Conditionals

1
Conditionals

• Concepts
• Conditional execution
• if statement
• Conditional expressions
• Relational and logical operators
• Compound statements

2
Control Flow

• Control flow is the order in which statements
  are executed

Sequential control flow the next statement
executed is the next one that appears, in
order, in the C program
Conditional control flow choosing which of two
(or more) statements to execute before
continuing OR
choosing whether or not to skip a statement
before continuing
3
Conditional Execution

• A conditional statement allows the computer to
  choose an execution path depending on the value
  of a variable or expression
• if the withdrawal is more than the bank
  balance, then print an error
• if today is my birthday, then add one to my age
• if using whole milk, add two eggs, otherwise add
  three eggs
• if (condition) statement
• In parentheses is a condition, also called a
  logical or Boolean expression
• Made up of variables, constants, arithmetic
  expressions, and the relational operators
• Value of condition is TRUE (non-zero) and FALSE
  (0)

4
Complex Conditionals

• if I have at least 15 or you have at least 15,
  then we can go to the movies
• if the temperature is below 32 degrees and its
  raining, then its snowing
• if its not the case that its Saturday or
  Sunday, then its a work day
• We use Boolean operators to code complex
  conditionals in C. ( !)
• if (myMoneygt15.0 yourMoneygt15.0)
  canGoToMovies TRUE

5
Multiple Actions

• if theres more than one conditional action
• If your temperature is high, then you have a
  fever and should take two aspirin and go to bed
  and call in sick tomorrow
• Compound Statement
• Groups together statements so that they are
  treated as a single statement - BLOCK
• if ( temperature gt 98.6 )
• printf ( You have a fever. \n )
• aspirin aspirin ? 2
• printf (Go to bed/n)
• printf (Sleep in tomorrow/n)

6
if-else Control Flow
yes
balance gt withdrawal
no
balance balance - withdrawal dispense_funds (
withdrawal )
printf ( No money! \n )
/ arrive here whether condition is TRUE or FALSE
/

• NESTED IF with relational op
• if (( time gt 0.) (time lt 12.))
• printf(Good Morning)
• else if ((time gt 12.) (time lt 18.))
• printf(Good Afternoon)
• else if ((time gt 18) (time lt 24.))
• printf(Good Evening)
• else printf(Time is out of range)

7
if-else Control Flow
NESTED IF with logical op if ( x 5 )
if ( y 5 ) printf ( Both are 5. \n )
else printf ( x is 5, but y is not. \n )
else if ( y 5 ) printf ( y is 5, but x is
not. \n ) else printf ( Neither is 5. \n )

• Consider
• this
• problem
• Print the tax based on income

8
Direct Solution
if ( income lt 15000 ) printf( No tax.
) if ( income gt 15000 income lt 30000 )
printf(18 tax.) if ( income gt 30000
income lt 50000 ) printf(22
tax.) if ( income gt 50000 income lt 100000
) printf(28 tax.) if ( income
gt100000) printf(31 tax.)

• Mutually exclusive conditions - only one will be
  true

9
Cascaded ifs
if ( income lt 15000 )
if ( income lt 15000 ) printf( No tax )
printf( No tax ) else

else if ( income lt 30000 ) if ( income lt
30000 ) printf( 18
tax. ) printf( 18 tax. )
else if ( income lt 50000 ) else

printf( 22 tax. ) if ( income lt 50000 )
else if ( income lt 100000 )
printf( 22 tax. )
printf( 28 tax. ) else else if (
income lt 100000 ) printf( 31 tax.
) printf( 28 tax. ) else printf(
31 tax. ) Order is important.
Conditions are evaluated in order given.
10
Warning Danger Ahead

• The idea of conditional execution is natural ,
  intuitive, and highly useful
• However...
• Programs can get convoluted and hard to
  understand
• There are syntactic pitfalls to avoid
• if ( x 10 )
• printf( x is 10 )
• Bug! is used instead of
• This is not a syntax error, so the program can
  execute
• The Worlds Last C Bug!

