1/ COP 3503 FALL 2012 SHAYAN JAVED LECTURE 16. Programming Fundamentals using Java
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1 1/ COP 3503 FALL 2012 SHAYAN JAVED LECTURE 16 Programming Fundamentals using Java
2 2/ 137 Sorting Another crucial problem. Used everywhere: Sorting numbers (prices/grades/ratings/etc..) Names Dates Rating
3 3/ 137 Sorting When shopping online (Amazon for ex.):
4 4/ 137 Sorting We designed a RedBox system where you can sort by different criteria
5 5/ 137 Sorting We designed a RedBox system where you can sort by different criteria How can you sort in Java?
6 6/ 137 Sorting We designed a RedBox system where you can sort by different criteria How can you sort in Java? Arrays.sort(..) but how does it work?
7 7/ 137 Sorting We designed a RedBox system where you can sort by different criteria How can you sort in Java? Arrays.sort(..) but how does it work? Going to look at a few different algorithms.
8 8/ 137 Sorting Let s see if we can come up with one on our own...
9 9/ 137 Sorting Let s see if we can come up with one on our own... array A (N = A.length): i A sorted array A: i A
10 10/ 137 Sorting Compare values at indices 0 and 1 first. i A
11 11/ 137 Sorting Compare values at indices 0 and 1 first. i A
12 12/ 137 Sorting Compare values at indices 0 and 1 first. i A Swap if A[1] < A[0]: i A
13 13/ 137 Sorting Compare values at indices 1 and 2. i A
14 14/ 137 Sorting Compare values at indices 1 and 2. i A Is A[2] < A[1]? No: i A
15 15/ 137 Sorting Compare values at indices 2 and 3. i A
16 16/ 137 Sorting Compare values at indices 2 and 3. i A Is A[3] < A[2]? Yes! Swap. i A
17 17/ 137 Sorting Keep repeating this process until you reach the end of the array.
18 18/ 137 Sorting Keep repeating this process until you reach the end of the array. Result: i A
19 19/ 137 Sorting Largest value in the array is now at the end of the array. Result: i A
20 20/ 137 Sorting What do we do next? i A
21 21/ 137 Sorting What do we do next? Repeat the process. i A
22 22/ 137 Sorting What do we do next? Repeat the process. Result: i A
23 23/ 137 Sorting Have the second largest value at index N - 2 Result: i A
24 24/ 137 Sorting Have the second largest value at index N - 2 How many more times to sort? Result: i A
25 25/ 137 Sorting Have the second largest value at index N - 2 How many more times to sort? Total of N times Result: i A
26 26/ 137 Sorting Have the second largest value at index N - 2 How many more times to sort? Total of N times Result: i A
27 27/ 137 Bubble Sort This algorithm is known as Bubble Sort
28 28/ 137 Bubble Sort This algorithm is known as Bubble Sort The max value bubbles to the end of the list at each pass.
29 29/ 137 Bubble Sort This algorithm is known as Bubble Sort The max value bubbles to the end of the list at each pass. Simplest sorting algorithm.
