CS253: Distribution-based Sort (2019)

https://github.com/emory-courses/cs253

Transcript

1. Sort: Distribution-based Data Structures and Algorithms Emory University Jinho D. Choi https://github.com/emory-courses/cs253
4. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5
5. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5
6. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
7. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
8. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
9. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
10. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
11. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
12. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
13. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
14. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
15. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket. Put all keys in each bucket back to the array.
16. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket. Put all keys in each bucket back to the array.
17. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket. Put all keys in each bucket back to the array.
18. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket. Put all keys in each bucket back to the array.
19. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket. Put all keys in each bucket back to the array.
20. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket. Put all keys in each bucket back to the array.
21. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket. Put all keys in each bucket back to the array. How many comparisons & assignments?
22. Bucket Sort - Integer 2 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket. Put all keys in each bucket back to the array. How many comparisons & assignments? How much extra spaces?
23. BucketSort.java public abstract class BucketSort<T extends Comparable<T>> extends AbstractSort<T> { protected List<Deque<T>> buckets; /** @param numBuckets the total number of buckets. */ public BucketSort(int numBuckets) { super(null); buckets = Stream.generate(ArrayDeque<T>::new) .limit(numBuckets) .collect(Collectors.toList()); } ArrayDeque
24. protected void sort(T[] array, int beginIndex, int endIndex, Function<T, T> f) { // add each element in the input array to the corresponding bucket for (int i = beginIndex; i < endIndex; i++) buckets.get(getBucketIndex(array[i], f)).add(array[i]); // merge elements in all buckets to the input array for (Deque<T> bucket : buckets) { while (!bucket.isEmpty()) array[beginIndex++] = bucket.remove(); } } /** * @param key a comparable key. * @param f takes one argument of type T, and return a value of type T (optional). * @return the index of the bucket that the key should be inserted. */ abstract protected int getBucketIndex(T key, Function<T, T> f); getBucketIndex() bucket.removeLast()
25. IntegerBucketSort.java public class IntegerBucketSort extends BucketSort<Integer> { private final int GAP; /** * @param min the minimum integer (inclusive). * @param max the maximum integer (exclusive). */ public IntegerBucketSort(int min, int max) { super(max - min); GAP = -min; } @Override public void sort(Integer[] array, int beginIndex, int endIndex) { sort(array, beginIndex, endIndex, null); } @Override protected int getBucketIndex(Integer key, Function<Integer, Integer> f) { return key + GAP; } } GAP
26. LSD Radix Sort 3 120 34 344 320 201 1 13 132
27. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4
28. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
29. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
30. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
31. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
32. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
33. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
34. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
35. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
36. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
37. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
38. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
39. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
40. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
41. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
42. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
43. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
44. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
45. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
46. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
47. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
48. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
49. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
50. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
51. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
52. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
53. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
54. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
55. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
56. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
57. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
58. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
59. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
60. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
61. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
62. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
63. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
64. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
65. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
66. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
67. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
68. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
69. LSD Radix Sort 3 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD How many comparisons & assignments?
70. RadixSort.java public abstract class RadixSort extends BucketSort<Integer> { public RadixSort() { super(10); } @Override protected int getBucketIndex(Integer key, Function<Integer, Integer> f) { return f.apply(key) % 10; } protected int getMaxBit(Integer[] array, int beginIndex, int endIndex) { Integer max = Arrays.stream(array, beginIndex, endIndex) .reduce(Integer::max) .orElse(null); return (max != null && max > 0) ? (int)Math.log10(max) + 1 : 0; } throw new UnsupportedOperationException() getMaxBit()
71. LSDRadixSort.java public class LSDRadixSort extends RadixSort { @Override public void sort(Integer[] array, int beginIndex, int endIndex) { int maxBit = getMaxBit(array, beginIndex, endIndex); for (int bit = 0; bit < maxBit; bit++) { int div = (int) Math.pow(10, bit); sort(array, beginIndex, endIndex, k -> k / div); } } } k -> k / div