factorial algorithm in pseudo code

Question

I've been given the following algorithm, that takes a positive integer K and returns a value:

X = 1
Y = 1
while X ≠ K do
    X = X + 1
    Y = Y * x
return Y

I'm supposed to figure out what it returns.

As it happens, I know the answer — it returns the factorial of K — but I don't understand why.

How do you go about figuring out what this pseudocode does?

Do you understand all the notations used? For example, do you know what X = X + 1 means? — ruakh
– ruakh, Commented Jul 20, 2013 at 16:43
Start by making a table of the values of X and Y for each round of the while loop asuming e.g. K = 5. — Terje D.
– Terje D., Commented Jul 20, 2013 at 16:46
@ruakh yes that bit i understand, i guess the main bit i dont understand @ Terje D. is the k bit and how it works, thanks again — Hi There
– Hi There, Commented Jul 20, 2013 at 16:47
The code in the loop is repeated as long as X is not equal to K. For each round X is increased by one (and eventually becoming equal to K), and Y is multiplied by the new value of X. — Terje D.
– Terje D., Commented Jul 20, 2013 at 17:09
The algorithm is wrong. Consider K=0, yet fac 0 = 1 per defintion. — Ingo
– Ingo, Commented Jul 20, 2013 at 19:04

rnbguy · Accepted Answer · 2013-07-20 16:54:51Z

1

X = 1 <- this is counter which you gonna multiply in every step
Y = 1 <- this is to store the cumulative product after each step
while X ≠ K do <- until you reach K
    X = X + 1 <- increase X
    Y = Y * X <- multiply with increased X
return Y <- return the product

So in the loop the cumulative product goes like this 1 -> 1*2 - > 2*3 -> 6*4 -> ... -> 1*2*..*(K-1)*K which is K!

answered Jul 20, 2013 at 16:54

rnbguy

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G.Srinivas Kishan · Accepted Answer · 2013-07-20 17:07:33Z

0

Now let's assume that K is 5. Therefore the factorial of 5 is 120. Then as you enter the loop X value is 2 and y gets the value 2.(1*2) Then the value of X is 3 after getting into loop, which then makes the value of Y 6 because (3*2). Then the value of X is 4 after getting into loop, which then makes the value of Y 24 because (4*6). Then the value of X is 5 after getting into loop, which then makes the value of Y 120. Then since X==Y the while loop exits and Y value which is the factorial is returned.

answered Jul 20, 2013 at 17:07

G.Srinivas Kishan

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Fallen · Accepted Answer · 2013-07-20 18:59:58Z

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this piece of code can be simply rewritten as (in C/C++/Java),

for(X=1;X<=K;X++){
    Y=Y*X;
}

Now it describes it self :-)

answered Jul 20, 2013 at 18:59

Fallen

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