30 30/ 137 Bubble Sort Let s write the code for it:
31 31/ 137 Bubble Sort Let s write the code for it: static void bubblesort(int[] A, int N) { for(int i = 0; i < N; i++) { for (int j = 1; j < N; j++) { if (A[j] < A[j-1]) { // swap int temp = A[j]; A[j] = A[j-1]; A[j-1] = temp; } } } }
32 32/ 137 Bubble Sort Let s write the code for it: static void bubblesort(int[] A, int N) { for(int i = 0; i < N; i++) { for (int j = 1; j < N; j++) { if (A[j] < A[j-1]) { // swap int temp = A[j]; A[j] = A[j-1]; A[j-1] = temp; } } } }
33 33/ 137 Bubble Sort Let s write the code for it: static void bubblesort(int[] A, int N) { for(int i = 0; i < N; i++) { for (int j = 1; j < N; j++) { if (A[j] < A[j-1]) { // swap int temp = A[j]; A[j] = A[j-1]; A[j-1] = temp; } } } }
34 34/ 137 Bubble Sort Let s write the code for it: static void bubblesort(int[] A, int N) { for(int i = 0; i < N; i++) { for (int j = 1; j < N; j++) { if (A[j] < A[j-1]) { // swap int temp = A[j]; A[j] = A[j-1]; A[j-1] = temp; } } } }
35 35/ 137 Bubble Sort Let s write the code for it: static void bubblesort(int[] A, int N) { for(int i = 0; i < N; i++) { for (int j = 1; j < N; j++) { if (A[j] < A[j-1]) { // swap int temp = A[j]; A[j] = A[j-1]; A[j-1] = temp; } } } }
36 36/ 137 Bubble Sort Efficiency How efficient is it?
37 37/ 137 Bubble Sort Efficiency How efficient is it? What is the O(..) of the algorithm?
38 38/ 137 Bubble Sort Efficiency Let s look at one pass.
39 39/ 137 Bubble Sort Efficiency Let s look at one pass. i A
40 40/ 137 Bubble Sort Efficiency Let s look at one pass. To: i A i A
41 41/ 137 Bubble Sort Efficiency Let s look at one pass. To: i A i A What s the efficiency of this pass?
42 42/ 137 Bubble Sort Efficiency Let s look at one pass. To: i A i A What s the efficiency of this pass? O(N)
43 43/ 137 Bubble Sort Efficiency How many of these passes do we have?
44 44/ 137 Bubble Sort Efficiency How many of these passes do we have? N passes.
45 45/ 137 Bubble Sort Efficiency How many of these passes do we have? N passes. Efficiency: O(N) * N = O(N 2 )
46 46/ 137 Bubble Sort Efficiency How can we make the algorithm a little more efficient/faster?
47 47/ 137 Bubble Sort Efficiency static void bubblesort(int[] A, int N) { for(int i = 0; i < N; i++) { for (int j = 1; j < (N-i); j++) { if (A[j] < A[j-1]) { // swap int temp = A[j]; A[j] = A[j-1]; A[j-1] = temp; } } } }
48 48/ 137 Bubble Sort Efficiency static void bubblesort(int[] A, int N) { for(int i = 0; i < N; i++) { for (int j = 1; j < (N-i); j++) { if (A[j] < A[j-1]) { // swap int temp = A[j]; A[j] = A[j-1]; A[j-1] = temp; } } } } We know the end keeps getting sorted properly
49 49/ 137 Bubble Sort Efficiency But efficiency is still O(N 2 )
50 50/ 137 Bubble Sort Efficiency But efficiency is still O(N 2 ) Thus bubble sort isn t really a good sorting algorithm...
51 51/ 137 Bubble Sort Efficiency But efficiency is still O(N 2 ) Thus bubble sort isn t really a good sorting algorithm... Going to look at other alternatives.
52 52/ 137 Find the minimum in an array How will you find the minimum number in an array? i A
53 53/ 137 Find the minimum in an array min = A[0] for i = 1 to A.length 1: if A[i] < min: min = A[i]
54 54/ 137 Find the minimum in an array What can we do with the minimum value?
55 55/ 137 Find the minimum in an array What can we do with the minimum value? Swap it with the value at index 0
56 56/ 137 Find the minimum in an array What can we do with the minimum value? Swap it with the value at index 0 Repeat for the rest of the indices...
57 57/ 137 Find the minimum in an array What can we do with the minimum value? Swap it with the value at index 0 Repeat for the rest of the indices... Result: Sorted array!
