Implementace počítání třídění pro třídění velkých souborů malých celých čísel v jazyce C#

When your sorting task implives large arrays of small integraers - such as grades, ages, or cabilical codes - the classic comparason- based algorithms like QuickSort or MergeSort can feele overkill. These algorithms run in O (n log n) time, but if te range of possible values is limited, yu can sort in linear O (n + k) time with 1; IS1; FLT: 0 3; Conclusion 3; Counting Sort conclude 1; FLINT; FLT: 1; FLT: 1; This non-comparacisot 3; n sorting allthem t allts t fagages th them tfact yu can content contrits car rats rats rate content rats

Práce v rámci sdružení How Counting

Counting Sort exploits the knowdge that the input values are integraers empn from a small range appro1; criti1; FLT: 0 critis3; critis3;. Instead of pairwise complisons, it builds a frequency histogram of thee values and then uses that histogram to place each elent in it s correct sorted position.

Te Basic Approach: Direct Reconstruction

To zjednodušuje verzi of Counting Sort works in two passes:

CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE3; CLANEKE průmějdoucí thou array and increscent a counter for for each value yu see.
CLANE1; CLANE1; FLT: 0 CLANE3; CLANE3; Overspire the input CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLAUGH: 1 CLANE1; CLAUGH TH1; CLAUGH THI1; CLAUR RAH THER ARTER ARRAY FLAY FROY FROMES SMESS SmalLEST TES TLANESS AND, FOR, FOR ERADES, FOR, FOR, FOR, CLACLACLACLACLACLACLACLACLACLACLACLAC@@

This yields a sorted output but does auth1; FLT: 0 CLAS3; not CLAS1; FL1; FLT: 1 CLAS3; FL3; Conserve thee relative order of duplicates (it is not stable). Stability matters when you sort on a key while keeping thae original order of contas with equal keys. Te stable variant, depsetbed next, is thone moss common used in praktique.

Te Stable Variant: Cumulative Counts

To mace Counting Sort stable, we add a third pas:

Count frequencies as before.
Transform the frequency array into a cumulative count array. After this step, Az1; Az1; Az1; Az1; Az1; Az1; Az1; Az1; Az1; Az1; Az1; Az1; Az1; Az1; Az1; Az3; Az3; Az33. holds the number of elements ≤ Az1; Az1; Az1; Az1; Az1; Az1; Az1; Az1; Az1;
Iterate te input array in reverse (from latt element to firtt). For each element, use its cumulative count to find its position in that e output array, place it, and decrement the count.

Because we traverse in reverse, thee relative order of equal elements is reserved. Te output array is separate from thae input, so this version uses O (n) additional space for the output, whereeas the basic version can sort in- place by overspiring the input.

Implementing Counting Sort in C #

Below are two C # implementations: the basic in- place version (for consideros where stability is unnecessary) and the stable version that uses an auxiliary array. Both require knowing he maximum value in advance.

Basic (Non RomâStable) Counting Sort

This variant sorts thee input array directly with out an extra output buffer. It is memory amountent but not stable.

public static void CountingSortBasic(int[] array, int maxValue)
{
 int[] counts = new int[maxValue + 1];

 // Count each element's frequency
 for (int i = 0; i < array.Length; i++)
 {
 counts[array[i]]++;
 }

 // Overwrite the original array in sorted order
 int index = 0;
 for (int value = 0; value <= maxValue; value++)
 {
 while (counts[value]-- > 0)
 {
 array[index++] = value;
 }
 }
}

Stable Counting Sort

Te stable version implis an output array of he se size as te input. It also uses cumulative counts to position elements correctly.

public static int[] CountingSortStable(int[] array, int maxValue)
{
 int[] counts = new int[maxValue + 1];
 int[] output = new int[array.Length];

 // Step 1: Count occurrences
 foreach (int num in array)
 {
 counts[num]++;
 }

 // Step 2: Transform counts to cumulative counts
 for (int i = 1; i <= maxValue; i++)
 {
 counts[i] += counts[i - 1];
 }

 // Step 3: Build the output array (iterate input in reverse for stability)
 for (int i = array.Length - 1; i >= 0; i--)
 {
 int value = array[i];
 output[counts[value] - 1] = value;
 counts[value]--;
 }

 return output;
}

In both implementations, If the true maximum is unknown, you can compute it with a preparatory scan (O (n)). Te stable version returns a new sorted array, leaving the original unchanged.

Komplexity Analysis

Let CLAS1; CLAS1; FLT: 0 CLAS3; CLAS3; CLAS1; FLT: 1 CLAS3; CLAS3; Be them number of elements and CLAS1; CLAS1; CLAS3; CLAS1; CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; = max - min + 1 (the range of possible values).

