CS253: Distribution-based Sort (2019)
1 like113 views
The document describes the bucket sort and radix sort algorithms. It shows the bucket sort algorithm sorting an array of integers by placing each integer into a corresponding bucket based on its value. It then puts the integers from each bucket back into the original array in sorted order. The document then describes the radix sort algorithm. It works by performing multiple passes of least significant digit (LSD) bucket sorts, sorting the integers based on each place value from right to left.
![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()](https://image.slidesharecdn.com/sortdistributionbased-190925013847/85/CS253-Distribution-based-Sort-2019-24-320.jpg)
![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](https://image.slidesharecdn.com/sortdistributionbased-190925013847/85/CS253-Distribution-based-Sort-2019-25-320.jpg)
![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()](https://image.slidesharecdn.com/sortdistributionbased-190925013847/85/CS253-Distribution-based-Sort-2019-70-320.jpg)
![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](https://image.slidesharecdn.com/sortdistributionbased-190925013847/85/CS253-Distribution-based-Sort-2019-71-320.jpg)
CS253: Distribution-based Sort (2019)
- 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