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Lecture 10

Lecture 10. CSE 331 Sep 21, 2012. HW 2 due today. Place Q2, Q3 and Q4 in separate piles. I will not accept HWs after 1:15pm. Other HW related stuff. HW 3 has been posted online: see blog/piazza. Solutions to HW 2 at the END of the lecture. Graded HW 1: pickup from TAs next week. EaGL-V.

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Lecture 10

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  1. Lecture 10 CSE 331 Sep 21, 2012

  2. HW 2 due today Place Q2, Q3 and Q4 in separate piles I will not accept HWs after 1:15pm

  3. Other HW related stuff HW 3 has been posted online: see blog/piazza Solutions to HW 2 at the END of the lecture Graded HW 1: pickup from TAs next week

  4. EaGL-V http://www.cse.buffalo.edu/events/theory-V/

  5. Gale-Shapley Algorithm Intially all men and women are free While there exists a free woman who can propose Let w be such a woman and m be the best man she has not proposed to w proposes to m If m is free (m,w) get engaged Else (m,w’) are engaged If m prefers w’ to w w remains free Else (m,w) get engaged and w’ is free Output the engaged pairs as the final output

  6. Implementation Steps How to represent the input? How do we find a free woman w? How would w pick her best unproposed man m? How do we know who m is engaged to? How do we decide if m prefers w’ to w?

  7. Arrays and Linked Lists n numbers a1,a2,…,an Last Front a1 an 1 a3 a1 a2 a2 2 3 a3 Array Linked List O(1) O(i) Access ith element O(n) (O(log n) if sorted) O(n) Is e present? O(n) Insert an element O(1) given pointer n an Delete an element O(n) O(1) given pointer Static vs Dynamic Static Dynamic

  8. Today’s agenda O(n2) implementation of the Gale-Shapley algorithm More practice with run time analysis

  9. Gale-Shapley Algorithm At most n2 iterations Intially all men and women are free While there exists a free woman who can propose Let w be such a woman and m be the best man she has not proposed to w proposes to m O(1) timeimplementation If m is free (m,w) get engaged Else (m,w’) are engaged If m prefers w’ to w w remains free Else (m,w) get engaged and w’ is free Output the engaged pairs as the final output

  10. HW 2 due today Place Q2, Q3 and Q4 in separate piles I will not accept HWs after 1:15pm

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