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CS 332: Algorithms Asymptotic Performance
Review: Asymptotic Performance ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Running Time ,[object Object],[object Object],[object Object],[object Object]
An Example: Insertion Sort ,[object Object],[object Object]
An Example: Insertion Sort ,[object Object],[object Object],30 10 40 20 1 2 3 4 i =  j =  key =  A[j] =  A[j+1] = 
An Example: Insertion Sort ,[object Object],[object Object],30 10 40 20 1 2 3 4 i = 2 j = 1 key = 10 A[j] = 30 A[j+1] = 10
An Example: Insertion Sort ,[object Object],[object Object],30 30 40 20 1 2 3 4 i = 2 j = 1 key = 10 A[j] = 30 A[j+1] = 30
An Example: Insertion Sort ,[object Object],[object Object],30 30 40 20 1 2 3 4 i = 2 j = 1 key = 10 A[j] = 30 A[j+1] = 30
An Example: Insertion Sort ,[object Object],[object Object],30 30 40 20 1 2 3 4 i = 2 j = 0 key = 10 A[j] =  A[j+1] = 30
An Example: Insertion Sort ,[object Object],[object Object],30 30 40 20 1 2 3 4 i = 2 j = 0 key = 10 A[j] =  A[j+1] = 30
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 20 1 2 3 4 i = 2 j = 0 key = 10 A[j] =  A[j+1] = 10
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 20 1 2 3 4 i = 3 j = 0 key = 10 A[j] =  A[j+1] = 10
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 20 1 2 3 4 i = 3 j = 0 key = 40 A[j] =  A[j+1] = 10
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 20 1 2 3 4 i = 3 j = 0 key = 40 A[j] =  A[j+1] = 10
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 20 1 2 3 4 i = 3 j = 2 key = 40 A[j] = 30 A[j+1] = 40
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 20 1 2 3 4 i = 3 j = 2 key = 40 A[j] = 30 A[j+1] = 40
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 20 1 2 3 4 i = 3 j = 2 key = 40 A[j] = 30 A[j+1] = 40
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 20 1 2 3 4 i = 4 j = 2 key = 40 A[j] = 30 A[j+1] = 40
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 20 1 2 3 4 i = 4 j = 2 key = 20 A[j] = 30 A[j+1] = 40
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 20 1 2 3 4 i = 4 j = 2 key = 20 A[j] = 30 A[j+1] = 40
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 20 1 2 3 4 i = 4 j = 3 key = 20 A[j] = 40 A[j+1] = 20
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 20 1 2 3 4 i = 4 j = 3 key = 20 A[j] = 40 A[j+1] = 20
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 40 1 2 3 4 i = 4 j = 3 key = 20 A[j] = 40 A[j+1] = 40
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 40 1 2 3 4 i = 4 j = 3 key = 20 A[j] = 40 A[j+1] = 40
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 40 1 2 3 4 i = 4 j = 3 key = 20 A[j] = 40 A[j+1] = 40
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 40 1 2 3 4 i = 4 j = 2 key = 20 A[j] = 30 A[j+1] = 40
An Example: Insertion Sort ,[object Object],[object Object],10 30 40 40 1 2 3 4 i = 4 j = 2 key = 20 A[j] = 30 A[j+1] = 40
An Example: Insertion Sort ,[object Object],[object Object],10 30 30 40 1 2 3 4 i = 4 j = 2 key = 20 A[j] = 30 A[j+1] = 30
An Example: Insertion Sort ,[object Object],[object Object],10 30 30 40 1 2 3 4 i = 4 j = 2 key = 20 A[j] = 30 A[j+1] = 30
An Example: Insertion Sort ,[object Object],[object Object],10 30 30 40 1 2 3 4 i = 4 j = 1 key = 20 A[j] = 10 A[j+1] = 30
An Example: Insertion Sort ,[object Object],[object Object],10 30 30 40 1 2 3 4 i = 4 j = 1 key = 20 A[j] = 10 A[j+1] = 30
An Example: Insertion Sort ,[object Object],[object Object],10 20 30 40 1 2 3 4 i = 4 j = 1 key = 20 A[j] = 10 A[j+1] = 20
An Example: Insertion Sort ,[object Object],[object Object],10 20 30 40 1 2 3 4 i = 4 j = 1 key = 20 A[j] = 10 A[j+1] = 20 Done!
Animating Insertion Sort ,[object Object],[object Object]
Insertion Sort ,[object Object],[object Object],What is the precondition for this loop?
Insertion Sort ,[object Object],[object Object],How many times will this loop execute?
Insertion Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Analyzing Insertion Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Analysis ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Upper Bound Notation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Insertion Sort Is O(n 2 ) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Big O Fact ,[object Object],[object Object],[object Object],[object Object],[object Object]
Lower Bound Notation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Asymptotic Tight Bound ,[object Object],[object Object],[object Object],[object Object]
Practical Complexity
Practical Complexity
Practical Complexity
Practical Complexity
Practical Complexity
Other Asymptotic Notations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Up Next ,[object Object],[object Object],[object Object]

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Lecture 2