58 58/ 137 Selection Sort static void selectionsort(int[] A) { for (int i = 0; i < A.length; i++) { int min = i; // index of minimum value for(int j = i; j <= A.length; j++) { if ( A[j] < A[min]) min = j; } // swap if (j!= i) swap(a, i, j); } }
59 59/ 137 Selection Sort static void selectionsort(int[] A) { for (int i = 0; i < A.length - 1; i++) { int min = i; // index of minimum value for(int j = i; j <= A.length; j++) { if ( A[j] < A[min]) min = j; } // swap if (j!= i) swap(a, i, j); } }
60 60/ 137 Selection Sort static void selectionsort(int[] A) { for (int i = 0; i < A.length - 1; i++) { int min = i; // index of minimum value for(int j = i; j <= A.length; j++) { if ( A[j] < A[min]) min = j; } // swap if (j!= i) swap(a, i, j); } }
61 61/ 137 Selection Sort static void selectionsort(int[] A) { for (int i = 0; i < A.length - 1; i++) { int min = i; // index of minimum value for(int j = i + 1; j < A.length; j++) { if ( A[j] < A[min]) min = j; } // swap if (j!= i) swap(a, i, j); } }
62 62/ 137 Selection Sort static void selectionsort(int[] A) { for (int i = 0; i < A.length - 1; i++) { int min = i; // index of minimum value for(int j = i + 1; j < A.length; j++) { if ( A[j] < A[min]) min = j; } // swap if (j!= i) swap(a, i, j); } }
63 63/ 137 Selection Sort static void selectionsort(int[] A) { for (int i = 0; i < A.length - 1; i++) { int min = i; // index of minimum value for(int j = i + 1; j < A.length; j++) { if ( A[j] < A[min]) min = j; } // swap if (min!= i) swap(a, i, min); } }
64 64/ 137 Selection Sort Efficiency O(N 2 )
65 65/ 137 Selection Sort Efficiency O(N 2 ) Better than Bubble Sort
66 66/ 137 Selection Sort Efficiency O(N 2 ) Better than Bubble Sort But rarely used
67 67/ 137 Insertion Sort Concept: Go through every element, insert it in it s correct position in the sub-array before it
68 68/ 137 Insertion Sort array A (N = A.length): i A
69 69/ 137 Insertion Sort array A (N = A.length): Value = 55 i A Look at sub-array between indices 0 and 0
70 70/ 137 Insertion Sort array A (N = A.length): Value = 55 i A Look at sub-array between indices 0 and 0 Already sorted, let s look at next index
71 71/ 137 Insertion Sort array A (N = A.length): Value = 19 i A Look at sub-array between indices 0 and 1
72 72/ 137 Insertion Sort array A (N = A.length): Value = 19 i A Look at sub-array between indices 0 and 1 Is Value < A[0]? Yes!
73 73/ 137 Insertion Sort array A (N = A.length): Value = 19 i A Look at sub-array between indices 0 and 1 Is Value < A[0]? Yes! Move 55 forward by 1 index.
74 74/ 137 Insertion Sort array A (N = A.length): Value = 19 i A Look at sub-array between indices 0 and 1 Is Value < A[0]? Yes! Move 55 forward by 1 index. Put 19 at index 0 (reached the beginning)
75 75/ 137 Insertion Sort array A (N = A.length): Value = 100 i A Look at sub-array between indices 0 and 2
76 76/ 137 Insertion Sort array A (N = A.length): Value = 100 i A Look at sub-array between indices 0 and 2 Is Value < A[1]? No.
77 77/ 137 Insertion Sort array A (N = A.length): Value = 100 i A Look at sub-array between indices 0 and 2 Is Value < A[1]? No. Continue
78 78/ 137 Insertion Sort array A (N = A.length): Value = 45 i A Look at sub-array between indices 0 and 3
79 79/ 137 Insertion Sort array A (N = A.length): Value = 45 i A Look at sub-array between indices 0 and 3 Is Value < A[2]? Yes.
