Procedural Languages

Example: Compute the greatest common divisor (GCD) of two natural numbers. Thanks to Euclid we know that

1. GCD(x,x) = x

2. GCD(x,y) = GCD(y,x)

3. x > y => GCD(x,y) = GCD(x-y,y)

This allows to compute the GCD of two natural numbers x and y using following method:

1. If x equals y stop.

2. If x < y, subtract y from x and continue with step 1.

3. Subtract x from y and continue with step 1.

When this algorithm stops, the GCD is to be found in x.

This algorithm can be directly expressed in procedural high-level languages:
GCD.java

while (x != y) { if (x > y) { x = x - y; } else { y = y - x; } }

1.	GCD(x,x) = x
2.	GCD(x,y) = GCD(y,x)
3.	x > y => GCD(x,y) = GCD(x-y,y)

1.	If x equals y stop.
2.	If x < y, subtract y from x and continue with step 1.
3.	Subtract x from y and continue with step 1.