostreamgt using namespace std void
whoAmI() cout ltlt Robert" ltlt endl cout ltlt
"Lethbridge" ltlt endl int main()
whoAmI() whoAmI() return 0
Robert Lethbridge Robert Lethbridge
Start Here
32
Output
include ltiostreamgt using namespace std void
whoAmI() cout ltlt Robert" ltlt endl cout ltlt
"Lethbridge" ltlt endl int main()
whoAmI() whoAmI() return 0
Robert Lethbridge Robert Lethbridge
At this point, we move to the first line in the
function whoAmI
33
Output
include ltiostreamgt using namespace std void
whoAmI() cout ltlt "Robert" ltlt endl cout ltlt
"Lethbridge" ltlt endl int main()
whoAmI() whoAmI() return 0
Robert Lethbridge Robert Lethbridge
Perform output
34
Output
include ltiostreamgt using namespace std void
whoAmI() cout ltlt "Robert" ltlt endl cout ltlt
"Lethbridge" ltlt endl int main()
whoAmI() whoAmI() return 0
Robert Lethbridge Robert Lethbridge
Perform output
35
Output
include ltiostreamgt using namespace std void
whoAmI() cout ltlt "Robert" ltlt endl cout ltlt
"Lethbridge" ltlt endl int main()
whoAmI() whoAmI() return 0
Robert Lethbridge Robert Lethbridge
Function ended, start again right after function
call
36
Output
include ltiostreamgt using namespace std void
whoAmI() cout ltlt "Robert" ltlt endl cout ltlt
"Lethbridge" ltlt endl int main()
whoAmI() whoAmI() return 0
Robert Lethbridge Robert Lethbridge
At this point, we move to the first line in the
function whoAmI
37
Output
include ltiostreamgt using namespace std void
whoAmI() cout ltlt "Robert" ltlt endl cout ltlt
"Lethbridge" ltlt endl int main()
whoAmI() whoAmI() return 0
Robert Lethbridge Robert Lethbridge
Perform output
38
Output
include ltiostreamgt using namespace std void
whoAmI() cout ltlt "Robert" ltlt endl cout ltlt
"Lethbridge" ltlt endl int main()
whoAmI() whoAmI() return 0
Robert Lethbridge Robert Lethbridge
Perform output
39
Output
include ltiostreamgt using namespace std void
whoAmI() cout ltlt "Robert" ltlt endl cout ltlt
"Lethbridge" ltlt endl int main()
whoAmI() whoAmI() return 0
Robert Lethbridge Robert Lethbridge
Function ended, start again right after function
call
40
Output
include ltiostreamgt using namespace std void
whoAmI() cout ltlt "Robert" ltlt endl cout ltlt
"Lethbridge" ltlt endl int main()
whoAmI() whoAmI() return 0
Robert Lethbridge Robert Lethbridge ...
At this point, program terminates
41

Example Write a program with a function called
factorial that computes the factorial of 5 and
writes the value to output. Call that function
from the main function.

Write a program with a function called factorial
that computes the factorial of 5 and writes the
value to output. Call that function from the
main function.

include ltiostreamgt include ltiomanipgt using
namespace std void factorial() double
result 1.0 for (int i 1 i lt 5 i)
result i cout ltlt fixed ltlt
setprecision(0) cout ltlt result int main()
cout ltlt "The factorial of 5 is
" factorial() cout ltlt endl return 0
43

Write a program with a function called factorial
that computes the factorial of 5 and writes the
value to output. Call that function from the
main function.

Write a program with a function called factorial
that computes the factorial of 5 and writes the
value to output. Call that function from the
main function.

Write a program with a function called factorial
that computes the factorial of 5 and writes the
value to output. Call that function from the
main function.

Write a program with a function called factorial
that computes the factorial of 5 and writes the
value to output. Call that function from the
main function.

Write a program with a function called factorial
that computes the factorial of 5 and writes the
value to output. Call that function from the
main function.