80 80/ 137 Insertion Sort array A (N = A.length): Value = 45 i A Look at sub-array between indices 0 and 3 Is Value < A[2]? Yes. Move A[2] forward by one position
81 81/ 137 Insertion Sort array A (N = A.length): Value = 45 i A Look at sub-array between indices 0 and 3 Is Value < A[1]? Yes.
82 82/ 137 Insertion Sort array A (N = A.length): Value = 45 i A Look at sub-array between indices 0 and 3 Is Value < A[1]? Yes.
83 83/ 137 Insertion Sort array A (N = A.length): Value = 45 i A Look at sub-array between indices 0 and 3 Is Value < A[1]? Yes. Move A[1] forward by one position
84 84/ 137 Insertion Sort array A (N = A.length): Value = 45 i A Look at sub-array between indices 0 and 3 Is Value < A[0]? No.
85 85/ 137 Insertion Sort array A (N = A.length): Value = 45 i A Look at sub-array between indices 0 and 3 Is Value < A[0]? No.
86 86/ 137 Insertion Sort array A (N = A.length): Value = 45 i A Look at sub-array between indices 0 and 3 Is Value < A[0]? No. STOP!
87 87/ 137 Insertion Sort array A (N = A.length): Value = 45 i A Look at sub-array between indices 0 and 3 Is Value < A[0]? No. STOP! Put Value at index 1 (where we stopped)
88 88/ 137 Insertion Sort array A (N = A.length): Value = 45 i A Look at sub-array between indices 0 and 3 Note how this sub-array is sorted.
89 89/ 137 Insertion Sort array A (N = A.length): Value = 45 i A Look at sub-array between indices 0 and 3 Note how this sub-array is sorted. Repeat for Value = 87 & sub-array between 0 and 4
90 90/ 137 Insertion Sort Exercise: Write the code by yourselves.
91 91/ 137 Insertion Sort Exercise: Write the code by yourselves. (Without looking it up online of course...) Try to challenge yourself
92 92/ 137 Insertion Sort Efficiency Also O(N 2 )
93 93/ 137 Insertion Sort Efficiency Also O(N 2 ) But:
94 94/ 137 Insertion Sort Efficiency Also O(N 2 ) But: Very fast for sorted/partially sorted arrays.
95 95/ 137 Insertion Sort Efficiency Also O(N 2 ) But: Very fast for sorted/partially sorted arrays. Efficient for small data sets
96 96/ 137 Insertion Sort Efficiency Also O(N 2 ) But: Very fast for sorted/partially sorted arrays. Efficient for small data sets Online: Sort a list as it receives input
97 97/ 137 Insertion Sort Efficiency Also O(N 2 ) But: Very fast for sorted/partially sorted arrays. Efficient for small data sets Online: Sort a list as it receives input Better than Bubble and Selection Sort
98 98/ 137 Sorting None of the algorithms seen so far are good enough
99 99/ 137 Sorting None of the algorithms seen so far are good enough Especially Bubble and Selection
100 100/ 137 Sorting None of the algorithms seen so far are good enough Especially Bubble and Selection Merge Sort and QuickSort are the best algorithms
101 101/ 137 Sorting None of the algorithms seen so far are good enough Especially Bubble and Selection Merge Sort and QuickSort are the best algorithms Going to look at Merge Sort
102 102/ 137 Merge Sort Concept: Divide a list equally into two
103 103/ 137 Merge Sort Concept: Divide a list equally into two Sort the two lists
104 104/ 137 Merge Sort Concept: Divide a list equally into two Sort the two lists Merge them
105 105/ 137 Merge Sort Concept: Divide a list equally into two Sort the two lists Merge them Repeat process recursively
106 106/ 137 Merge Sort i A
107 107/ 137 Merge Sort i A Split
108 108/ 137 Merge Sort i A Split
109 109/ 137 Merge Sort i A Split
110 110/ 137 Merge Sort i A Split Now Sort and Merge
111 111/ 137 Merge Sort
112 112/ 137 Merge Sort 0 55 Already sorted Already Sorted
113 113/ 137 Merge Sort 0 55 Already sorted Already Sorted Merge the two in the proper order:
114 114/ 137 Merge Sort 0 55 Already sorted Already Sorted Merge the two in the proper order: s Sorted!
