5. The recursive algorithm given below can be used to compute gcd(a, b) where a and b are non-negative integer, not both zero.
procedure gcd(a, b)
if a b then gcd(a, b) := = gcd (b, a)
else if a = 0 then gcd (a, b) = b
else if a = 1 then gcd (a, b) :
:=1
else if a and b are even then gcd(a, b) 2gcd(a/2, b/2) := else if a is odd and b is even then gcd(a, b) := gcd(a, b/2)
else gcd(a, b) := gcd(a, b - a)
Use this algorithm to compute
(a) gcd(124, 244)
(b) gcd (4424, 2111).u
Answers
Implementating the given algorithm in python 3, the greatest common divisors of (124 and 244) and (4424 and 2111) are 4 and 1 respectively.
The program implementation is given below and the output of the sample run is attached.
def gcd(a, b):
#initialize a function named gcd which takes in two parameters
if a>b:
#checks if a is greater than b
return gcd (b, a)
#if true interchange the Parameters and Recall the function
elif a == 0:
return b
elif a == 1:
return 1
elif((a%2 == 0)and(b%2==0)):
#even numbers leave no remainder when divided by 2, checks if a and b are even
return 2 * gcd(a/2, b/2)
elif((a%2 !=0) and (b%2==0)):
#checks if a is odd and B is even
return gcd(a, b/2)
else :
return gcd(a, b-a)
#since it's a recursive function, it recalls the function with new parameters until a certain condition is satisfied
print(gcd(124, 244))
print()
#leaves a space after the first output
print(gcd(4424, 2111))
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v = 54y = 0u = 6w = -48x = -1===================================================
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[tex]-6\begin{bmatrix}3 & -1 & 3\\8 & x & -9\\4 & -1 & y\end{bmatrix}= \begin{bmatrix}-18 & 6 & -18\\-48 & -6x & 54\\-24 & 6 & -6y\end{bmatrix}[/tex]
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-----------------------------
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The -48 in the first spot pairs up with the w in the other matrix. So we can see that w = -48. Similarly, we have v = 54.
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-----------------------------
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Question 19
A game consists of black and white pieces. The number of black pieces is 5 more than 3 times the white pieces. Seven white and 15 black pieces are removed each round. After several rounds, there are 3 white and 56 black pieces left. How many pieces were there in the beginning?
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Answer:
D. 213Step-by-step explanation:
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https://brainly.com/question/9682526
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