Design and Analysis of Computer AlgorithmChapter 4, Lecture notes of Advanced Algorithms

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Design and Analysis of Computer Algorithm November 26, 2019 1

Design and Analysis of

Computer Algorithm

Chapter 4

Dr. M. Mezher

Department of Computer Science

Design and Analysis of Computer Algorithm November 26, 2019 2

Divide and Conquer

Merge Sort

Insertion Sort

Mergesort: Divide Step

Mergesort: Divide Step

Mergesort: Combine Step

Mergesort: Algorithm

Mergesort: Running Time

Design and Analysis of Computer Algorithm November 26, 2019 11

SORTING

An Example: Insertion Sort

InsertionSort(A, n) { for i = 2 to n { key = A[i] j = i - 1; while (j > 0) and (A[j] > key) { A[j+1] = A[j] j = j - 1 } A[j+1] = key } }

i =  j =  key = 

A[j] =  A[j+1] = 

An Example: Insertion Sort

InsertionSort(A, n) { for i = 2 to n { key = A[i] j = i - 1; while (j > 0) and (A[j] > key) { A[j+1] = A[j] j = j - 1 } A[j+1] = key } }

i = 2 j = 1 key = 10

A[j] = 30 A[j+1] = 10

An Example: Insertion Sort

InsertionSort(A, n) { for i = 2 to n { key = A[i] j = i - 1; while (j > 0) and (A[j] > key) { A[j+1] = A[j] j = j - 1 } A[j+1] = key } }

i = 2 j = 1 key = 10

A[j] = 30 A[j+1] = 30

An Example: Insertion Sort

InsertionSort(A, n) { for i = 2 to n { key = A[i] j = i - 1; while (j > 0) and (A[j] > key) { A[j+1] = A[j] j = j - 1 } A[j+1] = key } }

i = 2 j = 0 key = 10

A[j] =  A[j+1] = 30

An Example: Insertion Sort

InsertionSort(A, n) { for i = 2 to n { key = A[i] j = i - 1; while (j > 0) and (A[j] > key) { A[j+1] = A[j] j = j - 1 } A[j+1] = key } }

i = 2 j = 0 key = 10

A[j] =  A[j+1] = 10

An Example: Insertion Sort

InsertionSort(A, n) { for i = 2 to n { key = A[i] j = i - 1; while (j > 0) and (A[j] > key) { A[j+1] = A[j] j = j - 1 } A[j+1] = key } }

i = 3 j = 0 key = 10

A[j] =  A[j+1] = 10