CP222 Computer Science II. Searching and Sorting
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1 CP222 Computer Science II Searching and Sorting
2 New Boston Dynamics wheeled robot Tech News!
3 Tech News! New Boston Dynamics wheeled robot Man charged with arson based on pacemaker data
4 Quiz! How do you determine the order of a recursive method? What's the difference between a greedy recursive algorithm and a non-greedy one? What is recursive backtracking and how is it useful?
5 Searching and Sorting Given a data structure, how do we find a particular element? How long does it take? How can we put data into sorted order? How can we do it quickly?
6 Suppose we want to write a program to check if a bingo is legal in Scrabble. We have a dictionary of legal Scrabble words.
7 Is Bingo Legal? // Assume we have an ArrayList of legal words // called words public boolean islegal(string possiblebingo) { for (int i = 0; i < words.size(); i++) { if (possiblebingo.equals(words.get(i))) { return true; } } return false; }
8 What is the time complexity of islegal()? Best case? Average case? Worst case?
9 This process is called linear search.
10 Do humans use linear search when checking if words are legal when playing Scrabble?
11 If we assume the wordlist is sorted, can we search with fewer comparisons? Let's try writing pseudocode for a faster search.
12 Binary Search // Assume words is in sorted order islegal(possiblebingo, start, end): if start == end: return false else: nextindex = (start + end) / 2 current = words[nextindex] if (current == possiblebingo) { return true; } else if (current < possiblebingo) { return islegal(possiblebingo, nextindex + 1, end) } else { return islegalhelper(possiblebingo, start, nextindex - 1) }
13 OK, binary search is faster. How do we get the wordlist in sorted order in the first place?
14 Sorting Problem [ 8, 3, 1, 7, 9, 2, 4 ] [ 1, 2, 3, 4, 7, 8, 9 ]
15 How do humans sort?
16 Selection Sort Algorithm Find smallest element left to be sorted This is done by linear search Put it at the end of the sorted part of the list For the first smallest, put it at the very beginning of the list The next smallest goes at position 2, etc.
17 Selection Sort [ 8, 3, 1, 7, 9, 2, 4 ]
18 Selection Sort [ 8, 3, 1, 7, 9, 2, 4 ] Scan list (linearly) for smallest element
19 Selection Sort [ 8, 3, 1, 7, 9, 2, 4 ] Here's the smallest.
20 Selection Sort [ 8, 3, 1, 7, 9, 2, 4 ] Flip the position of the smallest with the next unsorted value.
21 Selection Sort [ 1, 3, 8, 7, 9, 2, 4 ] Flip the position of the smallest with the next unsorted value.
22 Selection Sort [ 1, 3, 8, 7, 9, 2, 4 ] Part of the list is now sorted.
23 Selection Sort [ 1, 3, 8, 7, 9, 2, 4 ] Find the smallest element not in the sorted part of the list.
24 Selection Sort [ 1, 3, 8, 7, 9, 2, 4 ] Here's the next smallest.
25 Selection Sort [ 1, 3, 8, 7, 9, 2, 4 ] Flip it with the first unsorted element.
26 Selection Sort [ 1, 2, 8, 7, 9, 3, 4 ] Flip it with the first unsorted element.
27 Insertion Sort Algorithm Maintain two parts of the list: unsorted and sorted For each unsorted element, insert it into the sorted part of the list in the correct location This insertion may require shifting values over to make room
28 Insertion Sort [ 8, 3, 1, 7, 9, 2, 4 ]
29 Insertion Sort [ 8, 3, 1, 7, 9, 2, 4 ] The sorted part of the array starts out as just the first value.
30 Insertion Sort [ 8, 3, 1, 7, 9, 2, 4 ] The rest of the list is unsorted.
31 Insertion Sort [ 8, 3, 1, 7, 9, 2, 4 ] Start with the next unsorted element.
32 Insertion Sort [ 8, 3, 1, 7, 9, 2, 4 ] Insert it in the correct location of the sorted part of the list. Here it needs to go before the 8.
33 Insertion Sort [ 8, 3, 1, 7, 9, 2, 4 ] There isn't space before the 8, so we have to shift the 8 up.
34 Insertion Sort [ 8, 3, 1, 7, 9, 2, 4 ] Before we shift the 8, we store the 3 somewhere else so it is not lost. key = 3