Imagine a "factorial machine"
one input, for a number n
one output, for the computed number n!

double result 1.0 for (int i 1 i lt x i)
result i
x
5
result
120

3 questions
where does this code go?
how do we set the input (x)?
how do we get the output (result)?

Function Input
sending data to the function
accomplished through a list of parameters
a list of variables
contained in parameter list
we set these variables in the call using
arguments
a list of expressions

Function Inputs
declared as parameters
function can have 0 or more parameters
specify the type and the variable name
Function arguments
the value of each argument is assigned to
corresponding parameter variable

void square(int x) cout ltlt xx int main()
cout "2 x 2 " square(2) cout "(21)
x (21) " square(21) return 0
51
Output
include ltiostreamgt using namespace std void
square(int x) cout ltlt xx int main()
cout "2 x 2 " square(2) cout "\n(21)
(21) " square(21) return 0
2 x 2 4 (21) x (21) 9
Start Here
52
Output
include ltiostreamgt using namespace std void
square(int x) cout ltlt xx int main()
cout "2 x 2 " square(2) cout "\n(21)
(21) " square(21) return 0
2 x 2 4 (21) x (21) 9
Perform Output
53
Output
include ltiostreamgt using namespace std void
square(int x) cout ltlt xx int main()
cout "2 x 2 " square(2) cout "\n(21)
(21) " square(21) return 0
2 x 2 4 (21) x (21) 9
At this point, we move to the first line in the
function square The parameter x gets the value of
the expression in the call, which is 2
54
Output
include ltiostreamgt using namespace std void
square(int x) cout ltlt xx int main()
cout "2 x 2 " square(2) cout "\n(21)
(21) " square(21) return 0
2 x 2 4 (21) x (21) 9
Perform Output. Note that x has value 2.
55
Output
include ltiostreamgt using namespace std void
square(int x) cout ltlt xx int main()
cout "2 x 2 " square(2) cout "\n(21)
(21) " square(21) return 0
2 x 2 4 (21) x (21) 9
Function ended, start right after function call.
56
Output
include ltiostreamgt using namespace std void
square(int x) cout ltlt xx int main()
cout "2 x 2 " square(2) cout "\n(21)
(21) " square(21) return 0
2 x 2 4 (21) x (21) 9
Perform Output
57
Output
include ltiostreamgt using namespace std void
square(int x) cout ltlt xx int main()
cout "2 x 2 " square(2) cout "\n(21)
(21) " square(21) return 0
2 x 2 4 (21) x (21) 9
At this point, we move to the first line in the
function square The parameter x gets the value of
the expression in the call, which is 21 3
58
Output
include ltiostreamgt using namespace std void
square(int x) cout ltlt xx int main()
cout "2 x 2 " square(2) cout "\n(21)
(21) " square(21) return 0
2 x 2 4 (21) x (21) 9
Perform Output. Note that x has value 3.
59
Output
include ltiostreamgt using namespace std void
square(int x) cout ltlt xx int main()
cout "2 x 2 " square(2) cout "\n(21)
(21) " square(21) return 0
2 x 2 4 (21) x (21) 9
Function ended, start right after function call.
60
Output
include ltiostreamgt using namespace std void
square(int x) cout ltlt xx int main()
cout "2 x 2 " square(2) cout "\n(21)
(21) " square(21) return 0
2 x 2 4 (21) x (21) 9
Program terminates.
61

Example Write a program with a function called
factorial that computes the factorial of x (x is
an inputted number) and writes the value to
output. Call that function from the main
function with the value 5.

Write a program with a function called factorial
that computes the factorial of x and writes the
value to output. Call that function from the
main function with the value 5.

include ltiostreamgt include ltiomanipgt using
namespace std void factorial(int x) double
result 1.0 for (int i 1 i lt x i)
result i cout ltlt fixed ltlt
setprecision(0) cout ltlt result int main()
cout ltlt "The factorial of 5 is
" factorial(5) cout ltlt endl return 0
63

Write a program with a function called factorial
that computes the factorial of x and writes the
value to output. Call that function from the
main function with the value 5.

