Algorithm - Mergesort & Quicksort

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PRESENTATION

Course title : Algorithm - Mergesort & Quicksort CSE-225

• Submitted By: • Submitted ToName: Istiaque Ahmed

ShuvoId:141311057

5th batch ,5th semesterSec-BDept. Of CseVarendra University,rajshahi

Name: Atiquer Rahman Sarkar, CSE, Varendra University

Quick sort Algorithm

Merge sort Algorithm

Merge Sort

Merge sort is based on Divide and conquer method. It takes the list to be sorted and divide it in half to create two unsorted lists. The two unsorted lists are then sorted and merged to get a sorted list. The two unsorted lists are sorted by continually calling the merge-sort algorithm; we eventually get a list of size 1 which is already sorted. The two lists of size 1 are then merged.

Example sort Example

The most well known algorithm design strategy:

1.Divide instance of problem into two or more smaller instances

2.Solve smaller instances recursively

3.Obtain solution to original (larger) instance by combining these solutions

Divide-and-conquer Technique

subproblem 2 of size n/2

subproblem 1 of size n/2

a solution to subproblem 1

a solution tothe original problem

a solution to subproblem 2

a problem of size n

Divide and Conquer Examples

• Sorting: mergesort and quicksort

• Tree traversals

• Matrix multiplication-Strassen’s algorithm

• Closest pair problem

Merge Sort Algorithm

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14 23 45 98 6 33 42 67

Merge

23 45 98 33 42 6714 6

Merge

23 45 98 6 42 67

6

14 33

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14 45 98 6 42 67

6 14

23 33

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14 23 98 6 42 67

6 14 23

45 33

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14 23 98 6 33 67

6 14 23 33

45 42

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14 23 98 6 33 42

6 14 23 33 42

45 67

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14 23 45 6 33 42

6 14 23 33 42 45

98 67

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14 23 45 98 6 33 42 67

6 14 23 33 42 45 67

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14 23 45 98 6 33 42 67

6 14 23 33 42 45 67 98

Quick sort Algorithm

QUICKSORT (A, p, r)

1. if p < r2. q = PARTITION (A, p, r)3. QUICKSORT (A, p, q-1)4. QUICKSORT (A, q -1, r)

Partitioning the array

PARTITION (A, p, r)

1. X=A[r]2. i =p -13. for j = p to r -14. if A[j] X5. i = i + 16. exchange A[i] with A[j]7. exchange A[i+1] with A[r]8. return i+1