feat: add cycle sort algorithm (#634)

* feat: add cycle sort algorithm

* feat: add cycle sort algorithm

* feat: address code review comments

* feat: address code review comments

* Remove unnecessary newline

---------

Co-authored-by: Taj <[email protected]>

sort/cyclesort.go

@@ -0,0 +1,58 @@
+package sort
+
+import (
+	"github.com/TheAlgorithms/Go/constraints"
+)
+
+// Cycle sort is an in-place, unstable sorting algorithm that is particularly useful
+// when sorting arrays containing elements with a small range of values. It is theoretically
+// optimal in terms of the total number of writes to the original array.
+func Cycle[T constraints.Number](arr []T) []T {
+	counter, cycle, len := 0, 0, len(arr)
+	// Early return if the array too small
+	if len <= 1 {
+		return arr
+	}
+
+	for cycle = 0; cycle < len-1; cycle++ {
+		elem := arr[cycle]
+		// Find total smaller elements to right
+		pos := cycle
+		for counter = cycle + 1; counter < len; counter++ {
+			if arr[counter] < elem {
+				pos++
+			}
+		}
+		// In case this element is already in correct position, let's skip processing
+		if pos == cycle {
+			continue
+		}
+		// In case we have same elements, we want to skip to the end of that list as well, ignoring order
+		// This makes the algorithm unstable for composite elements
+		for elem == arr[pos] {
+			pos++
+		}
+		// Now let us put the item to it's right position
+		arr[pos], elem = elem, arr[pos]
+
+		//We need to rotate the array till we have reached the start of the cycle again
+		for pos != cycle {
+			pos = cycle
+			// Find smaller elements to right again
+			for counter = cycle + 1; counter < len; counter++ {
+				if arr[counter] < elem {
+					pos++
+				}
+			}
+			for elem == arr[pos] {
+				pos++
+			}
+			//We can do this unconditionally, but the check helps prevent redundant writes to the array
+			if elem != arr[pos] {
+				arr[pos], elem = elem, arr[pos]
+			}
+		}
+	}
+
+	return arr
+}

sort/sorts_test.go

@@ -169,6 +169,10 @@ func TestPatience(t *testing.T) {
 	testFramework(t, sort.Patience[int])
 }
 
+func TestCycle(t *testing.T) {
+	testFramework(t, sort.Cycle[int])
+}
+
 //END TESTS
 
 func benchmarkFramework(b *testing.B, f func(arr []int) []int) {
@@ -286,3 +290,7 @@ func BenchmarkPigeonhole(b *testing.B) {
 func BenchmarkPatience(b *testing.B) {
 	benchmarkFramework(b, sort.Patience[int])
 }
+
+func BenchmarkCycle(b *testing.B) {
+	benchmarkFramework(b, sort.Cycle[int])
+}