35 Insertion Sort [ 8, 8, 1, 7, 9, 2, 4 ] 8 is now shifted. key = 3
36 Insertion Sort [ 3, 8, 1, 7, 9, 2, 4 ] Now put the key value in its correct location. key = 3
37 Insertion Sort [ 3, 8, 1, 7, 9, 2, 4 ] Now this part of the list is sorted.
38 Insertion Sort [ 3, 8, 1, 7, 9, 2, 4 ] Repeat the process for the next unsorted element.
39 Insertion Sort [ 3, 8, 1, 7, 9, 2, 4 ] key = 1 Set the key.
40 Insertion Sort [ 3, 8, 1, 7, 9, 2, 4 ] key = 1 Find its insertion point.
41 Insertion Sort [ 3, 8, 1, 7, 9, 2, 4 ] key = 1 Shift both 3 and 8 up. Start by shifting 8. Why?
42 Insertion Sort [ 3, 8, 8, 7, 9, 2, 4 ] key = 1 8 was shifted.
43 Insertion Sort [ 3, 3, 8, 7, 9, 2, 4 ] key = 1 3 was shifted.
44 Insertion Sort [ 1, 3, 8, 7, 9, 2, 4 ] key = 1 Insert the key.
45 InsertionSort.java vs. SelectionSort.java
46 Bubble Sort Algorithm Bubble up larger values to the end of the list Scan through the unbubbled elements two at a time If the second of the two elements is smaller, flip their positions Now make the second element the new first and get the next element from the list as the new second
47 Bubble Sort [ 8, 3, 1, 7, 9, 2, 4 ] Compare the first two elements.
48 Bubble Sort [ 8, 3, 1, 7, 9, 2, 4 ] The second one is smaller, so flip them.
49 Bubble Sort [ 3, 8, 1, 7, 9, 2, 4 ] The second one is smaller, so flip them.
50 Bubble Sort [ 3, 8, 1, 7, 9, 2, 4 ] Compare the next group of two.
51 Bubble Sort [ 3, 8, 1, 7, 9, 2, 4 ] The second one is smaller, so flip them.
52 Bubble Sort [ 3, 1, 8, 7, 9, 2, 4 ] The second one is smaller, so flip them.
53 Bubble Sort [ 3, 1, 8, 7, 9, 2, 4 ] See how 8 is bubbling up?
54 Bubble Sort [ 3, 1, 8, 7, 9, 2, 4 ] Compare next two. Second is smaller.
55 Bubble Sort [ 3, 1, 7, 8, 9, 2, 4 ] Flip them.
56 Bubble Sort [ 3, 1, 7, 8, 2, 4, 9 ] At the end of the process the largest element has bubbled up.
57 Bubble Sort [ 3, 1, 7, 8, 2, 4, 9 ] Now bubble up the next largest element.
58 Bubble Sort [ 1, 3, 7, 2, 4, 8, 9 ] Stop bubbling up when you reach the values that have already bubbled.
59 Obama Bubble
60 Sorting 2.0 How do faster sorting algorithms work?
61 Merge Sort Algorithm Split the list in half For each half: If half is large, split again If half is tiny, merge with other half
62 Merge Sort [ 8, 2, 5, 4, 6, 9, 7, 1 ] Split in the middle
63 Merge Sort [ 8, 2, 5, 4, 6, 9, 7, 1 ] [ 8, 2, 5, 4 ] [ 6, 9, 7, 1 ] Split in the middle
64 Merge Sort [ 8, 2, 5, 4, 6, 9, 7, 1 ] [ 8, 2, 5, 4 ] [ 6, 9, 7, 1 ] Sublists are still big, split again
65 Merge Sort [ 8, 2, 5, 4, 6, 9, 7, 1 ] [ 8, 2, 5, 4 ] [ 6, 9, 7, 1 ] [ 8, 2 ] [ 5, 4 ] [ 6, 9 ] [ 7, 1 ]