status check_radar ( ) if (status 1)
launch_missiles ( )
11
Nested if vs. AND ()
if ( age lt 25 ) if ( sex M )
insurance_rate insurance_rate 2
if ( (age lt 25) (sex M) )
insurance_rate insurance_rate 2

• Suppose we want a while loop to terminate as
• soon as either x is 17 or x is 42
• Which is it?
• while (x!17 x!42)
• while (x!17 x!42)
• either way? something else?
• Truth tables and DeMorgans laws give us tools
  for answering such questions

12
Truth Tables

• A "truth table" lists all possible combinations
  of values, and the result of each combination,
  here P and Q stand for any conditional
  expressions
• P Q P Q P Q !P
• T T T T F
• T F F T F
• F T F T T
• F F F F T

int high_risk /NOT Example
/ high_risk (age lt 25 sex M )
if ( high_risk ) / Do nothing /
else printf ( Cheap rates. \n)
if ( ! high_risk ) printf ( Cheap
rates. \n)
13
DeMorgans Laws

• DeMorgans laws help determine when two complex
  conditions are equivalent
• They state
• ! ( P Q ) is equivalent to ( !P !Q )
• ! ( P Q ) is equivalent to ( !P !Q )
• This applies for any Boolean expressions P and Q,
  which might themselves be complex expressions

if ( ! (age lt 25 sex M ) )
printf ( Cheap rates. \n) is equivalent
to if ( age gt 25 sex ! M ) )
printf ( Cheap rates. \n) Is it?
14
Proof of DeMorgan

• Is it really true that
• !(PQ) (!P !Q) ?

P Q (PQ) !(PQ) !P !Q (! P !Q) T
T T F F T F F
T
F
F
F
F
F
T
F
T
T
F
T
F
T
T
F
T
T
T
T
We wanted a while loop to terminate as soon as
either x is 17 or x is 42. I.e., loop should
terminate if (x17 x42) So the loop
condition is while ( ! (x17 x42)
Using DeMorgans laws, we can rewrite
as while (x ! 17 x ! 42) A truth table
would show that while (x ! 17 x ! 42) is
wrong!
15
Repetition

• Sometimes we want to repeat a block of code.
  This is called a loop.
• A loop is a repeated (iterated)
• sequence of statements
• Like conditionals, loops (iteration) give us a
  huge increase in the power of our programs
• Alert loops are harder to master than if
  statements
• Even experienced programmers often make subtle
  errors when writing loops

16
Motivating Loops

• Problem add 4 numbers entered at the keyboard.
• int sumint x1, x2, x3, x4
• printf(Enter 4 numbers )scanf(dddd,
  x1, x2, x3, x4)sum x1 x2 x3 x4
• This works perfectly!
• But... what if we had 14 numbers? or 40? or 4000?

• The key to using loops to solve a problem is to
  discover steps that can be repeated
• Our algorithm for adding four numbers had no
  repeated statements at all
• But it does have some repetition buried in it.
• Lets rework the algorithm to make the repetition
  more explicit

17
Add 4 Numbers, Repetitively

• int sum, x
• sum 0printf(Enter 4 numbers )
• scanf(d, x)sum sum x
• scanf(d, x)sum sum x
• scanf(d, x)sum sum x
• scanf(d, x)sum sum x

int sum, xint count sum 0printf(Enter 4
numbers) count 1while (count lt 4)
scanf(d, x)sum sum xcount count
1
18
More general solution
int sum, x, count int number_inputs /
Number of inputs / sum 0printf(How many
numbers? )scanf(d, number_inputs)printf(
Enter d numbers , number_inputs) count
1while ( count lt number_inputs )
scanf(d, x) sum sum x count count
1 Problem Compute 7! What is 1 2 3
4 5 6 7? (seven factorial) x 1 2 3
4 5 6 7 printf ( d, x )
19
Moving to a Loop

