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How many times is the print statement executed, wehre i,j,k ∈ Z? Explain

For i := 1 to 12 do

For j :=5 to 10 do

For k:=15 downto 8 do

Print (i-j)*k

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OMG! When you don't know what to do, try multiplying... –  jpalecek Oct 10 '12 at 0:27
    
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1 Answer

up vote 3 down vote accepted

Start inside and work out. The innermost loop executes once for each value of $k$ from $15$ down to $8$; that’s $15-7=8$ values, so the print statement is executed $8$ times every time the innermost loop is entered.

Now how often is the innermost loop entered? Once for each value of $j$ from $5$ to $10$, i.e., $10-4=6$ times. That is, every time the middle loop is entered, the innermost loop runs $6$ times, so the print statement is executed $6\cdot8=48$ times.

Can you finish it from there? How often is the middle loop entered?

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Thank you very much :) –  Peter Ji Oct 10 '12 at 0:56
    
@Peter: You’re welcome. –  Brian M. Scott Oct 10 '12 at 0:59
    
@BrianM.Scott: Is the print command executed when $k=8$? Or is it possible to stop the process when $k=8$? Will this depend on the program language? –  Sigur Oct 10 '12 at 1:44
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@Sigur: I’m assuming that downto works like to, which in every language that I’ve used includes the limit. –  Brian M. Scott Oct 10 '12 at 1:47
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