66 Merge Sort Even two elements is too [ big! 8, 2, 5, 4, 6, 9, 7, 1 ] Split again [ 8, 2, 5, 4 ] [ 6, 9, 7, 1 ] [ 8, 2 ] [ 5, 4 ] [ 6, 9 ] [ 7, 1 ]
67 Merge Sort [ 8, 2, 5, 4, 6, 9, 7, 1 ] [ 8, 2, 5, 4 ] [ 6, 9, 7, 1 ] [ 8, 2 ] [ 5, 4 ] [ 6, 9 ] [ 7, 1 ] [8] [2] [5] [4] [6] [9] [7] [1]
68 Merge Sort [ 8, 2, 5, 4, 6, 9, 7, 1 ] Now they're small enough! [ 8, 2, 5, 4 ] [ 6, 9, 7, 1 ] Merge them up. [ 8, 2 ] [ 5, 4 ] [ 6, 9 ] [ 7, 1 ] [8] [2] [5] [4] [6] [9] [7] [1]
69 Merge Sort [ 8, 2, 5, 4, 6, 9, 7, 1 ] Compare 8 and 2. 2 is smaller so it [ 8, 2, 5, 4 ] [ 6, 9, 7, 1 ] goes first. [ 8, 2 ] [ 5, 4 ] [ 6, 9 ] [ 7, 1 ] [8] [2] [5] [4] [6] [9] [7] [1]
70 Merge Sort Compare 8 and 2. 2 is smaller so it goes first. [ 8, 2, 5, 4, 6, 9, 7, 1 ] [ 8, 2, 5, 4 ] [ 6, 9, 7, 1 ] [ 2, 8 ] [ 5, 4 ] [ 6, 9 ] [ 7, 1 ] [5] [4] [6] [9] [7] [1]
71 Merge Sort Notice that this sublist is sorted. [ 8, 2, 5, 4, 6, 9, 7, 1 ] [ 8, 2, 5, 4 ] [ 6, 9, 7, 1 ] [ 2, 8 ] [ 5, 4 ] [ 6, 9 ] [ 7, 1 ] [5] [4] [6] [9] [7] [1]
72 Merge Sort [ 8, 2, 5, 4, 6, 9, 7, 1 ] Merge up 5 and 4. [ 8, 2, 5, 4 ] [ 6, 9, 7, 1 ] [ 2, 8 ] [ 5, 4 ] [ 6, 9 ] [ 7, 1 ] [5] [4] [6] [9] [7] [1]
73 Merge Sort 4 is smaller so it [ 8, 2, goes 5, 4, first. 6, 9, 7, 1 ] [ 8, 2, 5, 4 ] [ 6, 9, 7, 1 ] [ 2, 8 ] [ 4, 5 ] [ 6, 9 ] [ 7, 1 ] [6] [9] [7] [1]
74 Merge Sort Do the other two. [ 8, 2, 5, 4, 6, 9, 7, 1 ] [ 8, 2, 5, 4 ] [ 6, 9, 7, 1 ] [ 2, 8 ] [ 4, 5 ] [ 6, 9 ] [ 1, 7 ]
75 Now merge up these two sublists. Merge Sort [ 8, 2, 5, 4, 6, 9, 7, 1 ] Remember, each sublist is in order. [ 8, 2, 5, 4 ] [ 6, 9, 7, 1 ] [ 2, 8 ] [ 4, 5 ] [ 6, 9 ] [ 1, 7 ]
76 Compare 2 to 4. One of those must be the smallest value. Merge Sort [ 8, 2, 5, 4, 6, 9, 7, 1 ] Why? [ 8, 2, 5, 4 ] [ 6, 9, 7, 1 ] [ 2, 8 ] [ 4, 5 ] [ 6, 9 ] [ 1, 7 ]
77 Merge Sort 2 is smallest so it merges up. [ 8, 2, 5, 4, 6, 9, 7, 1 ] [ 2, 8, 5, 4 ] [ 6, 9, 7, 1 ] [ 8 ] [ 4, 5 ] [ 6, 9 ] [ 1, 7 ]
78 Merge Sort Now compare 8 to 4. One must be the next smallest. [ 8, 2, 5, 4, 6, 9, 7, 1 ] [ 2, 8, 5, 4 ] [ 6, 9, 7, 1 ] [ 8 ] [ 4, 5 ] [ 6, 9 ] [ 1, 7 ]
79 Merge Sort 4 is the next smallest. [ 8, 2, 5, 4, 6, 9, 7, 1 ] [ 2, 4, 5, 8 ] [ 6, 9, 7, 1 ] [ 8 ] [ 5 ] [ 6, 9 ] [ 1, 7 ]
80 Merge Sort Do the last two. [ 8, 2, 5, 4, 6, 9, 7, 1 ] [ 2, 4, 5, 8 ] [ 6, 9, 7, 1 ] [ 6, 9 ] [ 1, 7 ]
81 Merge Sort Do the same for the other half. [ 8, 2, 5, 4, 6, 9, 7, 1 ] [ 2, 4, 5, 8 ] [ 1, 6, 7, 9 ]
82 Merge Sort [ 8, 2, 5, 4, 6, 9, 7, 1 ] [ 2, 4, 5, 8 ] [ 1, 6, 7, 9 ] Merge up the last two sublists in the same way.
83 Quick Sort Algorithm Choose a partition element (usually the middle element in the list) Move all elements smaller than the partition to the left Move all elements larger than the partition to the right