Write a program with a function called factorial
that computes the factorial of x and writes the
value to output. Call that function from the
main function with the value 5.

Write a program with a function called factorial
that computes the factorial of x and writes the
value to output. Call that function from the
main function with the value 5.

Write a program with a function called factorial
that computes the factorial of x and writes the
value to output. Call that function from the
main function with the value 5.

Write a program with a function called factorial
that computes the factorial of x and writes the
value to output. Call that function from the
main function with the value 5.

Write a program with a function called factorial
that computes the factorial of x and writes the
value to output. Call that function from the
main function with the value 5.

Imagine a "factorial machine"
one input, for a number n
one output, for the computed number n!

double result 1.0 for (int i 1 i lt x i)
result i
x
5
result
120

3 questions
where does this code go?
how do we set the input (x)?
how do we get the output (result)?

Function Output
receiving data from a function
accomplished through a return statement
recall that an expression in C has a value
2 // the value of this expression is 2
2 3 // the value of this expression is 5
2 gt 3 // the value of this expression is false
(0)
i 2 // the value of this expression is 2
a function call is an expression with a value
square(2)
square(21)

what is the value of these expressions?
71

Function Output
given by the return statement
Function call
the value of the function call is the value that
is returned
the type of the value returned by a function call
is given by its return type

int square(int x) int result x x
return result int main() cout "2 x 2
" cout ltlt square(2) cout "(21) x (21)
" cout ltlt square(21) return 0
72
Output
include ltiostreamgt using namespace std int
square(int x) int result x x return
result int main() cout "2 x 2 "
cout ltlt square(2) cout "(21) x (21) "
cout ltlt square(21) return 0
2 x 2 4 (21) x (21) 9
Start here
73
Output
include ltiostreamgt using namespace std int
square(int x) int result x x return
result int main() cout "2 x 2 "
cout ltlt square(2) cout "(21) x (21) "
cout ltlt square(21) return 0
2 x 2 4 (21) x (21) 9
Perform Output
74
Output
include ltiostreamgt using namespace std int
square(int x) int result x x return
result int main() cout "2 x 2 "
cout ltlt square(2) cout "(21) x (21) "
cout ltlt square(21) return 0
2 x 2 4 (21) x (21) 9
At this point, we move to the first line in the
function square The parameter x gets the value of
the expression in the call, which is 2
75
Output
include ltiostreamgt using namespace std int
square(int x) int result x x return
result int main() cout "2 x 2 "
cout ltlt square(2) cout "(21) x (21) "
cout ltlt square(21) return 0
2 x 2 4 (21) x (21) 9
Do calculation. Note that x has value 2.
76
Output
include ltiostreamgt using namespace std int
square(int x) int result x x return
result int main() cout "2 x 2 "
cout ltlt square(2) cout "(21) x (21) "
cout ltlt square(21) return 0
2 x 2 4 (21) x (21) 9
Returns value stored in result
The value of the expression square(2) is the
return value (4).
77
Output
include ltiostreamgt using namespace std int
square(int x) int result x x return
result int main() cout "2 x 2 "
cout ltlt square(2) cout "(21) x (21) "
cout ltlt square(21) return 0
2 x 2 4 (21) x (21) 9
Perform output.
78
Output
include ltiostreamgt using namespace std int
square(int x) int result x x return
result int main() cout "2 x 2 "
cout ltlt square(2) cout "(21) x (21) "
cout ltlt square(21) return 0
2 x 2 4 (21) x (21) 9
Perform output.
79
Output
include ltiostreamgt using namespace std int
square(int x) int result x x return
result int main() cout "2 x 2 "
cout ltlt square(2) cout "(21) x (21) "
cout ltlt square(21) return 0
2 x 2 4 (21) x (21) 9
At this point, we move to the first line in the
function square The parameter x gets the value of
the expression in the call, which is (21) 3
80
Output
include ltiostreamgt using namespace std int
square(int x) int result x x return
result int main() cout "2 x 2 "
cout ltlt square(2) cout "(21) x (21) "
cout ltlt square(21) return 0
2 x 2 4 (21) x (21) 9
Do calculation. Note that x has value 3.
81
Output
include ltiostreamgt using namespace std int
square(int x) int result x x return
result int main() cout "2 x 2 "
cout ltlt square(2) cout "(21) x (21) "
cout ltlt square(21) return 0
2 x 2 4 (21) x (21) 9
Returns value stored in result
The value of the expression square(3) is the
return value (9).
82
Output
include ltiostreamgt using namespace std int
square(int x) int result x x return
result int main() cout "2 x 2 "
cout ltlt square(2) cout "(21) x (21) "
cout ltlt square(21) return 0
2 x 2 4 (21) x (21) 9
Perform Output
83
Output
include ltiostreamgt using namespace std int
square(int x) int result x x return
result int main() cout "2 x 2 "
cout ltlt square(2) cout "(21) x (21) "
cout ltlt square(21) return 0
2 x 2 4 (21) x (21) 9
Terminate Program!
84

