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CS323: Sort - Distribution-based

Jinho Choi, profile picture
Jinho Choi

The document discusses bucket sort, a distribution-based sorting algorithm. It works by distributing the elements of an array into buckets representing ranges of values. Each element is added to the appropriate bucket based on its value. The buckets are then sorted individually if needed, and their elements are returned to the original array in sorted order. Bucket sort has a runtime of O(n) when the ranges of values are known, but requires additional space for the buckets. Examples are provided for sorting integers and doubles using bucket sort.

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Emory University Logo Guidelines - Sort: Distribution-based Data Structures and Algorithms Emory University Jinho D. Choi
Emory University Logo Guidelines - Sorting Algorithms 2
Emory University Logo Guidelines - Sorting Algorithms 2 Sort
Emory University Logo Guidelines - Sorting Algorithms 2 Sort Comparison
 based Distribution
 based
Emory University Logo Guidelines - Sorting Algorithms 2 Sort Comparison
 based Distribution
 based Selection Insertion Merge Quick
Emory University Logo Guidelines - Sorting Algorithms 2 Sort Comparison
 based Distribution
 based Selection Heap Insertion Shell Merge Quick Tim Intro
Emory University Logo Guidelines - Sorting Algorithms 2 Sort Comparison
 based Distribution
 based Bucket Radix Selection Heap Insertion Shell Merge Quick Tim Intro
Emory University Logo Guidelines - Sorting Algorithms 2 Sort Comparison
 based Distribution
 based Bucket Radix Selection Heap Insertion Shell Merge Quick vs.? Tim Intro
Emory University Logo Guidelines - Sorting Algorithms 2 Sort Comparison
 based Distribution
 based Bucket Radix Selection Heap Insertion Shell Merge Quick vs.? Tim Intro When range is known?
Emory University Logo Guidelines - Bucket Sort - Integer 3
Emory University Logo Guidelines - Bucket Sort - Integer 3 3 2 5 4 2 3 1 5
Emory University Logo Guidelines - Bucket Sort - Integer 3 3 2 5 4 2 3 1 5 1 2 3 4 5
Emory University Logo Guidelines - Bucket Sort - Integer 3 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
Emory University Logo Guidelines - Bucket Sort - Integer 3 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
Emory University Logo Guidelines - Bucket Sort - Integer 3 32 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
Emory University Logo Guidelines - Bucket Sort - Integer 3 32 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
Emory University Logo Guidelines - Bucket Sort - Integer 3 32 54 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
Emory University Logo Guidelines - Bucket Sort - Integer 3 32 54 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
Emory University Logo Guidelines - Bucket Sort - Integer 3 32 54 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
Emory University Logo Guidelines - Bucket Sort - Integer 3 32 54 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
Emory University Logo Guidelines - Bucket Sort - Integer 3 32 54 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
Emory University Logo Guidelines - Bucket Sort - Integer 3 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.
Emory University Logo Guidelines - Bucket Sort - Integer 3 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.
Emory University Logo Guidelines - Bucket Sort - Integer 3 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.
Emory University Logo Guidelines - Bucket Sort - Integer 3 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.
Emory University Logo Guidelines - Bucket Sort - Integer 3 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.
Emory University Logo Guidelines - Bucket Sort - Integer 3 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.
Emory University Logo Guidelines - Bucket Sort - Integer 3 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?
Emory University Logo Guidelines - Bucket Sort - Integer 3 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?
Emory University Logo Guidelines - Bucket Sort 4 public abstract class BucketSort<T extends Comparable<T>> extends AbstractSort<T> { private List<List<T>> buckets; private final boolean sort_bucket; public BucketSort(int bucketSize, boolean sort, Comparator<T> comparator) { super(comparator); buckets = createBuckets(bucketSize); sort_bucket = sort; } }
Emory University Logo Guidelines - Bucket Sort 4 public abstract class BucketSort<T extends Comparable<T>> extends AbstractSort<T> { private List<List<T>> buckets; private final boolean sort_bucket; public BucketSort(int bucketSize, boolean sort, Comparator<T> comparator) { super(comparator); buckets = createBuckets(bucketSize); sort_bucket = sort; } }
Emory University Logo Guidelines - Bucket Sort 4 public abstract class BucketSort<T extends Comparable<T>> extends AbstractSort<T> { private List<List<T>> buckets; private final boolean sort_bucket; public BucketSort(int bucketSize, boolean sort, Comparator<T> comparator) { super(comparator); buckets = createBuckets(bucketSize); sort_bucket = sort; } }
