feat: FlashSort implementation

DIRECTORY.md

@@ -501,6 +501,7 @@
             * [DualPivotQuickSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/DualPivotQuickSort.java)
             * [DutchNationalFlagSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/DutchNationalFlagSort.java)
             * [ExchangeSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/ExchangeSort.java)
+            * [FlashSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/FlashSort.java)
             * [GnomeSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/GnomeSort.java)
             * [HeapSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/HeapSort.java)
             * [InsertionSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/InsertionSort.java)
@@ -873,6 +874,7 @@
             * [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)
             * [ExchangeSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/ExchangeSortTest.java)
+            * [FlashSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/FlashSortTest.java)
             * [GnomeSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/GnomeSortTest.java)
             * [HeapSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/HeapSortTest.java)
             * [InsertionSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/InsertionSortTest.java)

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

@@ -0,0 +1,185 @@
+package com.thealgorithms.sorts;
+
+/**
+ * Implementation of Flash Sort algorithm that implements the SortAlgorithm interface.
+ *
+ * Sorts an array using the Flash Sort algorithm.
+ * <p>
+ * Flash Sort is a distribution sorting algorithm that partitions the data into
+ * different classes based on a classification array. It performs the sorting by
+ * first distributing the data elements into different buckets (or classes) and
+ * then permuting these buckets into the sorted order.
+ * <p>
+ * The method works as follows:
+ * <ol>
+ *     <li>Finds the minimum and maximum values in the array.</li>
+ *     <li>Initializes a classification array `L` to keep track of the number of elements in each class.</li>
+ *     <li>Computes a normalization constant `c1` to map elements into classes.</li>
+ *     <li>Classifies each element of the array into the corresponding bucket in the classification array.</li>
+ *     <li>Transforms the classification array to compute the starting indices of each bucket.</li>
+ *     <li>Permutes the elements of the array into sorted order based on the classification.</li>
+ *     <li>Uses insertion sort for the final arrangement to ensure complete sorting.</li>
+ * </ol>
+ */
+public class FlashSort implements SortAlgorithm {
+    private static final double CLASSIFICATION_RATIO = 0.45;
+
+    /**
+     * Sorts an array using the Flash Sort algorithm.
+     *
+     * @param array the array to be sorted.
+     * @param <T> the type of elements to be sorted, must be comparable.
+     * @return the sorted array.
+     */
+    @Override
+    public <T extends Comparable<T>> T[] sort(T[] array) {
+        flashSort(array);
+        return array;
+    }
+
+    /**
+     * Sorts an array using the Flash Sort algorithm.
+     *
+     * @param arr the array to be sorted.
+     * @param <T> the type of elements to be sorted, must be comparable.
+     */
+    private <T extends Comparable<? super T>> void flashSort(T[] arr) {
+        if (arr.length == 0) {
+            return;
+        }
+
+        final T min = findMin(arr);
+        final int maxIndex = findMaxIndex(arr);
+
+        if (arr[maxIndex].compareTo(min) == 0) {
+            return; // All elements are the same
+        }
+
+        final int m = (int) (CLASSIFICATION_RATIO * arr.length);
+
+        final int[] classificationArray = new int[m];
+
+        final double c1 = (double) (m - 1) / arr[maxIndex].compareTo(min);
+
+        classify(arr, classificationArray, c1, min);
+
+        transform(classificationArray);
+
+        permute(arr, classificationArray, c1, min, arr.length, m);
+
+        insertionSort(arr);
+    }
+
+    /**
+     * Finds the minimum value in the array.
+     *
+     * @param arr the array to find the minimum value in.
+     * @param <T> the type of elements in the array, must be comparable.
+     * @return the minimum value in the array.
+     */
+    private <T extends Comparable<? super T>> T findMin(final T[] arr) {
+        T min = arr[0];
+        for (int i = 1; i < arr.length; i++) {
+            if (arr[i].compareTo(min) < 0) {
+                min = arr[i];
+            }
+        }
+        return min;
+    }
+
+    /**
+     * Finds the index of the maximum value in the array.
+     *
+     * @param arr the array to find the maximum value index in.
+     * @param <T> the type of elements in the array, must be comparable.
+     * @return the index of the maximum value in the array.
+     */
+    private <T extends Comparable<? super T>> int findMaxIndex(final T[] arr) {
+        int maxIndex = 0;
+        for (int i = 1; i < arr.length; i++) {
+            if (arr[i].compareTo(arr[maxIndex]) > 0) {
+                maxIndex = i;
+            }
+        }
+        return maxIndex;
+    }
+
+    /**
+     * Classifies elements of the array into the classification array classificationArray.
+     *
+     * @param arr the array to be classified.
+     * @param classificationArray the classification array holding the count of elements in each class.
+     * @param c1 the normalization constant used to map the elements to the classification array.
+     * @param min the minimum value in the array.
+     * @param <T> the type of elements in the array, must be comparable.
+     */
+    private <T extends Comparable<? super T>> void classify(final T[] arr, final int[] classificationArray, final double c1, final T min) {
+        for (int i = 0; i < arr.length; i++) {
+            int k = (int) (c1 * arr[i].compareTo(min));
+            classificationArray[k]++;
+        }
+    }
+
+    /**
+     * Transforms the classification array classificationArray into the starting index array.
+     *
+     * @param classificationArray the classification array holding the count of elements in each class.
+     */
+    private void transform(final int[] classificationArray) {
+        for (int i = 1; i < classificationArray.length; i++) {
+            classificationArray[i] += classificationArray[i - 1];
+        }
+    }
+
+    /**
+     * Permutes the array into sorted order based on the classification array classificationArray.
+     *
+     * @param arr the array to be permuted.
+     * @param classificationArray the classification array holding the count of elements in each class.
+     * @param c1 the normalization constant used to map the elements to the classification array.
+     * @param min the minimum value in the array.
+     * @param n the length of the array.
+     * @param m the number of classes in the classification array.
+     * @param <T> the type of elements in the array, must be comparable.
+     */
+    private <T extends Comparable<? super T>> void permute(final T[] arr, final int[] classificationArray, final double c1, T min, int n, int m) {
+        int move = 0;
+        int j = 0;
+        int k = m - 1;
+        T flash;
+        while (move < n - 1) {
+            while (j > classificationArray[k] - 1) {
+                j++;
+                k = (int) (c1 * arr[j].compareTo(min));
+            }
+            flash = arr[j];
+            while (j != classificationArray[k]) {
+                k = (int) (c1 * flash.compareTo(min));
+                T temp = arr[classificationArray[k] - 1];
+                arr[classificationArray[k] - 1] = flash;
+                flash = temp;
+                classificationArray[k]--;
+                move++;
+            }
+        }
+    }
+
+    /**
+     * Sorts an array using the insertion sort algorithm.
+     *
+     * @param arr the array to be sorted.
+     * @param <T> the type of elements to be sorted, must be comparable.
+     */
+    private <T extends Comparable<? super T>> void insertionSort(final T[] arr) {
+        int n = arr.length;
+        for (int i = 1; i < n; i++) {
+            T key = arr[i];
+            int j = i - 1;
+            while (j >= 0 && arr[j].compareTo(key) > 0) {
+                arr[j + 1] = arr[j];
+                j--;
+            }
+            arr[j + 1] = key;
+        }
+    }
+}

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

@@ -0,0 +1,8 @@
+package com.thealgorithms.sorts;
+
+public class FlashSortTest extends SortingAlgorithmTest {
+    @Override
+    SortAlgorithm getSortAlgorithm() {
+        return new FlashSort();
+    }
+}