radixSortOf<E> function

void radixSortOf<E>(List<E> list, KeyOf<E, int> keyOf, { int? begin, int? end, bool reversed = false, int? radixPower, })

Sorts any list of items using radix sort algorithm with a radix value of 2^p.

Parameters

• list is any list of integers to be sorted.
• radixPower is the value of p in 2^p that is used as the radix.
• To perform partial sorting, you can specify the begin or end.
• begin is the start index of the range to be sorted.
• If begin is negative, range starts at the 0
• If begin is not below the length of the list, range will be empty.
• end is the final index if the range to be sorted. It is exclusive.
• If end is above the length of the list, it will be ignored.
• If end is negative, the absolute value of it will be subtracted from the length of the list to determine where the range ends.
• If end is not greater than the begin, the range will be empty.
• Set reversed to true if you want to sort in descending order.

Details

This function maps the list of items with the keyOf to generate a list of numbers. radixSort is applied to this list of numbers, and a sorted list is reconstructed with the mapped values from these numbers.

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Complexity: Time O(n * log_b n) | Space O(n) (where, b is the radix)

Implementation

void radixSortOf<E>(
  List<E> list,
  KeyOf<E, int> keyOf, {
  int? begin,
  int? end,
  bool reversed = false,
  int? radixPower,
}) {
  int b, e;
  int n = list.length;

  // Find the range given the parameters.
  b = 0;
  e = n;
  if (begin != null && b < begin) {
    b = begin;
  }
  if (end != null && end < e) {
    e = end;
    if (e < 0) e += n;
  }

  if (b + 1 >= e) return;

  int p = radixPower ?? (0.5 * log(n) / log(2)).ceil();
  if (p < 1) {
    throw RangeError("Radix power should be at least 2 or above");
  }

  // sorts range `[b, e)` with radix 2^p
  int l, h, i, j, k, m;
  List<int> keys =
      List<int>.generate(e, (i) => keyOf(list[i]), growable: false);

  // Find the minimum and maximum numbers in range [b, e)
  l = keys[b];
  h = keys[b];
  for (i = b + 1; i < e; ++i) {
    if (keys[i] < l) {
      l = keys[i];
    }
    if (keys[i] > h) {
      h = keys[i];
    }
  }

  int mask = (1 << p) - 1;
  List<List<E>> valueBins =
      List<List<E>>.generate(mask + 1, (i) => <E>[], growable: false);
  List<List<int>> keyBins =
      List<List<int>>.generate(mask + 1, (i) => <int>[], growable: false);

  // Put items inside the bin
  for (k = 0; ((h - l) >> k) != 0; k += p) {
    // Put items to bin using the mask
    for (i = b; i < e; i++) {
      m = ((keys[i] - l) >> k) & mask;
      keyBins[m].add(keys[i]);
      valueBins[m].add(list[i]);
    }

    // Reconstruct the list from bin
    i = b;
    for (m = 0; m <= mask; m++) {
      for (j = 0; j < keyBins[m].length; ++j) {
        keys[i] = keyBins[m][j];
        list[i] = valueBins[m][j];
        i++;
      }
      keyBins[m].clear();
      valueBins[m].clear();
    }
  }

  if (reversed) {
    // reverse the order of the list
    reverseList(list, b, e);
  }
}