Emory University Logo Guidelines - Bucket Sort 4 public abstract class BucketSort<T extends Comparable<T>> extends AbstractSort<T> { private List<List<T>> buckets; private final boolean sort_bucket; public BucketSort(int bucketSize, boolean sort, Comparator<T> comparator) { super(comparator); buckets = createBuckets(bucketSize); sort_bucket = sort; } } static public <T>List<List<T>> createBuckets(int size) { List<List<T>> buckets = new ArrayList<>(size); for (int i=0; i<size; i++) buckets.add(new ArrayList<>()); return buckets; }
Emory University Logo Guidelines - Bucket Sort 4 public abstract class BucketSort<T extends Comparable<T>> extends AbstractSort<T> { private List<List<T>> buckets; private final boolean sort_bucket; public BucketSort(int bucketSize, boolean sort, Comparator<T> comparator) { super(comparator); buckets = createBuckets(bucketSize); sort_bucket = sort; } } static public <T>List<List<T>> createBuckets(int size) { List<List<T>> buckets = new ArrayList<>(size); for (int i=0; i<size; i++) buckets.add(new ArrayList<>()); return buckets; }
Emory University Logo Guidelines - Bucket Sort 5 abstract protected int getBucketIndex(T key); @Override public void sort(T[] array, int beginIndex, int endIndex) { for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i])).add(array[i]); for (List<T> bucket : buckets) { if (sort_bucket) Collections.sort(bucket, comparator); for (T key : bucket) array[beginIndex++] = key; bucket.clear(); } }
Emory University Logo Guidelines - Bucket Sort 5 abstract protected int getBucketIndex(T key); @Override public void sort(T[] array, int beginIndex, int endIndex) { for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i])).add(array[i]); for (List<T> bucket : buckets) { if (sort_bucket) Collections.sort(bucket, comparator); for (T key : bucket) array[beginIndex++] = key; bucket.clear(); } }
Emory University Logo Guidelines - Bucket Sort 5 abstract protected int getBucketIndex(T key); @Override public void sort(T[] array, int beginIndex, int endIndex) { for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i])).add(array[i]); for (List<T> bucket : buckets) { if (sort_bucket) Collections.sort(bucket, comparator); for (T key : bucket) array[beginIndex++] = key; bucket.clear(); } }
Emory University Logo Guidelines - Bucket Sort 5 abstract protected int getBucketIndex(T key); @Override public void sort(T[] array, int beginIndex, int endIndex) { for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i])).add(array[i]); for (List<T> bucket : buckets) { if (sort_bucket) Collections.sort(bucket, comparator); for (T key : bucket) array[beginIndex++] = key; bucket.clear(); } }
Emory University Logo Guidelines - Integer Bucket Sort 6 public class IntegerBucketSort extends BucketSort<Integer> { private final int GAP; public IntegerBucketSort(int min, int max, Comparator<Integer> comparator) { super(max - min, false, comparator); GAP = -min; } @Override protected int getBucketIndex(Integer key) { return key + GAP; } }
Emory University Logo Guidelines - Integer Bucket Sort 6 public class IntegerBucketSort extends BucketSort<Integer> { private final int GAP; public IntegerBucketSort(int min, int max, Comparator<Integer> comparator) { super(max - min, false, comparator); GAP = -min; } @Override protected int getBucketIndex(Integer key) { return key + GAP; } }
Emory University Logo Guidelines - Integer Bucket Sort 6 public class IntegerBucketSort extends BucketSort<Integer> { private final int GAP; public IntegerBucketSort(int min, int max, Comparator<Integer> comparator) { super(max - min, false, comparator); GAP = -min; } @Override protected int getBucketIndex(Integer key) { return key + GAP; } }
Emory University Logo Guidelines - Integer Bucket Sort 6 public class IntegerBucketSort extends BucketSort<Integer> { private final int GAP; public IntegerBucketSort(int min, int max, Comparator<Integer> comparator) { super(max - min, false, comparator); GAP = -min; } @Override protected int getBucketIndex(Integer key) { return key + GAP; } }
Emory University Logo Guidelines - Double Bucket Sort 7
Emory University Logo Guidelines - Double Bucket Sort 7 .32 .26 .51 .44 .21 .31 .17 .52
Emory University Logo Guidelines - Double Bucket Sort 7 .32 .26 .51 .44 .21 .31 .17 .52 Add each key to an appropriate bucket.
Emory University Logo Guidelines - Double Bucket Sort 7 .32 .26 .51 .44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
Emory University Logo Guidelines - Double Bucket Sort 7 .32 .26 .51 .44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51 .44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51 .44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
Emory University Logo Guidelines - Double Bucket Sort 7 .32 .26 .51.44.21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
Emory University Logo Guidelines - Double Bucket Sort 7 .32 .26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
Emory University Logo Guidelines - Double Bucket Sort 7 .32 .26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31.17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51 .44.21 .31.17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44.21 .31.17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44.21 .31.17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array. How many comparisons & assignments?
