Loops

1
Programming

• Loops
• (Ch. 6)

2
Loops Iterative Constructs

• Provide
• Ability to control how many times a statement
  list is executed
• Three constructs
• while statement
• for statement
• do-while statement

3
The while Statement

• Syntax
• while (Expression)
• Action
• How it works
• If Expression is true then execute Action
• Repeat this process until Expression evaluates to
  false
• Action is either a single statement or a group of
  statements within braces

4
Example N! (while)

• int number, factorial, n
• cout ltlt "Enter number "
• cin gtgt number
• factorial 1
• n 1
• while(n lt number)
• factorial n
• n
• cout ltlt "The factorial of " ltlt number
• ltlt " is " ltlt factorial ltlt endl

5
The for Statement

• Syntax
• for (ForInit ForExpression PostExpression)
• Action
• How it works
• Execute ForInit statement
• As long as ForExpression
• is true
• Execute Action
• Execute PostExpression

6
Example N! (for)

• int number, factorial, n
• cout ltlt "Enter number "
• cin gtgt number
• factorial 1
• for (n1 nltnumber n)
• factorial n
• cout ltlt "The factorial of " ltlt number
• ltlt " is " ltlt factorial ltlt endl

7
The Do-While Statement

• Syntax
• do Action
• while (Expression)
• How it works
• Execute Action
• if Expression is true then execute Action again
• Repeat this process until Expression evaluates to
  false
• Action is either a single statement or a group of
  statements within braces

8
Example N! (do-while)

• int number, factorial, n
• cout ltlt "Enter number "
• cin gtgt number
• factorial 1
• n 1
• do
• factorial n
• n
• while(n lt number)
• cout ltlt "The factorial of " ltlt number
• ltlt " is " ltlt factorial ltlt endl

9
Which Loop to Use?

• For loop
• Usually best for sums, products, and counting
  loops.
• While loop
• You want to repeat an action without knowing
  exactly how many times it will be repeated.
• There are situations when the action should not
  be executed.
• Do-while loop
• The action should always be executed at least
  once.
• Otherwise, the do-while loops and while loops are
  used in similar situations.

10
How to Stop a Loop

• Known number of iterations before the loop stops
  (for)
• Test for a user-controlled
• condition before or after
• each iteration (while, do-while)
• Use the break command.

11
Stop a loop break

• The break command is the same as the one used
  previously in switch.
• break leaves the current loop immediately. It is
  recommended that break be used for situations
  where the loop needs to be terminated immediately
  (e.g., due to user intervention or if a fatal
  error occurs).
• Use with care !!

12
Example Maximum (while with break)
int value //input value int max0 //maximum
value while(true) cout ltlt "Enter a value (-1
to stop) " cin gtgt value if(value gt
max) max value if(value-1) break
cout ltlt "The maximum value found is " ltlt " is
" ltlt max ltlt endl
13
Common Loop Errors

• while(balance ! 0.0)
• balance balance - amount
• This will lead to an infinite loop!
• for(n1 nltcount n)
• cout ltlt "hello" ltlt endl
• "hello" only printed once!
• while(balance ! 0.0)
• balance balance - amount
• balance may not become equal zero due to
  numerical inaccuracies

14
Nested Loops

• Nested loops are loops within loops.

// Program to output the // multiplication
table int i //Outer loop counter int
j //Inner loop counter for(i1 ilt10
i) for(j1 jlt10 j) cout ltlt ij ltlt "
" cout ltlt endl
Output 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12 14 16
18 20 3 6 9 12 15 18 21 24 27 30
15
Programming

• Recursion
• (Ch.6, Section 6-9)

16
What is Recursion?

• A function calls itself.
• Recursion is one way to decompose a task into
  smaller subtasks.
• The smallest example of the same task has a
  non-recursive solution.
• Example The factorial function
• n! n (n-1) (n-2) ... 1
• or
• n! n (n-1)! and 1! 1
• A recursive solution may be simpler to write
  (once you get used to the idea) than a
  non-recursive solution.
• But a recursive solution may not be as efficient
  as a non-recursive solution of the same problem.

17
Real Life Recursions

• Recursive dreamer
• He dreams .
• He dreams that he dreams .
• He dreams that he dreams that he dreams ..
  .
• Natural Numbers Definition
• 1 1
• 2 1     1
• 3   1   1     1

18
Other Recursion Example

• Fibonacci numbers
• 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
• - where each number is the sum of the preceding
  two.
• Recursive definition
• F(0) 0
• F(1) 1
• F(n) F(n-1) F(n-2)

19
Recursion General Form

• How to write recursively?
• int rec(parameters)
• if(stopping condition)
• return stopping value
• value rec(revised parameters)
• return value

20
Example N! Recursion

• int fac(int n)
• int product
• // the base case
• if(n lt 1)
• return 1
• // the recursive part
• product n fac(n-1)
• return product
• void main()
• int number 3
• cout ltlt fac(number) ltlt endl

21
Execution trace

• fac(3)
• 3 lt 1 ? No.
• product3 3 fac(2)
• fac(2)
• 2 lt 1 ? No.
• product2 2 fac(1)
• fac(1)
• 1 lt 1 ? Yes.
• return 1
• product2 2 1 2
• return product2
• product3 3 2 6
• return product3
• fac(3) has the value 6

22
Exercise 4.1

• Write a recursive function for xy
• Suppose both x and y are intergers
• int exp(int x, int y)

23
Exercise 4.2

• zeros(10200) ?
• int zeros(int n)
• if(n0)
• return 1
• if(n lt 10)
• return 0
• if(n10 0)
• return 1 zeros(n/10)
• else
• return zeros(n/10)

24
Exercise 4.3
Write a recursive function to determine how many
factors m are part of n. For example, if n48
and m4, then the result is 2 (48443).