84 Quick Sort [ 8, 2, 5, 4, 6, 9, 1 ] Choose partition element as the middle element
85 Quick Sort [ 8, 2, 5, 4, 6, 9, 1 ] Search for a value on the left that is bigger than the partition element.
86 Quick Sort [ 8, 2, 5, 4, 6, 9, 1 ] Search for a value on the right that is smaller than the partition element.
87 Quick Sort [ 1, 2, 5, 4, 6, 9, 8 ] Flip those two values
88 Quick Sort [ 1, 2, 5, 4, 6, 9, 8 ] Find any other such elements
89 Quick Sort [ 1, 2, 4, 5, 6, 9, 8 ] Find any other such elements
90 Quick Sort [ 1, 2, 4, 5, 6, 9, 8 ] Now do the same process for both sides of the partition.
91 Quick Sort [ 1, 2, 4, 5, 6, 9, 8 ] Two new partitions.
92 Radix Sort Algorithm Sort elements into buckets one digit at a time Bucket 0 holds all elements with least sig. digit of 0 Bucket 1 holds all elements with least sig. digit of 1 Repeat the process k times where k is the length of the longest element in digits Use queues to simplify the process
93 Radix Sort [ 134, 15, 75, 366, 211, 401 ]
94 Radix Sort [ 134, 15, 75, 366, 211, 401 ] queue1: queue4: queue5: queue6:
95 Radix Sort [ 134, 15, 75, 366, 211, 401 ] queue1: queue4: queue5: queue6: We have queues for 0-9, but some aren't yet necessary to be shown.
96 Radix Sort [ 134, 15, 75, 366, 211, 401 ] queue1: queue4: queue5: Enqueue the elements based on the least sig. digit. queue6:
97 Radix Sort [ 134, 15, 75, 366, 211, 401 ] queue1: queue4: 134 queue5: queue6:
98 Radix Sort [ 134, 15, 75, 366, 211, 401 ] queue1: queue4: 134 queue5: 15 queue6:
99 Radix Sort [ 134, 15, 75, 366, 211, 401 ] queue1: queue4: 134 queue5: 15, 75 queue6:
100 Radix Sort [ 134, 15, 75, 366, 211, 401 ] queue1: queue4: 134 queue5: 15, 75 queue6: 366
101 Radix Sort [ 134, 15, 75, 366, 211, 401 ] queue1: 211 queue4: 134 queue5: 15, 75 queue6: 366
102 Radix Sort [ 134, 15, 75, 366, 211, 401 ] queue1: 211, 401 queue4: 134 queue5: 15, 75 queue6: 366
103 Radix Sort [ 134, 15, 75, 366, 211, 401 ] queue1: 211, 401 queue4: 134 queue5: 15, 75 queue6: 366 Done enqueueing! Now dequeue the queues in order back into the array.
104 Radix Sort [ 211 ] queue1: 211, 401 queue4: 134 queue5: 15, 75 queue6: 366
105 Radix Sort [ 211, 401 ] queue1: 401 queue4: 134 queue5: 15, 75 queue6: 366
106 Radix Sort [ 211, 401, 134 ] queue1: queue4: 134 queue5: 15, 75 queue6: 366
107 Radix Sort [ 211, 401, 134, 15 ] queue1: queue4: queue5: 15, 75 queue6: 366
108 Radix Sort [ 211, 401, 134, 15, 75 ] queue1: queue4: queue5: 75 queue6: 366
109 Radix Sort [ 211, 401, 134, 15, 75, 366 ] queue1: queue4: queue5: queue6: 366
110 Radix Sort [ 211, 401, 134, 15, 75, 366 ] queue0: queue1: queue3: queue6: queue7: Done dequeueing! Now enqueue the elements based on the second digit.
111 Radix Sort [ 211, 401, 134, 15, 75, 366 ] queue0: queue1: 211 queue3: queue6: queue7:
112 Radix Sort [ 211, 401, 134, 15, 75, 366 ] queue0: 401 queue1: 211 queue3: queue6: queue7:
113 Radix Sort [ 211, 401, 134, 15, 75, 366 ] queue0: 401 queue1: 211 queue3: 134 queue6: queue7:
114 Radix Sort [ 211, 401, 134, 15, 75, 366 ] queue0: 401 queue1: 211, 15 queue3: 134 queue6: queue7:
115 Radix Sort [ 211, 401, 134, 15, 75, 366 ] queue0: 401 queue1: 211, 15 queue3: 134 queue6: queue7: 75
116 Radix Sort [ 211, 401, 134, 15, 75, 366 ] queue0: 401 queue1: 211, 15 queue3: 134 queue6: 366 queue7: 75
117 Radix Sort [ 211, 401, 134, 15, 75, 366 ] queue0: 401 queue1: 211, 15 queue3: 134 queue6: 366 queue7: 75 Now dequeue again.
118 Radix Sort [ 401, 211, 15, 134, 366, 75 ] queue0: queue1: queue3: queue6: queue7:
119 Radix Sort [ 401, 211, 15, 134, 366, 75 ] queue0: queue1: queue2: queue3: queue4: Now enqueue based on the final digit.
120 Radix Sort [ 401, 211, 15, 134, 366, 75 ] queue0: 15, 75 queue1: 134 queue2: 211 queue3: 366 queue4: 401
121 Radix Sort [ 15, 75, 134, 211, 366, 401 ] queue0: queue1: queue2: queue3: queue4: Final dequeue and we're done!
122 Radix sort time complexity?
123 Radix with non-integers?
124 The Sorting Challenge
125 BREAK!
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