Emory University Logo Guidelines - Double Bucket Sort 8 public class DoubleBucketSort extends BucketSort<Double> { private static final int BUCKET_SIZE = 10; private final double GAP; public DoubleBucketSort(double min, double max, Comparator<Double> comparator) { super(BUCKET_SIZE, true, comparator); GAP = -min; } @Override protected int getBucketIndex(Double key) { return (int)((key+GAP) * BUCKET_SIZE); } }
Emory University Logo Guidelines - Double Bucket Sort 8 public class DoubleBucketSort extends BucketSort<Double> { private static final int BUCKET_SIZE = 10; private final double GAP; public DoubleBucketSort(double min, double max, Comparator<Double> comparator) { super(BUCKET_SIZE, true, comparator); GAP = -min; } @Override protected int getBucketIndex(Double key) { return (int)((key+GAP) * BUCKET_SIZE); } }
Emory University Logo Guidelines - Double Bucket Sort 8 public class DoubleBucketSort extends BucketSort<Double> { private static final int BUCKET_SIZE = 10; private final double GAP; public DoubleBucketSort(double min, double max, Comparator<Double> comparator) { super(BUCKET_SIZE, true, comparator); GAP = -min; } @Override protected int getBucketIndex(Double key) { return (int)((key+GAP) * BUCKET_SIZE); } }
Emory University Logo Guidelines - Double Bucket Sort 8 public class DoubleBucketSort extends BucketSort<Double> { private static final int BUCKET_SIZE = 10; private final double GAP; public DoubleBucketSort(double min, double max, Comparator<Double> comparator) { super(BUCKET_SIZE, true, comparator); GAP = -min; } @Override protected int getBucketIndex(Double key) { return (int)((key+GAP) * BUCKET_SIZE); } }
Emory University Logo Guidelines - LSD Radix Sort 9
Emory University Logo Guidelines - LSD Radix Sort • Least Significant Digit. 9
Emory University Logo Guidelines - LSD Radix Sort • Least Significant Digit. • For each digit (least to most): 9
Emory University Logo Guidelines - LSD Radix Sort • Least Significant Digit. • For each digit (least to most): - Put each key in a different bucket according to the current digit. 9
Emory University Logo Guidelines - LSD Radix Sort • Least Significant Digit. • For each digit (least to most): - Put each key in a different bucket according to the current digit. - Repeat this procedure for all digits. 9
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 113 132
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 113 132 0 1 2 3 4
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 113 132 0 1 2 3 4 1st LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 113 132 0 1 2 3 4 1st LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 113 132 0 1 2 3 4 1st LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 113 132 0 1 2 3 4 1st LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 113 132 0 1 2 3 4 1st LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 201 1 13 132 0 1 2 3 4 1st LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 201 1 13 132 0 1 2 3 4 1st LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 201 1 13132 0 1 2 3 4 1st LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13132 0 1 2 3 4 1st LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13132 0 1 2 3 4 1st LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13132 0 1 2 3 4 1st LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 201 1 13132 0 1 2 3 4 1st LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 201 1 13132 0 1 2 3 4 1st LSD 2nd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 201 1 13132 0 1 2 3 4 1st LSD 2nd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13132 0 1 2 3 4 1st LSD 2nd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13132 0 1 2 3 4 1st LSD 2nd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13132 0 1 2 3 4 1st LSD 2nd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 2011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 2011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 2011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 3202011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 3202011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 3202011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 3202011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 12034 344 320201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 12034 344 320 2011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 12034 3443202011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
Emory University Logo Guidelines - LSD Radix Sort 10 12034 3443202011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD How many comparisons & assignments?
Emory University Logo Guidelines - Radix Sort 11 public abstract class RadixSort extends AbstractSort<Integer> { protected List<List<Integer>> buckets; public RadixSort(Comparator<Integer> comparator) { super(comparator); buckets = BucketSort.createBuckets(10); } protected int getMaxBit(Integer[] array, int beginIndex, int endIndex) { int max = array[beginIndex]; for (int i=endIndex-1; i>beginIndex; i--) max = Math.max(max, array[i]); return Integer.toString(max).length(); } protected int getBucketIndex(Integer key, int div) { return (key / div) % 10; } }
Emory University Logo Guidelines - Radix Sort 11 public abstract class RadixSort extends AbstractSort<Integer> { protected List<List<Integer>> buckets; public RadixSort(Comparator<Integer> comparator) { super(comparator); buckets = BucketSort.createBuckets(10); } protected int getMaxBit(Integer[] array, int beginIndex, int endIndex) { int max = array[beginIndex]; for (int i=endIndex-1; i>beginIndex; i--) max = Math.max(max, array[i]); return Integer.toString(max).length(); } protected int getBucketIndex(Integer key, int div) { return (key / div) % 10; } }
Emory University Logo Guidelines - Radix Sort 11 public abstract class RadixSort extends AbstractSort<Integer> { protected List<List<Integer>> buckets; public RadixSort(Comparator<Integer> comparator) { super(comparator); buckets = BucketSort.createBuckets(10); } protected int getMaxBit(Integer[] array, int beginIndex, int endIndex) { int max = array[beginIndex]; for (int i=endIndex-1; i>beginIndex; i--) max = Math.max(max, array[i]); return Integer.toString(max).length(); } protected int getBucketIndex(Integer key, int div) { return (key / div) % 10; } } O(n)
Emory University Logo Guidelines - Radix Sort 11 public abstract class RadixSort extends AbstractSort<Integer> { protected List<List<Integer>> buckets; public RadixSort(Comparator<Integer> comparator) { super(comparator); buckets = BucketSort.createBuckets(10); } protected int getMaxBit(Integer[] array, int beginIndex, int endIndex) { int max = array[beginIndex]; for (int i=endIndex-1; i>beginIndex; i--) max = Math.max(max, array[i]); return Integer.toString(max).length(); } protected int getBucketIndex(Integer key, int div) { return (key / div) % 10; } } O(n)
Emory University Logo Guidelines - LSD Radix Sort 12 private List<List<Integer>> buckets = BucketSort.createBuckets(10); @Override public void sort(Integer[] array, int beginIndex, int endIndex) { int maxBit = getMaxBit(array, beginIndex, endIndex); for (int bit=0; bit<maxBit; bit++) sort(array, beginIndex, endIndex, bit); } private void sort(Integer[] array, int beginIndex, int endIndex, int bit) { int div = (int)Math.pow(10, bit); for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i], div)).add(array[i]); for (List<Integer> bucket : buckets) { idx = beginIndex = beginIndex + bucket.size(); while (bucket.size() > 0) array[--idx] = bucket.remove(bucket.size()-1); } }
Emory University Logo Guidelines - LSD Radix Sort 12 private List<List<Integer>> buckets = BucketSort.createBuckets(10); @Override public void sort(Integer[] array, int beginIndex, int endIndex) { int maxBit = getMaxBit(array, beginIndex, endIndex); for (int bit=0; bit<maxBit; bit++) sort(array, beginIndex, endIndex, bit); } private void sort(Integer[] array, int beginIndex, int endIndex, int bit) { int div = (int)Math.pow(10, bit); for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i], div)).add(array[i]); for (List<Integer> bucket : buckets) { idx = beginIndex = beginIndex + bucket.size(); while (bucket.size() > 0) array[--idx] = bucket.remove(bucket.size()-1); } }
Emory University Logo Guidelines - LSD Radix Sort 12 private List<List<Integer>> buckets = BucketSort.createBuckets(10); @Override public void sort(Integer[] array, int beginIndex, int endIndex) { int maxBit = getMaxBit(array, beginIndex, endIndex); for (int bit=0; bit<maxBit; bit++) sort(array, beginIndex, endIndex, bit); } private void sort(Integer[] array, int beginIndex, int endIndex, int bit) { int div = (int)Math.pow(10, bit); for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i], div)).add(array[i]); for (List<Integer> bucket : buckets) { idx = beginIndex = beginIndex + bucket.size(); while (bucket.size() > 0) array[--idx] = bucket.remove(bucket.size()-1); } } O(?)
