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Lecture 28

Lecture 28. CSE 331 Nov 3, 2014. Mini project report due WED. Mini Project Report. Response to Feedback. Oct Piazza Participation Report. Mergesort algorithm. Input: a 1 , a 2 , …, a n. Output: Numbers in sorted order. MergeSort ( a, n ). If n = 1 return the order a 1.

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Lecture 28

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  1. Lecture 28 CSE 331 Nov 3, 2014

  2. Mini project report due WED

  3. Mini Project Report

  4. Response to Feedback

  5. Oct Piazza Participation Report

  6. Mergesort algorithm Input: a1, a2, …, an Output: Numbers in sorted order MergeSort( a, n ) If n = 1 return the order a1 aL = a1,…, an/2 aR = an/2+1,…, an return MERGE ( MergeSort(aL, n/2), MergeSort(aR, n/2) )

  7. Correctness Input: a1, a2, …, an Output: Numbers in sorted order By induction on n MergeSort( a, n ) If n = 1 return the order a1 aL = a1,…, an/2 aR = an/2+1,…, an return MERGE ( MergeSort(aL, n/2), MergeSort(aR, n/2) ) Inductive step follows from correctness of MERGE

  8. Rest of today’s agenda Analyze runtime of mergesort algorithm

  9. Divide and Conquer Divide up the problem into at least two sub-problems Recursively solve the sub-problems “Patch up” the solutions to the sub-problems for the final solution

  10. Improvements on a smaller scale Greedy algorithms: exponential  poly time (Typical) Divide and Conquer: O(n2)  asymptotically smaller running time

  11. Multiplying two numbers Given two numbers a and b in binary a=(an-1,..,a0) and b = (bn-1,…,b0) Running time of primary school algorithm? Compute c = a x b

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