lecture_18

lecture_18 - BIOS 735 Statistical Computing Michael Wu...

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BIOS 735: Statistical Computing Michael Wu Lecture 18: Sorting Algorithms and Linear Algebra (1) October 11, 2011 Michael Wu (Lecture 18) BIOS 735 October 11, 2011 1 / 13
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Runtime Analysis: Common Sorting Algorithms Last class, we started talking about big Omicron notation and some issues in runtime analysis. In CS, sorting algorithms are commonly used to make the point. Bubble Sort Selection Sort Insertion Sort Shell Sort Merge Sort Quick Sort Radix Sort Heap Sort etc etc etc We cover some of these for the sake of completeness. Michael Wu (Lecture 18) BIOS 735 October 11, 2011 2 / 13
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Runtime Analysis: Bubble Sort set.seed(100) a = sample(1:10, 10 , replace = F); a Bubble = function(a, print = F) { n = length(a) for (i in 1:n){ for (i in seq(n-1)) { if (a[i+1]< a[i]) { temp = a[i] a[i] = a[i+1] a[i+1] = temp } } if (print) print(a) } return(a) } Bubble(a) Bubble(a, T) What is the runtime?? Michael Wu (Lecture 18) BIOS 735 October 11, 2011 3 / 13
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Runtime Analysis: Selection Sort set.seed(100) a = sample(1:10, 10 , replace = F); a Selection = function(a, print = F) { n = length(a) for (i in 1:(n-1)) { k = i for (j in (i+1):n) { if (a[j]<a[k]) k = j; } temp = a[k] a[k] = a[i] a[i] = temp if (print) print(a) } return(a) } Selection(a) Selection(a, T) What is the runtime?? Michael Wu (Lecture 18) BIOS 735 October 11, 2011 4 / 13
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Runtime Analysis: Quick Sort set.seed(100) a = sample(1:10, 10 , replace = F); a Quick = function(a, print = F) { if (print) print(a) if (length(a) <= 1) {
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lecture_18 - BIOS 735 Statistical Computing Michael Wu...

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