Emory University Logo Guidelines - LSD Radix Sort 12 private List<List<Integer>> buckets = BucketSort.createBuckets(10); @Override public void sort(Integer[] array, int beginIndex, int endIndex) { int maxBit = getMaxBit(array, beginIndex, endIndex); for (int bit=0; bit<maxBit; bit++) sort(array, beginIndex, endIndex, bit); } private void sort(Integer[] array, int beginIndex, int endIndex, int bit) { int div = (int)Math.pow(10, bit); for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i], div)).add(array[i]); for (List<Integer> bucket : buckets) { idx = beginIndex = beginIndex + bucket.size(); while (bucket.size() > 0) array[--idx] = bucket.remove(bucket.size()-1); } } O(?) O(n)
Emory University Logo Guidelines - LSD Radix Sort 12 private List<List<Integer>> buckets = BucketSort.createBuckets(10); @Override public void sort(Integer[] array, int beginIndex, int endIndex) { int maxBit = getMaxBit(array, beginIndex, endIndex); for (int bit=0; bit<maxBit; bit++) sort(array, beginIndex, endIndex, bit); } private void sort(Integer[] array, int beginIndex, int endIndex, int bit) { int div = (int)Math.pow(10, bit); for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i], div)).add(array[i]); for (List<Integer> bucket : buckets) { idx = beginIndex = beginIndex + bucket.size(); while (bucket.size() > 0) array[--idx] = bucket.remove(bucket.size()-1); } } O(?) O(n) O(n)
Emory University Logo Guidelines - Comparison - Speed 13
Emory University Logo Guidelines - Comparison - Speed 13 Σof1Kiterations(ms) 0 225 450 675 900 List sizes 100 200 300 400 500 600 700 800 900 1000 Bucket Radix Quick Heap Shell Merge
Emory University Logo Guidelines - Comparison - Speed 14
Emory University Logo Guidelines - Comparison - Speed 14 Σof1Kiterations(ms) 0 1000 2000 3000 4000 List sizes 100 300 500 700 900 1100 1300 1500 1700 1900 Bucket Radix Quick Heap Shell Merge
Emory University Logo Guidelines - Comparison - Speed 15
Emory University Logo Guidelines - Comparison - Speed 15 Σof1Kiterations(ms) 0 2000 4000 6000 8000 List sizes 100 300 500 700 900 11001300 15001700 1900 21002300 25002700 2900 Bucket Radix Quick Heap Shell Merge
Emory University Logo Guidelines - Agenda • Exercise - https://github.com/emory-courses/cs323/wiki/Distribution-based-Sort • Reading - https://en.wikipedia.org/wiki/Binary_search_tree 16

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CS323: Sort - Distribution-based

  • 1. Emory University Logo Guidelines - Sort: Distribution-based Data Structures and Algorithms Emory University Jinho D. Choi
  • 2. Emory University Logo Guidelines - Sorting Algorithms 2
  • 3. Emory University Logo Guidelines - Sorting Algorithms 2 Sort
  • 4. Emory University Logo Guidelines - Sorting Algorithms 2 Sort Comparison
 based Distribution
 based
  • 5. Emory University Logo Guidelines - Sorting Algorithms 2 Sort Comparison
 based Distribution
 based Selection Insertion Merge Quick
  • 6. Emory University Logo Guidelines - Sorting Algorithms 2 Sort Comparison
 based Distribution
 based Selection Heap Insertion Shell Merge Quick Tim Intro
  • 7. Emory University Logo Guidelines - Sorting Algorithms 2 Sort Comparison
 based Distribution
 based Bucket Radix Selection Heap Insertion Shell Merge Quick Tim Intro
  • 8. Emory University Logo Guidelines - Sorting Algorithms 2 Sort Comparison
 based Distribution
 based Bucket Radix Selection Heap Insertion Shell Merge Quick vs.? Tim Intro
  • 9. Emory University Logo Guidelines - Sorting Algorithms 2 Sort Comparison
 based Distribution
 based Bucket Radix Selection Heap Insertion Shell Merge Quick vs.? Tim Intro When range is known?
