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Flow of controlSequential

Executing instructions one by one, in exact order given

SelectionChoosing to execute a particular set of

statements depending on a condition

RepetitionExecuting a set of statements more than

one time (loops)

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Nesting

Similar items contained within

e.g., matryoshka dollshttp://hancocktownlibrary.blogspot.com/2007_11_01_archive.html

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Simple Nested IFs

if <condition A>if <condition B>

<action 1>else

<action 2>end

else<action 3>

end<action 4>

if <condition C><action 11>

elseif <condition D>

<action 12>else

<action 13>end

end<action 14>

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Alternative to Simple Nested IF

if <condition A>if <condition B>

<action 1>else

<action 2>end

else<action 3>

end<action 4>

if < A & B ><action 1>

endif < A & ~B >

<action 2>endif < ~A >

<action 3>end<action 4>

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Simple Nested Loops

for <control A><action 1>for <control B> <action 2>end<action 3>

end<action 4>

while <condition C><action 11>while <condition

D> <action 12> <change D>end<change C>

end<action 13>

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A Nested Loop Example

Problem: Use a Loop to create a Matrix M with n rows and m columns

The first row elements should get values equal to the number of their respective column

The values for the elements in the first column should be the number of their respective row

The rest of the elements get values equal to the sum of the element just above them and the element to their left

The program is interactive and prompts the user to enter the values for n and m

Sample M for n=4, m=5

1 2 3 4 5

2 4 7 11 16

3 7 14 25 41

4 11 25 50 91

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Recall … Design Steps for Loops

Identify a task that can be accomplished if some steps

are repeated

(These steps form the loop body)

Define a starting point

Define a stopping point

Keep track of (and measure) progress

Make sure the loop will stop!

If necessary use the “Break” command or the “Continue”

command

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n = input ('Enter the number of rows: ');m = input ('Enter the number of columns: ');

for k = 1:n % Start of the 1st For-end Loop for h = 1:m % Start of the 2nd For-end Loop (nested loop) if k == 1 % Start of the nested "if-elseif-else-end" M(k,h) = h; elseif h == 1 M (k, h) = k; else M(k,h) = M(k,h-1) + M(k-1,h); end % End of the if statement end % End of the 2nd For-end Loop (nested loop) end % End of the 1st For-end Loop M % Display M

Solution using 2 Nested “For-Loops”

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n = input ('Enter the number of rows ');m = input ('Enter the number of columns ');k = 1; while k <= n % Start of the 1st while-end Loop h = 1; while h <= m % Start of the 2nd while-end Loop if k == 1 % Start of the nested "if-elseif-else-end" M(k,h) = h; elseif h == 1 M (k, h) = k; else M(k,h) = M(k,h-1) + M(k-1,h); end % End of the if statement h = h + 1; end % End of the 2nd For-end Loop k = k + 1; end % End of the 1st For-end LoopM % Display M

Solution using 2 Nested “While-Loops”

Setup for Example 2

Determine whether a given number is prime:

Use the MATLAB rem() functionrem(x,y) returns the remainder from x/y

examples: rem(12, 5) is 2rem(24, 6) is 0rem(3, 5) is 3

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Algorithm to Determine if Prime

Check that number is > 0If number is 1, it is prime!Initialize divisor = 2Repeat:

let x = rem(number,divisor)if x == 0, then x is ‘not prime’, so

stop loopotherwise, set divisor = divisor + 1

If divisor == number, then number is prime!16

Solution to Determine if Primenumber = input('Please enter a positive integer: ');

if (number <= 0) %test validity of input

disp(‘not a positive integer; program ends');

elseif (number == 1) %and we’re done

disp('1 is indeed prime');

else

divisor = 2; %initialize factor value

while ((rem(number,divisor) ~= 0))

divisor = divisor + 1;

end

if (number == divisor)

fprintf('The number %d is prime\n',number);

else

fprintf('The number %d is NOT prime\n', number);

end

end17

Example 2: Find Primes

Find all the primes in a given range of numbers

Algorithm:obtain and check the range valuesstarting with the lower end, repeat:

if number is prime, print itif range is not complete, continue

with the next number

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What type of loop?

Solution for Find Primes in a Rangelowest = input('Please enter start of range (>=1): ');

highest = input('Please enter end of range: ');

if ((highest-lowest <= 0)||(lowest <= 1)) %test validity

disp('not an appropriate range; program ends');

else

disp('The primes within this range are: ');

for number = lowest:highest

divisor = 2; %initialize factor value

while ((rem(number,divisor) ~= 0))

divisor = divisor + 1;

end

if (number == divisor)

fprintf('%d ',number);

end

end

end19

One minor issue remains – can you find it? Hint: consider output from all cases…

Tracing Practice

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