ChenSort

ChenSort is an improved bucket sort, which is a general-purpose sorting algorithm.

The time complexity is O(n) at best and O(nlogn) at worst, the space complexity is O(n), and it is stable.

Randomly generate [1000,10000000] random numbers in the range [-2^63,2^63-1], average speed is 3 times faster than Quicksort, fastest is 20 times. Traditional counting sorts and bucket sorts cannot handle such a large range of values because the performance is worse than Quicksort.

Android APK demo, 6.05 MB

Windows exe demo, 5.8 MB

The demos are all built on Flutter.

Currently writing an academic paper and expecting to be recognized by the academic community.

Dart code:

/// The essence of Chen Sort is an improved bucket sort
void chenSort(List<int> list) {
  if (list.length < 2) {
    return;
  }

  int maxValue = list[0];
  int minValue = maxValue;
  for (final element in list.skip(1)) {
    if (element > maxValue) {
      maxValue = element;
    }
    if (element < minValue) {
      minValue = element;
    }
  }

  /// All elements are the same and do not need to be sorted.
  if (maxValue == minValue) {
    return;
  }

  /// Limit the maximum size of the bucket to ensure the performance of long list
  /// sorting, which can be adjusted according to the actual situation.
  ///
  /// The essential difference between this and bucket sorting is that the size of
  /// the bucket is only related to the length of the list, not the range of element values.
  int bucketSize = min(list.length, 50000);
  int maxBucketIndex = bucketSize - 1;

  List<List<int>?> buckets = List.filled(bucketSize, null);
  int slot;

  /// Calculate the bucket in which the element is located based on the value of the element
  /// and the maximum and minimum values.

  /// Overflow detection
  BigInt range = BigInt.from(maxValue) - BigInt.from(minValue);
  if (BigInt.from(range.toInt()) == range) {
    int range = maxValue - minValue;
    double factor = maxBucketIndex / range;
    for (final element in list) {
      // slot = (((element - minValue) / range) * maxBucketIndex).toInt();
      slot = ((element - minValue) * factor).toInt();
      if (buckets[slot] == null) {
        buckets[slot] = [];
      }
      buckets[slot]!.add(element);
    }
  } else {
    /// Overflowed(positive minus negative)
    int positiveRange = maxValue;
    int negativeRange = -1 - minValue;
    int positiveStartBucketIndex = maxBucketIndex ~/ 2 + 1;
    int positiveBucketLength = maxBucketIndex - positiveStartBucketIndex;
    int negativeBucketLength = positiveStartBucketIndex - 1;
    for (final element in list) {
      if (element < 0) {
        slot = (((element - minValue) / negativeRange) * negativeBucketLength)
            .toInt();
      } else {
        slot = positiveStartBucketIndex +
            ((element / positiveRange) * positiveBucketLength).toInt();
      }
      if (buckets[slot] == null) {
        buckets[slot] = [];
      }
      buckets[slot]!.add(element);
    }
  }

  int compare(int left, int right) {
    return left - right;
  }

  int index = 0;
  for (final bucket in buckets) {
    if (bucket != null) {
      if (bucket.length > 1) {
        if (bucket.length >= 1000) {
          chenSort(bucket);
        } else {
          /// The sort method here represents the fastest comparison-type algorithm (Quick sort, Tim sort, etc.)
          bucket.sort(compare);
        }
        for (final element in bucket) {
          list[index++] = element;
        }
      } else {
        list[index++] = bucket[0];
      }
    }
  }
}

Java code(Multi-thread):

static void chenSort(Integer[] list) {
    int length = list.length;
    if (length < 2) {
        return;
    }

    Integer maxValue = Integer.MIN_VALUE;
    Integer minValue = Integer.MAX_VALUE;
    for (Integer element : list) {
        if (element > maxValue) {
            maxValue = element;
        }
        if (element < minValue) {
            minValue = element;
        }
    }

    /// All elements are the same and do not need to be sorted.
    if (maxValue.equals(minValue)) {
        return;
    }

    /// Limit the maximum size of the bucket to ensure the performance of long list
    /// sorting, which can be adjusted according to the actual situation.
    ///
    /// The essential difference between this and bucket sorting is that the size of
    /// the bucket is only related to the length of the list, not the range of element values.
    int bucketSize = Math.min(length, 50000);
    int maxBucketIndex = bucketSize - 1;

    ArrayList<Integer>[] buckets = new ArrayList[bucketSize];
    int slot;

    /// Calculate the bucket in which the element is located based on the value of the element
    /// and the maximum and minimum values.

