feat: CountingSort implementation (#5287)

* feat: CountingSort

* checkstyle: fix formatting

* refactor: adding additional final modifiers

* refactor: restructure sorting, update docs and tests

* docs: typo fix

---------

Co-authored-by: Alex Klymenko <alx@alx.com>
Co-authored-by: Piotr Idzik <65706193+vil02@users.noreply.github.com>

DIRECTORY.md

@@ -494,6 +494,7 @@
             * [BucketSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/BucketSort.java)
             * [CircleSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/CircleSort.java)
             * [CocktailShakerSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/CocktailShakerSort.java)
+            * [CountingSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/CountingSort.java)
             * [CombSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/CombSort.java)
             * [CycleSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/CycleSort.java)
             * [DNFSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/DNFSort.java)
@@ -862,6 +863,7 @@
             * [BucketSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/BucketSortTest.java)
             * [CircleSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/CircleSortTest.java)
             * [CocktailShakerSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/CocktailShakerSortTest.java)
+            * [CountingSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/CountingSortTest.java)
             * [CombSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/CombSortTest.java)
             * [DualPivotQuickSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/DualPivotQuickSortTest.java)
             * [DutchNationalFlagSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/DutchNationalFlagSortTest.java)

src/main/java/com/thealgorithms/sorts/CountingSort.java

@@ -0,0 +1,60 @@
+package com.thealgorithms.sorts;
+
+import java.util.Arrays;
+
+/**
+ * A standard implementation of the Counting Sort algorithm for integer arrays.
+ * This implementation has a time complexity of O(n + k), where n is the number
+ * of elements in the input array and k is the range of the input.
+ * It works only with integer arrays.
+ *
+ * The space complexity is O(k), where k is the range of the input integers.
+ *
+ * Note: This implementation handles negative integers as it
+ * calculates the range based on the minimum and maximum values of the array.
+ *
+ */
+public final class CountingSort {
+    private CountingSort() {
+    }
+
+    /**
+     * Sorts an array of integers using the Counting Sort algorithm.
+     *
+     * @param array the array to be sorted
+     * @return the sorted array
+     */
+    public static int[] sort(int[] array) {
+        if (array.length == 0) {
+            return array;
+        }
+        final var stats = Arrays.stream(array).summaryStatistics();
+        final int min = stats.getMin();
+        int[] count = computeHistogram(array, min, stats.getMax() - min + 1);
+        toCumulative(count);
+        return reconstructSorted(count, min, array);
+    }
+
+    private static int[] computeHistogram(final int[] array, final int shift, final int spread) {
+        int[] res = new int[spread];
+        for (final var value : array) {
+            res[value - shift]++;
+        }
+        return res;
+    }
+
+    private static void toCumulative(int[] count) {
+        for (int i = 1; i < count.length; i++) {
+            count[i] += count[i - 1];
+        }
+    }
+
+    private static int[] reconstructSorted(final int[] cumulativeCount, final int shift, final int[] array) {
+        int[] res = new int[array.length];
+        for (int i = array.length - 1; i >= 0; i--) {
+            res[cumulativeCount[array[i] - shift] - 1] = array[i];
+            cumulativeCount[array[i] - shift]--;
+        }
+        return res;
+    }
+}

src/test/java/com/thealgorithms/sorts/CountingSortTest.java

@@ -0,0 +1,27 @@
+package com.thealgorithms.sorts;
+
+import static org.junit.jupiter.api.Assertions.assertArrayEquals;
+
+import java.util.stream.Stream;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.MethodSource;
+
+public class CountingSortTest {
+
+    record TestCase(int[] inputArray, int[] expectedArray) {
+    }
+
+    static Stream<TestCase> provideTestCases() {
+        return Stream.of(new TestCase(new int[] {}, new int[] {}), new TestCase(new int[] {4}, new int[] {4}), new TestCase(new int[] {6, 1, 99, 27, 15, 23, 36}, new int[] {1, 6, 15, 23, 27, 36, 99}), new TestCase(new int[] {6, 1, 27, 15, 23, 27, 36, 23}, new int[] {1, 6, 15, 23, 23, 27, 27, 36}),
+            new TestCase(new int[] {5, 5, 5, 5, 5}, new int[] {5, 5, 5, 5, 5}), new TestCase(new int[] {1, 2, 3, 4, 5}, new int[] {1, 2, 3, 4, 5}), new TestCase(new int[] {5, 4, 3, 2, 1}, new int[] {1, 2, 3, 4, 5}), new TestCase(new int[] {3, -1, 4, 1, 5, -9}, new int[] {-9, -1, 1, 3, 4, 5}),
+            new TestCase(new int[] {0, 0, 0, 0}, new int[] {0, 0, 0, 0}), new TestCase(new int[] {3, 3, -1, -1, 2, 2, 0, 0}, new int[] {-1, -1, 0, 0, 2, 2, 3, 3}), new TestCase(new int[] {-3, -2, -1, -5, -4}, new int[] {-5, -4, -3, -2, -1}),
+            new TestCase(new int[] {1000, 500, 100, 50, 10, 5, 1}, new int[] {1, 5, 10, 50, 100, 500, 1000}), new TestCase(new int[] {4, -5, 10, 0}, new int[] {-5, 0, 4, 10}));
+    }
+
+    @ParameterizedTest
+    @MethodSource("provideTestCases")
+    public void testCountingSortException(TestCase testCase) {
+        int[] outputArray = CountingSort.sort(testCase.inputArray);
+        assertArrayEquals(testCase.expectedArray, outputArray);
+    }
+}