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**mantastrike****Member**- Registered: 2011-04-24
- Posts: 64

How many times will the innermost loop of the following algorithm be run? Assume n and n and k are positive integers.

Please help me with this with a detailed answer. You don't have to explain but please show some working.

for i : = 1 to 17

for j: = 1 to n

for k: = 1 to m

[Statements in body]

next k

next j

next i

Please help me guys! THANK YOU!!

I love this forum for being a great help!

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**mantastrike****Member**- Registered: 2011-04-24
- Posts: 64

gAr wrote:

can u plz tell me how you got this? can u plz show work?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,309

Hi mantastrike;

The innermost k loop goes from 1 to m. If a loop goes from 1 to 5, that is 5 times. If it goes from 1 to 100, that is 100 times. If it goes from 1 to m that is m times.

Now the j loop goes from 1 to n. That is n times. Each time the j loop counts once the k loop goes m times.

So the two inner loops are n*m

The i loop goes from 1 to 17. Each time the i loop executes the j and k loop execute n*m

So all three loop s are 17 * n * m

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**umasou****Member**- Registered: 2011-05-29
- Posts: 2

I have the same problem but different different values [assume a,b,c,d are all +ve]:

assume a ≤ b and c ≤ d

for j= a to b

for h = c to d

[Statements in body]

next h

next j

hmm..should there be more than 1 answer..?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,309

Hi umasou;

Welcome to the forum! There is still a unique answer. The body of the loops will executed ( b - a + 1 ) ( d - c + 1 ) times.

This is assuming an increment of 1.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**umasou****Member**- Registered: 2011-05-29
- Posts: 2

hiya. thanks for welcoming me , this place is cool.

I'm not clear with, if a=b, c=d, what will happen to the loop?

thanks again

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,309

If a = b then it will execute 1 time.

Use the formula, if a = b and c =d then the body will be executed:

( b - a + 1 ) ( d - c + 1 ) = ( 0 + 1) ( 0 + 1 ) = 1 time

And wait, I forgot to mention this. Why are you asking this question? All you have to do to answer this for yourself is program two loops and put a print statement between them. You are both missing the whole point of programming. It is to answer experimentally, questions like this.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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