[FEATURE] Add Deterministic QuickSelect (Median of Medians) algorithm Fixes #6660

src/main/java/com/thealgorithms/divideandconquer/DeterministicQuickSelect.java

@@ -0,0 +1,84 @@
+package com.thealgorithms.divideandconquer;
+
+/**
+ * Deterministic QuickSelect (Median of Medians) algorithm.
+ *
+ * Finds the kth smallest element in an unsorted array in O(n) worst-case time.
+ *
+ * Reference: https://en.wikipedia.org/wiki/Median_of_medians
+ */
+public final class DeterministicQuickSelect {
+
+    private DeterministicQuickSelect() {
+    }
+
+    public static int select(int[] arr, int k) {
+        if (arr == null) {
+            throw new IllegalArgumentException("Input array cannot be null");
+        }
+        if (k < 1 || k > arr.length) {
+            throw new IllegalArgumentException("k is out of bounds");
+        }
+        return quickSelect(arr, 0, arr.length - 1, k - 1);
+    }
+
+    private static int quickSelect(int[] arr, int left, int right, int k) {
+        if (left == right) {
+            return arr[left];
+        }
+
+        int pivotIndex = medianOfMedians(arr, left, right);
+        pivotIndex = partition(arr, left, right, pivotIndex);
+
+        if (k == pivotIndex) {
+            return arr[k];
+        } else if (k < pivotIndex) {
+            return quickSelect(arr, left, pivotIndex - 1, k);
+        } else {
+            return quickSelect(arr, pivotIndex + 1, right, k);
+        }
+    }
+
+    private static int partition(int[] arr, int left, int right, int pivotIndex) {
+        int pivotValue = arr[pivotIndex];
+        swap(arr, pivotIndex, right);
+        int storeIndex = left;
+        for (int i = left; i < right; i++) {
+            if (arr[i] < pivotValue) {
+                swap(arr, storeIndex, i);
+                storeIndex++;
+            }
+        }
+        swap(arr, right, storeIndex);
+        return storeIndex;
+    }
+
+    private static int medianOfMedians(int[] arr, int left, int right) {
+        int n = right - left + 1;
+        if (n <= 5) {
+            return partition5(arr, left, right);
+        }
+
+        int numMedians = (int) Math.ceil((double) n / 5);
+        int[] medians = new int[numMedians];
+
+        for (int i = 0; i < numMedians; i++) {
+            int subLeft = left + i * 5;
+            int subRight = Math.min(subLeft + 4, right);
+            medians[i] = arr[partition5(arr, subLeft, subRight)];
+        }
+
+        return quickSelect(medians, 0, medians.length - 1, medians.length / 2);
+    }
+
+    private static int partition5(int[] arr, int left, int right) {
+        java.util.Arrays.sort(arr, left, right + 1);
+        return (left + right) / 2;
+    }
+
+    private static void swap(int[] arr, int i, int j) {
+        int tmp = arr[i];
+        arr[i] = arr[j];
+        arr[j] = tmp;
+    }
+}

src/test/java/com/thealgorithms/divideandconquer/DeterministicQuickSelect.java

@@ -0,0 +1,109 @@
+package com.thealgorithms.divideandconquer;
+
+/**
+ * Deterministic QuickSelect (Median of Medians) algorithm.
+ * <p>
+ * Finds the kth smallest element in an unsorted array in O(n) worst-case time
+ * complexity using the Median of Medians method to select a well-balanced pivot.
+ * <p>
+ * Reference: https://en.wikipedia.org/wiki/Median_of_medians
+ */
+public final class DeterministicQuickSelect {
+
+    private DeterministicQuickSelect() {
+        // Private constructor to prevent instantiation
+    }
+
+    /**
+     * Returns the kth smallest element in the array.
+     *
+     * @param arr The input array
+     * @param k   The order statistic (1-based). k=1 returns the smallest element.
+     * @return The kth smallest element in the array
+     */
+    public static int selectKthSmallest(int[] arr, int k) {
+        if (arr == null) {
+            throw new IllegalArgumentException("Input array cannot be null");
+        }
+        if (k < 1 || k > arr.length) {
+            throw new IllegalArgumentException("k is out of bounds");
+        }
+        return quickSelect(arr, 0, arr.length - 1, k - 1);
+    }
+
+    private static int quickSelect(int[] arr, int left, int right, int k) {
+        if (left == right) {
+            return arr[left];
+        }
+
+        int pivotIndex = medianOfMedians(arr, left, right);
+        pivotIndex = partition(arr, left, right, pivotIndex);
+
+        if (k == pivotIndex) {
+            return arr[k];
+        } else if (k < pivotIndex) {
+            return quickSelect(arr, left, pivotIndex - 1, k);
+        } else {
+            return quickSelect(arr, pivotIndex + 1, right, k);
+        }
+    }
+
+    private static int medianOfMedians(int[] arr, int left, int right) {
+        int n = right - left + 1;
+        if (n <= 5) {
+            insertionSort(arr, left, right);
+            return left + n / 2;
+        }
+
+        int numMedians = (int) Math.ceil((double) n / 5);
+        int[] medians = new int[numMedians];
+
+        for (int i = 0; i < numMedians; i++) {
+            int subLeft = left + i * 5;
+            int subRight = Math.min(subLeft + 4, right);
+            insertionSort(arr, subLeft, subRight);
+            medians[i] = arr[subLeft + (subRight - subLeft) / 2];
+        }
+
+        int medianValue = quickSelect(medians, 0, medians.length - 1, medians.length / 2);
+        for (int i = left; i <= right; i++) {
+            if (arr[i] == medianValue) {
+                return i; // Return the index of the median in original array
+            }
+        }
+        throw new IllegalStateException("Median value not found in the array");
+    }
+
+    private static int partition(int[] arr, int left, int right, int pivotIndex) {
+        int pivotValue = arr[pivotIndex];
+        swap(arr, pivotIndex, right);
+        int storeIndex = left;
+
+        for (int i = left; i < right; i++) {
+            if (arr[i] < pivotValue) {
+                swap(arr, storeIndex, i);
+                storeIndex++;
+            }
+        }
+        swap(arr, storeIndex, right);
+        return storeIndex;
+    }
+
+    private static void swap(int[] arr, int i, int j) {
+        int temp = arr[i];
+        arr[i] = arr[j];
+        arr[j] = temp;
+    }
+
+    private static void insertionSort(int[] arr, int left, int right) {
+        for (int i = left + 1; i <= right; i++) {
+            int key = arr[i];
+            int j = i - 1;
+            while (j >= left && arr[j] > key) {
+                arr[j + 1] = arr[j];
+                j--;
+            }
+            arr[j + 1] = key;
+        }
+    }
+}