Example Write a program with a function called
factorial that computes the factorial of x (x is
an inputted number) and returns that value. Call
that function from the main function with the
value 5.

Write a program with a function called factorial
that computes the factorial of x and returns that
value. Call that function from the main function
with the value 5.

include ltiostreamgt include ltiomanipgt using
namespace std double factorial(int x)
double result 1.0 for (int i 1 i lt x
i) result i return
result int main() cout ltlt fixed ltlt
setprecision(0) cout ltlt "The factorial of 5 is
" cout ltlt factorial(5) cout ltlt endl return
0
86

Write a program with a function called factorial
that computes the factorial of x and returns that
value. Call that function from the main function
with the value 5.

Write a program with a function called factorial
that computes the factorial of x and returns that
value. Call that function from the main function
with the value 5.

Write a program with a function called factorial
that computes the factorial of x and returns that
value. Call that function from the main function
with the value 5.

Write a program with a function called factorial
that computes the factorial of x and returns that
value. Call that function from the main function
with the value 5.

Write a program with a function called factorial
that computes the factorial of x and returns that
value. Call that function from the main function
with the value 5.

Write a program with a function called factorial
that computes the factorial of x and returns that
value. Call that function from the main function
with the value 5.

Write a program with a function called factorial
that computes the factorial of x and returns that
value. Call that function from the main function
with the value 5.

Imagine a "factorial machine"
one input, for a number n
one output, for the computed number n!

double result 1.0 for (int i 1 i lt x i)
result i cout ltlt result
x
5
result
120

3 questions
where does this code go?
how do we set the input (x)?
how do we get the output (result)?

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers, and displays the results.

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers.

include ltiostreamgt include ltiomanipgt using
namespace std int main() int n, r cout ltlt
"Please enter n and r" cin gtgt n gtgt r
double factn 1.0 for (int i 1 i lt n
i) factn i double factr
1.0 for (int i 1 i lt r i)
factr i double factnr 1.0 for
(int i 1 i lt n-r i) factnr i
double result factn / (factr
factnr) cout ltlt fixed ltlt setprecision(0) cout
ltlt n ltlt " choose " ltlt r ltlt " " ltlt result ltlt
endl return 0
Rewrite this program using the factorial function.
96

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers.

include ltiostreamgt include ltiomanipgt using
namespace std double factorial(int x)
double result 1.0 for (int i 1 i lt x
i) result i return result int
main() int n, r cout ltlt "Please enter n and
r" cin gtgt n gtgt r double factn 1.0
for (int i 1 i lt n i) factn
i double factr 1.0 for (int i 1 i
lt r i) factr i double
factnr 1.0 for (int i 1 i lt n-r i)
factnr i double result factn
/ (factr factnr) cout ltlt fixed ltlt
setprecision(0) cout ltlt n ltlt " choose " ltlt r ltlt
" " ltlt result ltlt endl return 0
97

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers.