  • 10. Emory University Logo Guidelines - Bucket Sort - Integer 3
  • 11. Emory University Logo Guidelines - Bucket Sort - Integer 3 3 2 5 4 2 3 1 5
  • 12. Emory University Logo Guidelines - Bucket Sort - Integer 3 3 2 5 4 2 3 1 5 1 2 3 4 5
  • 13. Emory University Logo Guidelines - Bucket Sort - Integer 3 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
  • 14. Emory University Logo Guidelines - Bucket Sort - Integer 3 3 2 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
  • 15. Emory University Logo Guidelines - Bucket Sort - Integer 3 32 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
  • 16. Emory University Logo Guidelines - Bucket Sort - Integer 3 32 5 4 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
  • 17. Emory University Logo Guidelines - Bucket Sort - Integer 3 32 54 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
  • 18. Emory University Logo Guidelines - Bucket Sort - Integer 3 32 54 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
  • 19. Emory University Logo Guidelines - Bucket Sort - Integer 3 32 54 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
  • 20. Emory University Logo Guidelines - Bucket Sort - Integer 3 32 54 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
  • 21. Emory University Logo Guidelines - Bucket Sort - Integer 3 32 54 2 3 1 5 1 2 3 4 5 Add each key to an appropriate bucket.
  • 22. Emory University Logo Guidelines - Bucket Sort - Integer 3 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.
  • 23. Emory University Logo Guidelines - Bucket Sort - Integer 3 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.
  • 24. Emory University Logo Guidelines - Bucket Sort - Integer 3 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.
  • 25. Emory University Logo Guidelines - Bucket Sort - Integer 3 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.
  • 26. Emory University Logo Guidelines - Bucket Sort - Integer 3 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.
  • 27. Emory University Logo Guidelines - Bucket Sort - Integer 3 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.
  • 28. Emory University Logo Guidelines - Bucket Sort - Integer 3 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?
  • 29. Emory University Logo Guidelines - Bucket Sort - Integer 3 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?
  • 30. Emory University Logo Guidelines - Bucket Sort 4 public abstract class BucketSort<T extends Comparable<T>> extends AbstractSort<T> { private List<List<T>> buckets; private final boolean sort_bucket; public BucketSort(int bucketSize, boolean sort, Comparator<T> comparator) { super(comparator); buckets = createBuckets(bucketSize); sort_bucket = sort; } }
  • 31. Emory University Logo Guidelines - Bucket Sort 4 public abstract class BucketSort<T extends Comparable<T>> extends AbstractSort<T> { private List<List<T>> buckets; private final boolean sort_bucket; public BucketSort(int bucketSize, boolean sort, Comparator<T> comparator) { super(comparator); buckets = createBuckets(bucketSize); sort_bucket = sort; } }
  • 32. Emory University Logo Guidelines - Bucket Sort 4 public abstract class BucketSort<T extends Comparable<T>> extends AbstractSort<T> { private List<List<T>> buckets; private final boolean sort_bucket; public BucketSort(int bucketSize, boolean sort, Comparator<T> comparator) { super(comparator); buckets = createBuckets(bucketSize); sort_bucket = sort; } }
  • 33. Emory University Logo Guidelines - Bucket Sort 4 public abstract class BucketSort<T extends Comparable<T>> extends AbstractSort<T> { private List<List<T>> buckets; private final boolean sort_bucket; public BucketSort(int bucketSize, boolean sort, Comparator<T> comparator) { super(comparator); buckets = createBuckets(bucketSize); sort_bucket = sort; } } static public <T>List<List<T>> createBuckets(int size) { List<List<T>> buckets = new ArrayList<>(size); for (int i=0; i<size; i++) buckets.add(new ArrayList<>()); return buckets; }
  • 34. Emory University Logo Guidelines - Bucket Sort 4 public abstract class BucketSort<T extends Comparable<T>> extends AbstractSort<T> { private List<List<T>> buckets; private final boolean sort_bucket; public BucketSort(int bucketSize, boolean sort, Comparator<T> comparator) { super(comparator); buckets = createBuckets(bucketSize); sort_bucket = sort; } } static public <T>List<List<T>> createBuckets(int size) { List<List<T>> buckets = new ArrayList<>(size); for (int i=0; i<size; i++) buckets.add(new ArrayList<>()); return buckets; }
  • 35. Emory University Logo Guidelines - Bucket Sort 5 abstract protected int getBucketIndex(T key); @Override public void sort(T[] array, int beginIndex, int endIndex) { for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i])).add(array[i]); for (List<T> bucket : buckets) { if (sort_bucket) Collections.sort(bucket, comparator); for (T key : bucket) array[beginIndex++] = key; bucket.clear(); } }
  • 36. Emory University Logo Guidelines - Bucket Sort 5 abstract protected int getBucketIndex(T key); @Override public void sort(T[] array, int beginIndex, int endIndex) { for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i])).add(array[i]); for (List<T> bucket : buckets) { if (sort_bucket) Collections.sort(bucket, comparator); for (T key : bucket) array[beginIndex++] = key; bucket.clear(); } }
  • 37. Emory University Logo Guidelines - Bucket Sort 5 abstract protected int getBucketIndex(T key); @Override public void sort(T[] array, int beginIndex, int endIndex) { for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i])).add(array[i]); for (List<T> bucket : buckets) { if (sort_bucket) Collections.sort(bucket, comparator); for (T key : bucket) array[beginIndex++] = key; bucket.clear(); } }
