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Analysis of MergeSort Algorithm Using Divide and Conquer Strategy

This mini-project report covers the MergeSort algorithm's correctness, runtime analysis, Divide and Conquer approach, and improvements. It explains the Divide and Conquer strategy, patching up solutions, and enhancements to achieve better efficiency.

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Analysis of MergeSort Algorithm Using Divide and Conquer Strategy

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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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