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers.

include ltiostreamgt include ltiomanipgt using
namespace std double factorial(int x)
double result 1.0 for (int i 1 i lt x
i) result i return result int
main() int n, r cout ltlt "Please enter n and
r" cin gtgt n gtgt r double factn
factorial(n) double factr 1.0 for (int i
1 i lt r i) factr i
double factnr 1.0 for (int i 1 i lt
n-r i) factnr i double
result factn / (factr factnr) cout ltlt fixed
ltlt setprecision(0) cout ltlt n ltlt " choose " ltlt r
ltlt " " ltlt result ltlt endl return 0
99

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers.

include ltiostreamgt include ltiomanipgt using
namespace std double factorial(int x)
double result 1.0 for (int i 1 i lt x
i) result i return result int
main() int n, r cout ltlt "Please enter n and
r" cin gtgt n gtgt r double factn
factorial(n) double factr 1.0 for (int i
1 i lt r i) factr i
double factnr 1.0 for (int i 1 i lt
n-r i) factnr i double
result factn / (factr factnr) cout ltlt fixed
ltlt setprecision(0) cout ltlt n ltlt " choose " ltlt r
ltlt " " ltlt result ltlt endl return 0
100

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers.

include ltiostreamgt include ltiomanipgt using
namespace std double factorial(int x)
double result 1.0 for (int i 1 i lt x
i) result i return result int
main() int n, r cout ltlt "Please enter n and
r" cin gtgt n gtgt r double factn
factorial(n) double factr factorial(r)
double factnr 1.0 for (int i 1 i lt
n-r i) factnr i double
result factn / (factr factnr) cout ltlt fixed
ltlt setprecision(0) cout ltlt n ltlt " choose " ltlt r
ltlt " " ltlt result ltlt endl return 0
101

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers.

include ltiostreamgt include ltiomanipgt using
namespace std double factorial(int x)
double result 1.0 for (int i 1 i lt x
i) result i return result int
main() int n, r cout ltlt "Please enter n and
r" cin gtgt n gtgt r double factn
factorial(n) double factr factorial(r)
double factnr 1.0 for (int i 1 i lt
n-r i) factnr i double
result factn / (factr factnr) cout ltlt fixed
ltlt setprecision(0) cout ltlt n ltlt " choose " ltlt r
ltlt " " ltlt result ltlt endl return 0
102

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers.

include ltiostreamgt include ltiomanipgt using
namespace std double factorial(int x)
double result 1.0 for (int i 1 i lt x
i) result i return result int
main() int n, r cout ltlt "Please enter n and
r" cin gtgt n gtgt r double factn
factorial(n) double factr factorial(r)
double factnr factorial(n r) double
result factn / (factr factnr) cout ltlt fixed
ltlt setprecision(0) cout ltlt n ltlt " choose " ltlt r
ltlt " " ltlt result ltlt endl return 0
103

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers.

include ltiostreamgt include ltiomanipgt using
namespace std double factorial(int x)
double result 1.0 for (int i 1 i lt x
i) result i return result int
main() int n, r cout ltlt "Please enter n and
r" cin gtgt n gtgt r double result
factorial(n) / (factorial(r) factorial(n
r)) cout ltlt fixed ltlt setprecision(0) cout ltlt
n ltlt " choose " ltlt r ltlt " " ltlt result ltlt
endl return 0
104

Write a program that takes two integers n and r
from the user, and calculates Cnr for those two
numbers.

include ltiostreamgt include ltiomanipgt using
namespace std double factorial(int x)
double result 1.0 for (int i 1 i lt x
i) result i return result int
main() int n, r cout ltlt "Please enter n and
r" cin gtgt n gtgt r cout ltlt fixed ltlt
setprecision(0) cout ltlt n ltlt " choose " ltlt r ltlt
" " ltlt factorial(n) /
(factorial(r) factorial(n r)) ltlt
endl return 0
105