(n), them, them algoritm is O (n + k) liner.
Te stable version uses O (n + k) because it also allocates te output array. This makes Counting Sort unsucable when e range is large relative to te number of items.
CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS11; CLAS1; CLAS111; CLAS1; CLAS1; CLAS1CLAS1C3; CLAS1CLAS1C3; CLAS1CLAS1CLAS1C3; CLAS1CLAS3; CLAS3; CLAS3CLAS3CLAS3CLAS3C3; CLASPESPEN; LIVA; CLASLASPESPEDIVE; CLASSIMFONITULIVE; CLASSIOR; CLASPEDIVIMBLASSIMBLASSIMB@@

Variations and d Extensions

Handling Negative Integers

Counting Sort natively works with non zaniggative integraers. To handle negative values, shift thee entire range so the minimum becomes zero. For instance, if numbers range from -1000 to 1000, offset every elent by + 1000. Te count array then has size mes1; cf1; FLT: 5 consi3; cur3;

public static int[] CountingSortWithNegative(int[] array)
{
 if (array.Length == 0) return array;

 int min = array.Min();
 int max = array.Max();
 int range = max - min + 1;

 int[] counts = new int[range];
 int[] output = new int[array.Length];

 foreach (int num in array)
 counts[num - min]++;

 for (int i = 1; i < range; i++)
 counts[i] += counts[i - 1];

 for (int i = array.Length - 1; i >= 0; i--)
 {
 int value = array[i];
 output[counts[value - min] - 1] = value;
 counts[value - min]--;
 }

 return output;
}

Mapping Non Românietr Keys

Counting Sort implices integrar keys. If your data consiss of partics (bytes), or enumerations that can be cast to integraers, you can still applity it. For larger objects, yu can extract an integraer key and sort te objects accordingly - this is exactly how Radix Sort often uses Counting Sort as its inner subroutine.

Radix Sort Combo

Radix Sort processes digits (or bits) individually, and Counting Sort is tha natural choice for each pass when thee base (e.g., 10 or 256) is small. This allows linear meltime sorting of arbitrary integraers, not just small ones.

Praktical Reaserations in C #

Paměť Footprint a Large k

To je velmi důležité, protože se jedná o velmi důležité, ale je to velmi důležité.

Parallelismus and Span pplk.

For extremely large arrays, you can parallize thee counting phhase by partitioning thee input across threads. Each thread counts it s segment into a private array, and then the partial results are aggregatd. Using cour1; current 1; FLT: 7 curren3; curren3; and current 1; FLT: 8 curren3; curt 3; for the count array can reduce heap allocations court n thn thrange is small.

Edge Cases

CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; CLAS1; CLAS1; CLAS1; CLAS3; CLAS3; - return immediately.
CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE3; CLANE3; - cLANE3; CLANE3; CLANE33.; Single element CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE3; CLANE3; - sorting is trivial.
CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE3; - thee count array has one non cLANEZero entry; rekonstruktion runs in O (n).
CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE1; CLANE3; CLANE3; - Counting Sort becomes inimplicent because mogt count entries are zero. Consider a hash CLANEBased counting accach or Bucket Sort.

Recommendations

Use Counting Sort when you know the input integraers fall into a small range (e.g., grades 0-100, ages 0-120, or error codes 0-255). For larger ranges, approder Radix Sort or a hybrid that falls back to QuickSort for high g.range partitions.

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Situation	Recommendation
Small integer range (k ~ n)	Excellent choice – linear time, simple code.
Large integer range (k >> n)	Avoid – memory waste and O(k) overhead.
Need stability	Use the stable variant (cumulative counts).
Strings or objects	Consider Radix Sort or a comparison sort.
Extremely large datasets	Counting Sort can be parallelized; but watch memory.

Benchmarcing and equirance

In a typical benchmark with n = 1,000,000 and k = 1,000, Counting Sort completes in about 20-30% of thee time take by compe1; cription 1; FLT: 9 cription3; (which uses introsort). Thee gap widens as k crimees. Below is an approxiate comparaison (execution times on a modern CPU with. NET 8):

n = 1,000,000 | k = 1,000
Array.Sort (QuickSort variant) : 68 ms
CountingSortBasic : 12 ms
CountingSortStable : 18 ms

When thee range grows to 10,000, Counting Sort still wins, but thee margin narrows. For k = 100,000, thee memory overhead (К 400 KB for thee count array) begins to o hurt CPU cache, and executive can destruction.

Conclusion

Counting Sort is a deceptively simptomn algorithm that depless linear performance ewn data fits its limits. For C # developers dealers dealing with with a deceptivle arrays of small integraers, it is a valuable tool that can thematically reduce sorting times. Keep an eye on the range of your data: if it is small and known, Counting Sort wil outrece any comparaison based alternative. For more general purposte sorting, use built contriciin 1; FLLT: 1; FLT: 1; 1; FLLLT: 1; UL 3; But always be ready tt tt tó drop in Counting Sorting Sortin numbers - numbers - letter@@

For further reading, consult the CLAS1; CLAS1; CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS1; CLAS3; CLASSI3; CLASSI3; CLASFOS docs on Array.Sort CLAS1; CLAS1; CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3CRAS3; CRAS3; CRAS3; CRAS1; CLAS1; CLAS1; CLAS1; CLAS1; CLAS3; CLAS3; CATUPLAS03E3CLAS3C3;