Here is a sample of how the Gale-Shapley algorithm would solve a stable matching problem:

INPUT

Xavier Amy Bertha Clare

Yancey Bertha Amy Clare

Zeus Amy Bertha Clare

Amy Yancey Xavier Zeus

Bertha Xavier Yancey Zeus

Clare Xavier Yancey Zeus

Gale-Shapley ALGORITHM RUN script

1. Xavier proposes to Amy.

2. Amy pairs with Xavier because she is free.

3. Yancey proposes to Bertha.

4. Bertha pairs with Yancey because she is free.

5. Zeus proposes to Amy.

6. Amy rejects Zeus because she likes her current match, Xavier, more.

7. Zeus remains free.

8. Zeus proposes to Bertha.

9. Bertha rejects Zeus because she likes her current match, Yancey, more.

10. Zeus remains free.

11. Zeus proposes to Clare.

12. Clare pairs with Zeus because she is free.

Now everyone has a match.

Here Are The Matches:

WOMEN MEN

Amy Xavier

Bertha Yancey

Clare Zeus

Your Assignment:

Process the following input in the same manner the sample input was

processed, as illustrated above.

Produce the same kind of script (step-by-step) of the actions taken by

the Gale-Shapley algorithm, plus write what the final matching is.

The men are Abe, Ben, Cal, and Dan.

The women are Eve, Fey, Gem, and Hil.

The preference lists are

Abe Hil Fey Gem Eve

Ben Gem Hil Fey Eve

Cal Gem Fey Hil Eve

Dan Gem Hil Eve Fey

Eve Abe Ben Dan Cal

Fey Ben Cal Abe Dan

Gem Ben Abe Dan Cal

Hil Abe Ben Cal Dan

My professor assigned this question for my Theory of Algorithms class. Can someone please answer the question precisely how he wants it so I can understand it?