The anatomy of a function

return type
function name
parameter list
double factorial(int x) double result
1.0 for (int i 1 i lt x i) result
i return result
function header (declaration)
function body (definition)
106

Functions with no return value
sometimes, we do not need a value back from our
function
we indicate this with the void return type
return keyword in void function simply exits
function

void square(int x) int result x x cout
ltlt result
void inverse(int x) if (x 0) return
double result 1.0 / x cout ltlt result
107

Functions as expressions
the value of a function call is its return value
return value can be used in other expressions

int square(int x) int result x x
return result int main() cout ltlt
square(2) // outputs 4 cout ltlt square(2)
square(3) // outputs 13 cout ltlt
square(square(2)) // outputs 16 return 0
108

Functions with multiple inputs
functions can have as many parameters as you like
first argument aligns with first parameter,
second with second, etc

int sum(int x, int y) return x y int
main() cout ltlt sum(2, 3) // outputs 5
return 0
109

More than one return statement
a function may have more than one return
statement
function terminates as soon as return statement
is reached

int max(int x, int y) if (x gt y) return
x return y int main() cout ltlt max(2,
3) ltlt endl // outputs 3 cout ltlt max(3, 2)
ltlt endl // outputs 3 return 0
110

Where have we seen functions?

111

The main function
a function called by operating system
can have parameters (more on this later)
has a return value
0 program terminated normally
nonzero program terminated abnormally

int main() return 0
112

Functions can call other functions
Example write a program that takes an integer
n, and outputs a table of all values Cnr for all
values 0 lt r lt n

113
(No Transcript)
114

Without functions

include ltiostreamgt include ltiomanipgt using
namespace std int main() int n cout ltlt
"Please enter n" cin gtgt n cout ltlt " r
n choose r" ltlt endl cout ltlt "---
----------" ltlt endl for (int r 0 r lt n
r) double factn 1.0 for (int i
1 i lt n i) factn i
double factr 1.0 for (int i 1 i lt r
i) factr i double
factnr 1.0 for (int i 1 i lt n-r i)
factnr i double result
factn / (factr factnr) cout ltlt fixed ltlt
setprecision(0) cout ltlt setw(3) ltlt r ltlt
setw(15) ltlt result ltlt endl return 0
115

With function factorial

include ltiostreamgt include ltiomanipgt using
namespace std double factorial(int x)
double result 1.0 for (int i 1 i lt x
i) result i return result int
main() int n cout ltlt "Please enter
n" cin gtgt n cout ltlt " r n choose r"
ltlt endl cout ltlt "--- ----------" ltlt
endl for (int r 0 r lt n r) double
factn factorial(n) double factr
factorial(r) double factnr
factorial(n-r) double result factn /
(factr factnr) cout ltlt fixed ltlt
setprecision(0) cout ltlt setw(3) ltlt r ltlt
setw(15) ltlt result ltlt endl return 0
116

With function factorial

include ltiostreamgt include ltiomanipgt using
namespace std double factorial(int x)
double result 1.0 for (int i 1 i lt x
i) result i return result int
main() int n cout ltlt "Please enter
n" cin gtgt n cout ltlt " r n choose r"
ltlt endl cout ltlt "--- ----------" ltlt
endl for (int r 0 r lt n r) double
result factorial(n) / (factorial(r)
factorial(n-r)) cout ltlt fixed ltlt
setprecision(0) cout ltlt setw(3) ltlt r ltlt
setw(15) ltlt result ltlt endl return 0
117

With factorial, looks much better
what is a good candidate for a function in this
code?
calculating n choose r
write a function called choose that takes two
values n and r, and returns n choose r
inputs n (int), r(int)
output an integer