  • 38. Emory University Logo Guidelines - Bucket Sort 5 abstract protected int getBucketIndex(T key); @Override public void sort(T[] array, int beginIndex, int endIndex) { for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i])).add(array[i]); for (List<T> bucket : buckets) { if (sort_bucket) Collections.sort(bucket, comparator); for (T key : bucket) array[beginIndex++] = key; bucket.clear(); } }
  • 39. Emory University Logo Guidelines - Integer Bucket Sort 6 public class IntegerBucketSort extends BucketSort<Integer> { private final int GAP; public IntegerBucketSort(int min, int max, Comparator<Integer> comparator) { super(max - min, false, comparator); GAP = -min; } @Override protected int getBucketIndex(Integer key) { return key + GAP; } }
  • 40. Emory University Logo Guidelines - Integer Bucket Sort 6 public class IntegerBucketSort extends BucketSort<Integer> { private final int GAP; public IntegerBucketSort(int min, int max, Comparator<Integer> comparator) { super(max - min, false, comparator); GAP = -min; } @Override protected int getBucketIndex(Integer key) { return key + GAP; } }
  • 41. Emory University Logo Guidelines - Integer Bucket Sort 6 public class IntegerBucketSort extends BucketSort<Integer> { private final int GAP; public IntegerBucketSort(int min, int max, Comparator<Integer> comparator) { super(max - min, false, comparator); GAP = -min; } @Override protected int getBucketIndex(Integer key) { return key + GAP; } }
  • 42. Emory University Logo Guidelines - Integer Bucket Sort 6 public class IntegerBucketSort extends BucketSort<Integer> { private final int GAP; public IntegerBucketSort(int min, int max, Comparator<Integer> comparator) { super(max - min, false, comparator); GAP = -min; } @Override protected int getBucketIndex(Integer key) { return key + GAP; } }
  • 43. Emory University Logo Guidelines - Double Bucket Sort 7
  • 44. Emory University Logo Guidelines - Double Bucket Sort 7 .32 .26 .51 .44 .21 .31 .17 .52
  • 45. Emory University Logo Guidelines - Double Bucket Sort 7 .32 .26 .51 .44 .21 .31 .17 .52 Add each key to an appropriate bucket.
  • 46. Emory University Logo Guidelines - Double Bucket Sort 7 .32 .26 .51 .44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
  • 47. Emory University Logo Guidelines - Double Bucket Sort 7 .32 .26 .51 .44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
  • 48. Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51 .44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
  • 49. Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51 .44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
  • 50. Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
  • 51. Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
  • 52. Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
  • 53. Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
  • 54. Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket.
  • 55. Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
  • 56. Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
  • 57. Emory University Logo Guidelines - Double Bucket Sort 7 .32 .26 .51.44.21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
  • 58. Emory University Logo Guidelines - Double Bucket Sort 7 .32 .26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
  • 59. Emory University Logo Guidelines - Double Bucket Sort 7 .32 .26 .51.44 .21 .31 .17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
  • 60. Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44 .21 .31.17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
  • 61. Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51 .44.21 .31.17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
  • 62. Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44.21 .31.17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array.
  • 63. Emory University Logo Guidelines - Double Bucket Sort 7 .32.26 .51.44.21 .31.17 .52 [.1, .2) [.2, .3) [.3, .4) [.4, .5) [.5, .6) Add each key to an appropriate bucket. Sort and put all keys in each bucket back to the array. How many comparisons & assignments?
  • 64. Emory University Logo Guidelines - Double Bucket Sort 8 public class DoubleBucketSort extends BucketSort<Double> { private static final int BUCKET_SIZE = 10; private final double GAP; public DoubleBucketSort(double min, double max, Comparator<Double> comparator) { super(BUCKET_SIZE, true, comparator); GAP = -min; } @Override protected int getBucketIndex(Double key) { return (int)((key+GAP) * BUCKET_SIZE); } }
  • 65. Emory University Logo Guidelines - Double Bucket Sort 8 public class DoubleBucketSort extends BucketSort<Double> { private static final int BUCKET_SIZE = 10; private final double GAP; public DoubleBucketSort(double min, double max, Comparator<Double> comparator) { super(BUCKET_SIZE, true, comparator); GAP = -min; } @Override protected int getBucketIndex(Double key) { return (int)((key+GAP) * BUCKET_SIZE); } }
  • 66. Emory University Logo Guidelines - Double Bucket Sort 8 public class DoubleBucketSort extends BucketSort<Double> { private static final int BUCKET_SIZE = 10; private final double GAP; public DoubleBucketSort(double min, double max, Comparator<Double> comparator) { super(BUCKET_SIZE, true, comparator); GAP = -min; } @Override protected int getBucketIndex(Double key) { return (int)((key+GAP) * BUCKET_SIZE); } }
  • 67. Emory University Logo Guidelines - Double Bucket Sort 8 public class DoubleBucketSort extends BucketSort<Double> { private static final int BUCKET_SIZE = 10; private final double GAP; public DoubleBucketSort(double min, double max, Comparator<Double> comparator) { super(BUCKET_SIZE, true, comparator); GAP = -min; } @Override protected int getBucketIndex(Double key) { return (int)((key+GAP) * BUCKET_SIZE); } }