115 115/ 137 Merge Sort
116 116/ 137 Merge Sort Already sorted Sort it:
117 117/ 137 Merge Sort Already sorted Sort it:
118 118/ 137 Merge Sort Already sorted Now Merge: Sort it:
119 119/ 137 Merge Sort
120 120/ 137 Merge Sort Both already sorted.
121 121/ 137 Merge Sort Both already sorted. Merge: i A
122 122/ 137 Merge Sort mergesort(a[]): if size(a) <= 1: return A // split into two lists middleindex = size(a)/2 left[] = A[0 middleindex-1] right[] = A[middleIndex size(a)-1] left = mergesort(left) right = mergesort(right) result[] = merge(left, right) return result
123 123/ 137 Merge Sort mergesort(a[]): if size(a) <= 1: return A // split into two lists middleindex = size(a)/2 left[] = A[0 middleindex-1] right[] = A[middleIndex size(a)-1] left = mergesort(left) right = mergesort(right) result[] = merge(left, right) return result
124 124/ 137 Merge Sort mergesort(a[]): if size(a) <= 1: return A // split into two lists middleindex = size(a)/2 left[] = A[0 middleindex-1] right[] = A[middleIndex size(a)-1] left = mergesort(left) right = mergesort(right) result[] = merge(left, right) return result
125 125/ 137 Merge Sort mergesort(a[]): if size(a) <= 1: return A // split into two lists middleindex = size(a)/2 left[] = A[0 middleindex-1] right[] = A[middleIndex size(a)-1] left = mergesort(left) right = mergesort(right) result[] = merge(left, right) return result
126 126/ 137 Merge Sort mergesort(a[]): if size(a) <= 1: return A // split into two lists middleindex = size(a)/2 left[] = A[0 middleindex-1] right[] = A[middleIndex size(a)-1] left = mergesort(left) right = mergesort(right) result[] = merge(left, right) return result
127 127/ 137 Merge Sort mergesort(a[]): if size(a) <= 1: return A // split into two lists middleindex = size(a)/2 left[] = A[0 middleindex-1] right[] = A[middleIndex size(a)-1] left = mergesort(left) right = mergesort(right) result[] = merge(left, right) return result
128 128/ 137 Merge Sort mergesort(a[]): if size(a) <= 1: return A // split into two lists middleindex = size(a)/2 left[] = A[0 middleindex-1] right[] = A[middleIndex size(a)-1] left = mergesort(left) right = mergesort(right) result[] = merge(left, right) return result
129 129/ 137 Merge Sort mergesort(a[]): if size(a) <= 1: return A // split into two lists middleindex = size(a)/2 left[] = A[0 middleindex-1] right[] = A[middleIndex size(a)-1] left = mergesort(left) right = mergesort(right) result[] = merge(left, right) return result
130 130/ 137 Merge Sort How to merge two sorted lists?
131 131/ 137 Merge Sort How to merge two sorted lists? Figure that out yourself
132 132/ 137 Merge Sort How to merge two sorted lists? Figure that out yourself Try to to do it on paper first
133 133/ 137 Merge Sort How to merge two sorted lists? Figure that out yourself Try to to do it on paper first Exercise: Implement Merge Sort Can it be done iteratively?
134 134/ 137 Merge Sort Efficiency O(NlogN)
135 135/ 137 Merge Sort Efficiency O(NlogN) Much faster than the previous algorithms
136 136/ 137 Merge Sort Efficiency O(NlogN) Much faster than the previous algorithms Used in java.util.arrays.sort( )
137 137/ 137 Summary Sorting is a very important problem. Bubble, Selection and Insertion Sort. Insertion Sort great for small arrays. Merge Sort much faster than others
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