please help me understand the euclids algorithm

This is a discussion on please help me understand the euclids algorithm within the C++ Programming forums, part of the General Programming Boards category; i don't understand why this works: Code: int gcd(int a, int b) { if (b == 0) return a; return ...

  1. #1
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    please help me understand the euclids algorithm

    i don't understand why this works:

    Code:
    int gcd(int a, int b)
    {
        if (b == 0)
            return a;
    
        return gcd(b, a % b);
    }
    so if i have the fracking 10/4 and i call gcd(10,4) it would return 2? how the hell does it work? i really don't understand this....recursion-wah?

  2. #2
    & the hat of GPL slaying Thantos's Avatar
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    trace it out:
    10 , 4 : 10 doesn't == 0 so we call again
    4, 2 : 2 doesn't == 0 so we call again
    2, 0 : 0 == 0 so we return 2

    http://en.wikipedia.org/wiki/Euclidean_algorithm

  3. #3
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    yeah but i really don't understand HOW this works....i don't want to use this code if i don't understand it

  4. #4
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    would this bit of code work????
    Code:
    int gcd (int numer, int denom)
    {
    	if (denom == 0)
    		return numer;
    	return gcd(denom,numer % denom);
    }
    
    //
    //
    //
    void reduceRational (int& numer, int& denom)
    {
    	int factor = gcd (numer, denom);
    	numer /= factor;
    	denom /= factor;
    }
    ????

  5. #5
    & the hat of GPL slaying Thantos's Avatar
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    Did you read the link?

  6. #6
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    Quote Originally Posted by Thantos
    Did you read the link?

    ya but it didn't make a whole lot of sense...what about my code?

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    Code:
    int gcd(int a, int b)
    {
    Above is a function that takes two ints and gives them the name a and b

    Code:
        if (b == 0)
    This checks to see if b is equal to zero

    Code:
            return a;
    if b was equal to zero than return a
    Code:
        return gcd(b, a % b);
    }
    if b does not equal zero then the function calls it self over and over again until b finally equals zero

    so in the above is you called the function with the two ints 10 and 4 like so:
    Code:
    gcd(10, 4);
    it will check to see if 4 is eqaul to zero and if it is not then it recalls the function using gcd(4, 10%4) which is really gcd(4, 2) (the % finds the remainder of the two numbers). So now we repeat the same proccess. 2 does not equal zero so we do gcd(2, 4%2) which is gcd(2,0). Now that b (0) is equal to zero we return a which is 2.

    I am not sure how to explain it any easier.

  8. #8
    & the hat of GPL slaying Thantos's Avatar
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    the reduceRational function should work and the gcd should work. However the gcd parameter names are a little misleading since its only the numerator and the denomitor during the first call.

  9. #9
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    Quote Originally Posted by Bitphire
    Code:
    int gcd(int a, int b)
    {
    Above is a function that takes two ints and gives them the name a and b

    Code:
        if (b == 0)
    This checks to see if b is equal to zero

    Code:
            return a;
    if b was equal to zero than return a
    Code:
        return gcd(b, a % b);
    }
    if b does not equal zero then the function calls it self over and over again until b finally equals zero

    so in the above is you called the function with the two ints 10 and 4 like so:
    Code:
    gcd(10, 4);
    it will check to see if 4 is eqaul to zero and if it is not then it recalls the function using gcd(4, 10%4) which is really gcd(4, 2) (the % finds the remainder of the two numbers). So now we repeat the same proccess. 2 does not equal zero so we do gcd(2, 4%2) which is gcd(2,0). Now that b (0) is equal to zero we return a which is 2.

    I am not sure how to explain it any easier.
    i understand HOW the function actually goes about working

    i don't understand WHY it works...WHY does calling itself over and over get you the gcd????????????\





    what about my code? does that work?

  10. #10
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    Maybe think of it like this:
    Code:
    int gcd1(int a, int b)
    {
        if (b == 0)
            return a;
        int x = gcd2(b, a % b);
        return x; 
    }
    
    int gcd2(int a, int b)
    {
        if (b == 0)
            return a;
        in y = gcd3(b, a % b);
        return y;
    }
    int gcd3(int a, int b)
    {
        if (b == 0)
            return a;
    
       }
    Last edited by 7stud; 03-02-2005 at 07:47 PM.

  11. #11
    & the hat of GPL slaying Thantos's Avatar
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    try using the non recursive version and see if that helps you understand it better.

    Note this is a very old algoirthm created by a freakin genius.
    The proof for this may be outside of your comprehension.

  12. #12
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    Quote Originally Posted by Thantos
    try using the non recursive version and see if that helps you understand it better.

    Note this is a very old algoirthm created by a freakin genius.
    The proof for this may be outside of your comprehension.
    ouch. try me.

  13. #13
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    i don't understand WHY it works...WHY does calling itself over and over get you the gcd
    Then why did you post any code?

  14. #14
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    i dunno...i just wanna know how this works so when my teacher asks me im not all "well i got it off the internet"

  15. #15

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