    /// Overflow detection
    BigInteger bigRange = BigInteger.valueOf(maxValue).subtract(BigInteger.valueOf(minValue));
    if (BigInteger.valueOf(bigRange.intValue()).equals(bigRange)) {
        double factor = maxBucketIndex * 1.0 / (maxValue - minValue);
        for (Integer element : list) {
            slot = (int) ((element - minValue) * factor);
            if (buckets[slot] == null) {
                buckets[slot] = new ArrayList<>();
            }
            buckets[slot].add(element);
        }
    } else {
        /// Overflowed(positive minus negative)
        double positiveRange = maxValue;
        double negativeRange = -1 - minValue;
        int positiveStartBucketIndex = maxBucketIndex / 2 + 1;
        int positiveBucketLength = maxBucketIndex - positiveStartBucketIndex;
        int negativeBucketLength = positiveStartBucketIndex - 1;
        Integer zero = 0;
        for (Integer element : list) {
            if (element < zero) {
                slot = (int) (((element - minValue) / negativeRange) * negativeBucketLength);
            } else {
                slot = (int) (positiveStartBucketIndex + ((element / positiveRange) * positiveBucketLength));
            }
            if (buckets[slot] == null) {
                buckets[slot] = new ArrayList<>();
            }
            buckets[slot].add(element);
        }
    }

    Comparator<Integer> comparator = Comparator.comparingInt(left -> left);

    // Multi-thread sorting between buckets
    CountDownLatch countDownLatch = new CountDownLatch(buckets.length);
    for (ArrayList<Integer> bucket : buckets) {
        if (bucket != null) {
            if (bucket.size() > 1) {
                executor.execute(() -> {
                    bucket.sort(comparator);
                    countDownLatch.countDown();
                });
            } else {
                countDownLatch.countDown();
            }
        } else {
            countDownLatch.countDown();
        }
    }
    try {
        countDownLatch.await();
    } catch (InterruptedException ignored) {
    }

    int index = 0;
    for (ArrayList<Integer> bucket : buckets) {
        if (bucket != null) {
            if (bucket.size() > 1) {
                for (Integer element : bucket) {
                    list[index++] = element;
                }
            } else {
                list[index++] = bucket.get(0);
            }
        }
    }
}

Performance(10 million random numbers sorted):

Random random = new Random();
Integer[] arr = new Integer[10000000];
long maxValue = Integer.MAX_VALUE;
long minValue = Integer.MIN_VALUE;
long range = maxValue - minValue + 1;
for (int i = 0; i < arr.length; i++) {
    arr[i] = (int) (minValue + random.nextLong(range));
}
Integer[] copy = new Integer[arr.length];
System.arraycopy(arr, 0, copy, 0, arr.length);
long start = System.currentTimeMillis();
chenSort(arr);
long chenSortTimeUsage = System.currentTimeMillis() - start;
start = System.currentTimeMillis();
Arrays.sort(copy);
long quickSortTimeUsage = System.currentTimeMillis() - start;

chen sort: 3384 ms, quick sort: 9366 ms, 63.869314541960286%(2.767730496453901x) faster
chen sort: 3450 ms, quick sort: 7223 ms, 52.2359130555171%(2.093623188405797x) faster
chen sort: 1693 ms, quick sort: 5000 ms, 66.14%(2.9533372711163617x) faster
chen sort: 2306 ms, quick sort: 6267 ms, 63.204084889101644%(2.717692974848222x) faster
chen sort: 2922 ms, quick sort: 10145 ms, 71.19763430261213%(3.471937029431896x) faster
chen sort: 3285 ms, quick sort: 9211 ms, 64.33611985669309%(2.803957382039574x) faster
chen sort: 2661 ms, quick sort: 9236 ms, 71.18882633174535%(3.4708756106726795x) faster
chen sort: 2538 ms, quick sort: 6422 ms, 60.47960137028963%(2.530338849487786x) faster
chen sort: 1749 ms, quick sort: 4928 ms, 64.50892857142857%(2.8176100628930816x) faster
chen sort: 1775 ms, quick sort: 5254 ms, 66.21621621621621%(2.96x) faster
chen sort: 1626 ms, quick sort: 5155 ms, 68.45780795344326%(3.1703567035670357x) faster
chen sort: 2375 ms, quick sort: 4877 ms, 51.302029936436334%(2.0534736842105263x) faster
chen sort: 1923 ms, quick sort: 5250 ms, 63.37142857142857%(2.730109204368175x) faster
chen sort: 3028 ms, quick sort: 9237 ms, 67.21879398072967%(3.0505284015852046x) faster
chen sort: 2692 ms, quick sort: 9030 ms, 70.18826135105205%(3.3543833580980684x) faster

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