  • 68. Emory University Logo Guidelines - LSD Radix Sort 9
  • 69. Emory University Logo Guidelines - LSD Radix Sort • Least Significant Digit. 9
  • 70. Emory University Logo Guidelines - LSD Radix Sort • Least Significant Digit. • For each digit (least to most): 9
  • 71. Emory University Logo Guidelines - LSD Radix Sort • Least Significant Digit. • For each digit (least to most): - Put each key in a different bucket according to the current digit. 9
  • 72. Emory University Logo Guidelines - LSD Radix Sort • Least Significant Digit. • For each digit (least to most): - Put each key in a different bucket according to the current digit. - Repeat this procedure for all digits. 9
  • 73. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 113 132
  • 74. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 113 132 0 1 2 3 4
  • 75. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 113 132 0 1 2 3 4 1st LSD
  • 76. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 113 132 0 1 2 3 4 1st LSD
  • 77. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 113 132 0 1 2 3 4 1st LSD
  • 78. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 113 132 0 1 2 3 4 1st LSD
  • 79. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 113 132 0 1 2 3 4 1st LSD
  • 80. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
  • 81. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 201 1 13 132 0 1 2 3 4 1st LSD
  • 82. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 201 1 13 132 0 1 2 3 4 1st LSD
  • 83. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 201 1 13132 0 1 2 3 4 1st LSD
  • 84. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13132 0 1 2 3 4 1st LSD
  • 85. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13132 0 1 2 3 4 1st LSD
  • 86. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD
  • 87. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13132 0 1 2 3 4 1st LSD
  • 88. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 201 1 13132 0 1 2 3 4 1st LSD
  • 89. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 201 1 13132 0 1 2 3 4 1st LSD 2nd LSD
  • 90. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 201 1 13132 0 1 2 3 4 1st LSD 2nd LSD
  • 91. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13132 0 1 2 3 4 1st LSD 2nd LSD
  • 92. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13132 0 1 2 3 4 1st LSD 2nd LSD
  • 93. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13132 0 1 2 3 4 1st LSD 2nd LSD
  • 94. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
  • 95. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
  • 96. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
  • 97. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
  • 98. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
  • 99. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
  • 100. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
  • 101. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
  • 102. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD
  • 103. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
  • 104. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
  • 105. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 2011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
  • 106. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 2011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
  • 107. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344320 2011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
  • 108. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 3202011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
  • 109. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 3202011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
  • 110. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 3202011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
  • 111. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 3202011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
  • 112. Emory University Logo Guidelines - LSD Radix Sort 10 120 34 344 320201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
  • 113. Emory University Logo Guidelines - LSD Radix Sort 10 12034 344 320201 1 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
  • 114. Emory University Logo Guidelines - LSD Radix Sort 10 12034 344 320 2011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
  • 115. Emory University Logo Guidelines - LSD Radix Sort 10 12034 3443202011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD
  • 116. Emory University Logo Guidelines - LSD Radix Sort 10 12034 3443202011 13 132 0 1 2 3 4 1st LSD 2nd LSD 3rd LSD How many comparisons & assignments?
  • 117. Emory University Logo Guidelines - Radix Sort 11 public abstract class RadixSort extends AbstractSort<Integer> { protected List<List<Integer>> buckets; public RadixSort(Comparator<Integer> comparator) { super(comparator); buckets = BucketSort.createBuckets(10); } protected int getMaxBit(Integer[] array, int beginIndex, int endIndex) { int max = array[beginIndex]; for (int i=endIndex-1; i>beginIndex; i--) max = Math.max(max, array[i]); return Integer.toString(max).length(); } protected int getBucketIndex(Integer key, int div) { return (key / div) % 10; } }
  • 118. Emory University Logo Guidelines - Radix Sort 11 public abstract class RadixSort extends AbstractSort<Integer> { protected List<List<Integer>> buckets; public RadixSort(Comparator<Integer> comparator) { super(comparator); buckets = BucketSort.createBuckets(10); } protected int getMaxBit(Integer[] array, int beginIndex, int endIndex) { int max = array[beginIndex]; for (int i=endIndex-1; i>beginIndex; i--) max = Math.max(max, array[i]); return Integer.toString(max).length(); } protected int getBucketIndex(Integer key, int div) { return (key / div) % 10; } }
