Assignment1-Sangtian的MacBook Pro-2.pdf

Assignment1-Sangtian的MacBook Pro-2.pdf - CSE373...

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CSE373 Assignment 1 Sangtian Wang, 111578610 Question 1. We use M i to represent man and W i represent woman, where i [1 , n ]. The pref- erence list for man M i can be represent as, for example, { M i : W 1 , W 2 , ..., W n } , which means he prefers W 1 to W 2 , and his least preferred woman is W n . And the notation is same for women’s prefer list. We use ( M i , W i ) to represent a matching pair. Question 1.(a). The worst-case for a woman is that she matched with their least favorite man. In some cases, every woman can be matched with her least favorite woman. We start from n = 2 and construct worst cases for women. - n = 2. - Men’s prefer list: { M 1 : W 1 , W 2 } , { M 2 : W 1 , W 2 } - Women’s prefer list: { W 1 : M 2 , M 1 } , { W 2 : M 1 , M 2 } - Worst case for women: ( M 1 , W 1 ), ( M 2 , W 2 ). Every woman is matched with her least favorite man. This case comes from M 1 chooses first and M 2 chooses second. - n = 3. - Men’s prefer list: { M 1 : W 1 , W 2 , W 3 } , { M 2 : W 1 , W 2 , W 3 } , { M 3 : W 1 , W 2 , W 3 } - Women’s prefer list: { W 1 : M 3 , M 2 , M 1 } , { W 2 : M 1 , M 3 , M 2 } , { W 3 : M 1 , M 2 , M 3 } - Worst case for women: ( M 1 , W 1 ), ( M 2 , W 2 ), ( M
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