• Bite size pieces More Regular
  As a loop
• x 1 x 1 i 2
  x 1
• x x 2 x x i i i 1
  i 2
• x x 3 x x i i i 1
  while ( i lt 7 )
• x x 4 x x i i i 1
  x x i
• x x 5 x x i i i 1
  i i 1
• x x 6 x x i i i 1
  
• x x 7 x x i i i 1

x 1 i 2
yes
x x i i i 1
i lt 7 ?
no
20
Tracing the Loop
/ What is 1 2 3 ...7 / x 1 / A
/ i 2 / B / while ( i lt 7 ) / C
/ x x i / D / i i 1 / E
/ / F / printf ( d, x ) / G /
line i x I lt7? A ? 1 B 2 1 C 2 1 T D 2 2 E 3 2
C 3 2 T ...................... C 6
120 T D 6 720 E 7 720 C 7 720 T D 7 5040 E
8 5040 C 8 5040 F G (Print 5040)
21
Examples

• Double Your Money!
• / Suppose your 1,000 is earning interest at 5
  per
• year. How many years until you double your
  money? /
• my_money 1000.0 n 0
• while ( my_money lt 2000.0 )
• my_money my_money 1.05
• n n 1
• printf( My money will double in d years., n)
• Average Inputs
• printf ( Enter values to average, end with -1.0
  \n)
• sum 0.0 count 0 sentinel
• scanf ( lf, next )
• while ( next ! -1.0 )
• sum sum next
• count count 1
• scanf ( lf, next )
• if (count gt 0)

22
A For Loop

• / What is 1 2 3 ... n ? /
• x 1
• i 2
• while ( i lt n )
• x x i
• i i1
• printf ( d, x )

x 1 for ( i 2 i lt n i i1 ) x
x i printf ( d, x)

• for ( initialization condition
  update expression)
• statement1
• statement2
• ...

23
for Loop Control Flow
Initialization
yes
Condition
For Loop Body
Update Expression
no

• Any for loop can be written as a while loop
• These two loops mean exactly the same thing
• for (initialization condition
  update) statement
• initialization while (condition)
  statement update

24
a 2-D Figure

• How would you print the following diagram?
• ?
• ? ?
• ? ? ?
• ? ? ? ?
• ? ? ? ? ?
• For every row ( row 1, 2, 3, 4, 5 )
• Print row stars

• define ROWS 5
• ...
• int row, col
• for ( row 1 row lt ROWS row row 1 )
• for ( col 1 col lt row col col 1)
• printf( ? )
• printf( \n )

25
Summary

• Conditional
• Complex conditions are useful in while loops, for
  loops, if statements, and even in assignment
  statements
• Operators , , and ! are part of C
• TRUE and FALSE can be defined
• Truth tables and DeMorgans laws help evaluate
  complex expressions
• Iteration
• General pattern
• Initialize, test, do stuff, repeat . . .
• while and "for" are equally general in C
• Use for when initialize/test/update are closely
  related and simple, especially when counting
• Use ints in loop counters (use increment/decrement
  ) BUT
• Don't combine these with other operators in
  expressions! E.g., don't try
• x y / (3 --x--)
• Switch expression
• Missing BREAK is a common problem
• Switch is a form of conditional statement
• Switch is suitable for multi-way conditions that
  depend upon an integer (or char) value

26
the SWITCH expression

• The switch expression is not a conditional
  expression as it is in an if statement
• Only an integer expression is allowed
• Most often, the expression is a single integer
  variable
• The value of the variable determines which case
  is chosen

• month 6
• switch ( month )
• case 2 /
  February /
• days 28
• break
• case 9 /
  September /
• case 4 /
  April /
• case 6
  / June /
• case 11 /
  November /
• days 30
• break
• default / All the rest have 31
  .../
• days 31
• printf ( There are d days. \n , days )

27
More on SWITCH

• switch on char is also legal
• char marital_status
• ...
• switch ( marital_status )
• case m
• case M
• printf ( Married \n )
• break int or char expression
• case s
• case S
• printf ( Single \n )
• break
• default
• printf ( Sorry, I dont recognize that code. \n
  )