Problem 1
a) Compute the stable matching determined by Gale-Shapley algorithm for these
preferences when the Males propose to the Females.
Answer: A-W, B-V, C-X, D-Y, E-Z
b) Compute the stable matching determined by Gale-Shapley algorithm for these
preferences when the Females propose to the Males.
Answer: V-B, W-A, X-C, Y-D, Z-E
Problem 2
a) Describe an algorithm that solves the problem and give a brief argument as to why
your algorithm is correct.
Algorithm:
for (X in A){ loop every value in array A, store in variable X
for (Y in A){ loop every value in array A, store in variable Y
if (Y/X =V) test Y divided by X , if the result equal V
print X,Y print out X,Y , the printed results are two integers a, b
}
}
Argument:
For example:
Assume array A=[1,3,7,6],v=2;
when I loop X as 3 and loop Y as 6,
the result of Y divider by X is 2(equal to v)
so, 3,6 is the integers a,b.
b) Analyse the running time of your algorithm.
assume the amount of value in array A is n，running time：
inner for-loop is performed n times
outer for-loop is performed n times
Total 𝑇(𝑛)= 𝑂(𝑛 ∗ 𝑛)= 𝑂(𝑛2)
