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

1. Sort:
Distribution-based
Data Structures and Algorithms
Emory University
Jinho D. Choi

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
32
5 4 2 3 1 5
1 2 3 4 5
Add each key to an appropriate bucket.

9. Bucket Sort - Integer
2
32 5
4 2 3 1 5
1 2 3 4 5
Add each key to an appropriate bucket.

10. Bucket Sort - Integer
2
32 54
2 3 1 5
1 2 3 4 5
Add each key to an appropriate bucket.

11. Bucket Sort - Integer
2
32 54
2
3 1 5
1 2 3 4 5
Add each key to an appropriate bucket.

12. Bucket Sort - Integer
2
32 54
2 3
1 5
1 2 3 4 5
Add each key to an appropriate bucket.

13. Bucket Sort - Integer
2
32 54
2 3
1
5
1 2 3 4 5
Add each key to an appropriate bucket.

14. Bucket Sort - Integer
2
32 54
2 3
1
5
1 2 3 4 5
Add each key to an appropriate bucket.

15. Bucket Sort - Integer
2
32 54
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
32 54
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
54
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
32
54
2 31
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
32
5
42 31
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
32 542 31 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
32 542 31 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
32 542 31 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 320201 113 132

27. LSD Radix Sort
3
120 34 344 320201 113 132
0 1 2 3 4

28. LSD Radix Sort
3
120 34 344 320201 113 132
0 1 2 3 4
1st LSD

29. LSD Radix Sort
3
120
34 344 320201 113 132
0 1 2 3 4
1st LSD

30. LSD Radix Sort
3
120 34
344 320201 113 132
0 1 2 3 4
1st LSD

31. LSD Radix Sort
3
120 34
344 320
201
113 132
0 1 2 3 4
1st LSD

32. LSD Radix Sort
3
120 34
344
320
201
113 132
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
344320
201
1
13
132
0 1 2 3 4
1st LSD

35. LSD Radix Sort
3
120 34
344320
201
1
13
132
0 1 2 3 4
1st LSD

36. LSD Radix Sort
3
120 34
344320
201
1
13132
0 1 2 3 4
1st LSD

37. LSD Radix Sort
3
120
34
344
320
201
1
13132
0 1 2 3 4
1st LSD

38. LSD Radix Sort
3
120
34
344
320 201 1
13132
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 13132
0 1 2 3 4
1st LSD

41. LSD Radix Sort
3
120 34 344320 201 1 13132
0 1 2 3 4
1st LSD

42. LSD Radix Sort
3
120 34 344320 201 1 13132
0 1 2 3 4
1st LSD 2nd LSD

43. LSD Radix Sort
3
120
34 344320 201 1 13132
0 1 2 3 4
1st LSD 2nd LSD

44. LSD Radix Sort
3
120
34 344
320
201 1 13132
0 1 2 3 4
1st LSD 2nd LSD

45. LSD Radix Sort
3
120
34 344
320
201
1 13132
0 1 2 3 4
1st LSD 2nd LSD

46. LSD Radix Sort
3
120
34 344
320
201
1
13132
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
320201 1 13
132
0 1 2 3 4
1st LSD 2nd LSD

54. LSD Radix Sort
3
120 34
344
320201 1 13 132
0 1 2 3 4
1st LSD 2nd LSD

55. LSD Radix Sort
3
120 34 344320201 1 13 132
0 1 2 3 4
1st LSD 2nd LSD

56. LSD Radix Sort
3
120 34 344320201 1 13 132
0 1 2 3 4
1st LSD 2nd LSD 3rd LSD

57. LSD Radix Sort
3
120 34 344320
201
1 13 132
0 1 2 3 4
1st LSD 2nd LSD 3rd LSD

58. LSD Radix Sort
3
120 34 344320
2011
13 132
0 1 2 3 4
1st LSD 2nd LSD 3rd LSD

59. LSD Radix Sort
3
120 34 344320
2011
13
132
0 1 2 3 4
1st LSD 2nd LSD 3rd LSD

60. LSD Radix Sort
3
120
34 344320
2011
13
132
0 1 2 3 4
1st LSD 2nd LSD 3rd LSD

61. LSD Radix Sort
3
120
34 344
3202011
13
132
0 1 2 3 4
1st LSD 2nd LSD 3rd LSD

62. LSD Radix Sort
3
120
34 344
3202011
13 132
0 1 2 3 4
1st LSD 2nd LSD 3rd LSD

63. LSD Radix Sort
3
120
34
344
3202011
13 132
0 1 2 3 4
1st LSD 2nd LSD 3rd LSD

64. LSD Radix Sort
3
120
34
344
3202011
13 132
0 1 2 3 4
1st LSD 2nd LSD 3rd LSD

65. LSD Radix Sort
3
120
34
344
320201
1 13
132
0 1 2 3 4
1st LSD 2nd LSD 3rd LSD

66. LSD Radix Sort
3
12034
344
320201
1 13 132
0 1 2 3 4
1st LSD 2nd LSD 3rd LSD

67. LSD Radix Sort
3
12034
344
320
2011 13 132
0 1 2 3 4
1st LSD 2nd LSD 3rd LSD

68. LSD Radix Sort
3
12034 3443202011 13 132
0 1 2 3 4
1st LSD 2nd LSD 3rd LSD

69. LSD Radix Sort
3
12034 3443202011 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