118

write a function called choose that takes two
values n and r, and calculates and returns n
choose r
inputs n (int), r(int)
output an integer

int choose(int n, int r) double result
factorial(n) / (factorial(r) factorial(n-r))
return static_castltintgt(result)
119

write a function called choose that takes two
values n and r, and calculates and returns n
choose r
inputs n (int), r(int)
output an integer

int choose(int n, int r) double result
factorial(n) / (factorial(r) factorial(n-r))
return static_castltintgt(result)
120

write a function called choose that takes two
values n and r, and calculates and returns n
choose r
inputs n (int), r(int)
output an integer

int choose(int n, int r) double result
factorial(n) / (factorial(r) factorial(n-r))
return static_castltintgt(result)
121

write a function called choose that takes two
values n and r, and calculates and returns n
choose r
inputs n (int), r(int)
output an integer

int choose(int n, int r) double result
factorial(n) / (factorial(r) factorial(n-r))
return static_castltintgt(result)
122

write a function called choose that takes two
values n and r, and calculates and returns n
choose r
inputs n (int), r(int)
output an integer

int choose(int n, int r) double factn
1.0 for (int i 1 i lt n i)
factn i double factr 1.0
for (int i 1 i lt r i) factr
i double factnr 1.0 for (int i
1 i lt n-r i) factnr i
double result factn / (factr factnr)
double result
123

write a function called choose that takes two
values n and r, and calculates and returns n
choose r
inputs n (int), r(int)
output an integer
note this assumes that we have the factorial
function defined in our program!!!

int choose(int n, int r) double result
factorial(n) / (factorial(r) factorial(n-r))
return static_castltintgt(result)
124

write a function called choose that takes two
values n and r, and calculates and returns n
choose r
inputs n (int), r(int)
output an integer

int choose(int n, int r) double result
factorial(n) / (factorial(r) factorial(n-r))
return static_castltintgt(result)
125

write a function called choose that takes two
values n and r, and calculates and returns n
choose r
inputs n (int), r(int)
output an integer

int choose(int n, int r) double result
factorial(n) / (factorial(r) factorial(n-r))
return static_castltintgt(result)
126

write a function called choose that takes two
values n and r, and calculates and returns n
choose r
inputs n (int), r(int)
output an integer

int choose(int n, int r) double result
factorial(n) / (factorial(r) factorial(n-r))
return static_castltintgt(result)
127

With function factorial and choose

include ltiostreamgt include ltiomanipgt using
namespace std double factorial(int x)
double result 1.0 for (int i 1 i lt x
i) result i return result int
choose(int n, int r) double result
factorial(n) / (factorial(r) factorial(n-r))
return static_castltintgt(result) int main()
int n cout ltlt "Please enter n" cin gtgt
n cout ltlt " r n choose r" ltlt endl
cout ltlt "--- ----------" ltlt endl for (int
r 0 r lt n r) cout ltlt setw(3) ltlt r ltlt
setw(15) ltlt choose(n, r) ltlt endl return
0
128
Function Placement

2 key ideas
The engine of a C program is the main method
allocates tasks to other functions
program functionality can usually be inferred
from a well written main method, as opposed to a
poorly written one
ie. suppose someone asks "What does your
program do?"
"program outputs n choose r for all 0 lt r lt n"
the user is typically interested in what function
does, not how it does it
ex. square root

129

Main function code is more interesting to user
than helper functions
thus, it is typically placed near the top of your
file, before other functions
however, if we place a function after the main
function, we can't call it from main
C must know the parameter types and return type
of a function before it can be called, for type
checking

130

With function factorial and choose

include ltiostreamgt include ltiomanipgt using
namespace std int main() int n cout ltlt
"Please enter n" cin gtgt n cout ltlt " r
n choose r" ltlt endl cout ltlt "---
----------" ltlt endl for (int r 0 r lt n
r) cout ltlt setw(3) ltlt r ltlt setw(15) ltlt
choose(n, r) ltlt endl return 0 double
factorial(int x) double result 1.0 for
(int i 1 i lt x i) result i return
result int choose(int n, int r) double
result factorial(n) / (factorial(r)
factorial(n-r)) return static_castltintgt(result)

131