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Lecture 9

Lecture 9. CSE 331 Sep 19, 2011. 6 more to go…. I’ll need confirmation in writing. No graded material will be handed back till I get this signed form from you!. Clarification on HW hints. Hint points to just one way of solving the problem. Reading Assignments.

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Lecture 9

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  1. Lecture 9 CSE 331 Sep 19, 2011

  2. 6 more to go… I’ll need confirmation in writing. No graded material will be handed back till I get this signed form from you!

  3. Clarification on HW hints Hint points to just one way of solving the problem

  4. Reading Assignments Sections 1.2, 2.1, 2.2 and 2.4 in [KT]

  5. Asymptotic Notation ≤ is O with glasses ≥ is Ω with glasses = is Θ with glasses

  6. Run time of an algorithm (Worst-case) run time T(n) for input size n Maximum number of steps taken by the algorithm for any input of size n

  7. g(n) is O(f(n)) c*f(n) for some c>0 g(n) n n0

  8. g(n) is Ω(f(n)) g(n) ε*f(n) for some ε>0 n n1

  9. g(n) is Θ(f(n)) c*f(n) for some c>0 g(n) is O(f(n))ANDg(n) is Ω(f(n)) g(n) ε*f(n) for some ε>0 n0 n1 n

  10. For the find algo from last lecture T(n) is Θ(n)

  11. Questions?

  12. Today’s agenda Analyzing the running time of the GS algo

  13. 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

  14. 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?

  15. 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

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

  17. 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

  18. Time to convert from array to linked list and vice versa?

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