  • 119. Emory University Logo Guidelines - Radix Sort 11 public abstract class RadixSort extends AbstractSort<Integer> { protected List<List<Integer>> buckets; public RadixSort(Comparator<Integer> comparator) { super(comparator); buckets = BucketSort.createBuckets(10); } protected int getMaxBit(Integer[] array, int beginIndex, int endIndex) { int max = array[beginIndex]; for (int i=endIndex-1; i>beginIndex; i--) max = Math.max(max, array[i]); return Integer.toString(max).length(); } protected int getBucketIndex(Integer key, int div) { return (key / div) % 10; } } O(n)
  • 120. Emory University Logo Guidelines - Radix Sort 11 public abstract class RadixSort extends AbstractSort<Integer> { protected List<List<Integer>> buckets; public RadixSort(Comparator<Integer> comparator) { super(comparator); buckets = BucketSort.createBuckets(10); } protected int getMaxBit(Integer[] array, int beginIndex, int endIndex) { int max = array[beginIndex]; for (int i=endIndex-1; i>beginIndex; i--) max = Math.max(max, array[i]); return Integer.toString(max).length(); } protected int getBucketIndex(Integer key, int div) { return (key / div) % 10; } } O(n)
  • 121. Emory University Logo Guidelines - LSD Radix Sort 12 private List<List<Integer>> buckets = BucketSort.createBuckets(10); @Override public void sort(Integer[] array, int beginIndex, int endIndex) { int maxBit = getMaxBit(array, beginIndex, endIndex); for (int bit=0; bit<maxBit; bit++) sort(array, beginIndex, endIndex, bit); } private void sort(Integer[] array, int beginIndex, int endIndex, int bit) { int div = (int)Math.pow(10, bit); for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i], div)).add(array[i]); for (List<Integer> bucket : buckets) { idx = beginIndex = beginIndex + bucket.size(); while (bucket.size() > 0) array[--idx] = bucket.remove(bucket.size()-1); } }
  • 122. Emory University Logo Guidelines - LSD Radix Sort 12 private List<List<Integer>> buckets = BucketSort.createBuckets(10); @Override public void sort(Integer[] array, int beginIndex, int endIndex) { int maxBit = getMaxBit(array, beginIndex, endIndex); for (int bit=0; bit<maxBit; bit++) sort(array, beginIndex, endIndex, bit); } private void sort(Integer[] array, int beginIndex, int endIndex, int bit) { int div = (int)Math.pow(10, bit); for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i], div)).add(array[i]); for (List<Integer> bucket : buckets) { idx = beginIndex = beginIndex + bucket.size(); while (bucket.size() > 0) array[--idx] = bucket.remove(bucket.size()-1); } }
  • 123. Emory University Logo Guidelines - LSD Radix Sort 12 private List<List<Integer>> buckets = BucketSort.createBuckets(10); @Override public void sort(Integer[] array, int beginIndex, int endIndex) { int maxBit = getMaxBit(array, beginIndex, endIndex); for (int bit=0; bit<maxBit; bit++) sort(array, beginIndex, endIndex, bit); } private void sort(Integer[] array, int beginIndex, int endIndex, int bit) { int div = (int)Math.pow(10, bit); for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i], div)).add(array[i]); for (List<Integer> bucket : buckets) { idx = beginIndex = beginIndex + bucket.size(); while (bucket.size() > 0) array[--idx] = bucket.remove(bucket.size()-1); } } O(?)
  • 124. Emory University Logo Guidelines - LSD Radix Sort 12 private List<List<Integer>> buckets = BucketSort.createBuckets(10); @Override public void sort(Integer[] array, int beginIndex, int endIndex) { int maxBit = getMaxBit(array, beginIndex, endIndex); for (int bit=0; bit<maxBit; bit++) sort(array, beginIndex, endIndex, bit); } private void sort(Integer[] array, int beginIndex, int endIndex, int bit) { int div = (int)Math.pow(10, bit); for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i], div)).add(array[i]); for (List<Integer> bucket : buckets) { idx = beginIndex = beginIndex + bucket.size(); while (bucket.size() > 0) array[--idx] = bucket.remove(bucket.size()-1); } } O(?) O(n)
  • 125. Emory University Logo Guidelines - LSD Radix Sort 12 private List<List<Integer>> buckets = BucketSort.createBuckets(10); @Override public void sort(Integer[] array, int beginIndex, int endIndex) { int maxBit = getMaxBit(array, beginIndex, endIndex); for (int bit=0; bit<maxBit; bit++) sort(array, beginIndex, endIndex, bit); } private void sort(Integer[] array, int beginIndex, int endIndex, int bit) { int div = (int)Math.pow(10, bit); for (int i=beginIndex; i<endIndex; i++) buckets.get(getBucketIndex(array[i], div)).add(array[i]); for (List<Integer> bucket : buckets) { idx = beginIndex = beginIndex + bucket.size(); while (bucket.size() > 0) array[--idx] = bucket.remove(bucket.size()-1); } } O(?) O(n) O(n)
  • 126. Emory University Logo Guidelines - Comparison - Speed 13
  • 127. Emory University Logo Guidelines - Comparison - Speed 13 Σof1Kiterations(ms) 0 225 450 675 900 List sizes 100 200 300 400 500 600 700 800 900 1000 Bucket Radix Quick Heap Shell Merge
  • 128. Emory University Logo Guidelines - Comparison - Speed 14
  • 129. Emory University Logo Guidelines - Comparison - Speed 14 Σof1Kiterations(ms) 0 1000 2000 3000 4000 List sizes 100 300 500 700 900 1100 1300 1500 1700 1900 Bucket Radix Quick Heap Shell Merge
  • 130. Emory University Logo Guidelines - Comparison - Speed 15
  • 131. Emory University Logo Guidelines - Comparison - Speed 15 Σof1Kiterations(ms) 0 2000 4000 6000 8000 List sizes 100 300 500 700 900 11001300 15001700 1900 21002300 25002700 2900 Bucket Radix Quick Heap Shell Merge
  • 132. Emory University Logo Guidelines - Agenda • Exercise - https://github.com/emory-courses/cs323/wiki/Distribution-based-Sort • Reading - https://en.wikipedia.org/wiki/Binary_search_tree 16