Added MaxFrequencyAfterOperations code

src/main/java/com/thealgorithms/slidingwindow/MaxFrequencyAfterOperations.java

@@ -0,0 +1,123 @@
+package com.thealgorithms.slidingwindow;
+
+import java.util.Arrays;
+
+/**
+ * Implementation of the algorithm to compute the maximum possible frequency of
+ * any element
+ * in an integer array after performing a fixed number of operations.
+ *
+ * <p>
+ * In each operation, you can:
+ * <ul>
+ * <li>Select an index that hasn't been used in previous operations.</li>
+ * <li>Add an integer in the range [-k, k] to the element at that index.</li>
+ * </ul>
+ *
+ * <p>
+ * The goal is to maximize the frequency of the most common element after all
+ * operations.
+ * </p>
+ *
+ * <p>
+ * <b>Example:</b>
+ * </p>
+ * 
+ * <pre>
+ * Input: nums = [1,4,5], k = 1, numOperations = 2
+ * Output: 2
+ * Explanation:
+ * - Add 0 to nums[1] → [1,4,5]
+ * - Add -1 to nums[2] → [1,4,4]
+ * The maximum frequency is 2.
+ * </pre>
+ *
+ * <p>
+ * <b>Time Complexity:</b> O(n log n)
+ * <br>
+ * Because the array is sorted initially using {@link Arrays#sort}, which takes
+ * O(n log n),
+ * and the sliding window traversal over the sorted array runs in O(n) time.
+ * </p>
+ *
+ * <p>
+ * <b>Space Complexity:</b> O(1)
+ * <br>
+ * The algorithm modifies and scans the array in place without using any
+ * additional data structures proportional to the input size.
+ * </p>
+ */
+public final class MaxFrequencyAfterOperations {
+
+    private MaxFrequencyAfterOperations() {
+        // Utility class; prevent instantiation
+    }
+
+    /**
+     * Computes the maximum possible frequency of any element in {@code nums}
+     * after performing {@code numOperations} modifications where each modification
+     * allows adding an integer in [-k, k] to a previously unused index.
+     *
+     * @param nums          the input array of integers
+     * @param k             the maximum absolute value that can be added or
+     *                      subtracted per operation
+     * @param numOperations the number of operations allowed
+     * @return the maximum achievable frequency after operations
+     * @throws NullPointerException if {@code nums} is {@code null}
+     *
+     *                              <p>
+     *                              <b>Time Complexity:</b> O(n log n)
+     *                              </p>
+     *                              <p>
+     *                              <b>Space Complexity:</b> O(1)
+     *                              </p>
+     */
+    public static int maxFrequency(int[] nums, int k, int numOperations) {
+        if (nums == null) {
+            throw new NullPointerException("Input array cannot be null.");
+        }
+
+        // Sort the array for efficient sliding window traversal
+        Arrays.sort(nums);
+        int n = nums.length;
+
+        // Sliding window pointers and counters
+        int l1 = 0, r1 = 0, cnt1 = 0;
+        int l2 = 0, cnt2 = 0;
+        int sameCnt = 0, prev = Integer.MIN_VALUE;
+        int maxF = 0;
+
+        for (int x : nums) {
+            if (x == prev)
+                sameCnt++;
+            else {
+                prev = x;
+                sameCnt = 1;
+            }
+
+            // Window for elements within [x - k, x]
+            while (nums[l1] < x - k) {
+                cnt1--;
+                l1++;
+            }
+            while (r1 < n && nums[r1] <= x + k) {
+                cnt1++;
+                r1++;
+            }
+
+            // Option 1: Adjust within ±k
+            maxF = Math.max(maxF, sameCnt + Math.min(cnt1 - sameCnt, numOperations));
+
+            // Option 2: Adjust within ±2k
+            cnt2++;
+            while (nums[l2] < x - 2L * k) {
+                cnt2--;
+                l2++;
+            }
+
+            maxF = Math.max(maxF, Math.min(cnt2, numOperations));
+        }
+
+        return maxF;
+    }
+}

src/test/java/com/thealgorithms/slidingwindow/MaxFrequencyAfterOperationsTest.java

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+package com.thealgorithms.slidingwindow;
+
+import static org.junit.jupiter.api.Assertions.*;
+import org.junit.jupiter.api.Test;
+
+/**
+ * Unit tests for {@link MaxFrequencyAfterOperations}.
+ */
+public class MaxFrequencyAfterOperationsTest {
+
+    @Test
+    public void testExample1() {
+        int[] nums = { 1, 4, 5 };
+        int k = 1, ops = 2;
+        int result = MaxFrequencyAfterOperations.maxFrequency(nums, k, ops);
+        assertEquals(2, result);
+    }
+
+    @Test
+    public void testExample2() {
+        int[] nums = { 5, 11, 20, 20 };
+        int k = 5, ops = 1;
+        int result = MaxFrequencyAfterOperations.maxFrequency(nums, k, ops);
+        assertEquals(2, result);
+    }
+
+    @Test
+    public void testNoOperations() {
+        int[] nums = { 1, 2, 3, 4 };
+        int k = 2, ops = 0;
+        int result = MaxFrequencyAfterOperations.maxFrequency(nums, k, ops);
+        assertEquals(1, result);
+    }
+
+    @Test
+    public void testAllSameElements() {
+        int[] nums = { 7, 7, 7, 7 };
+        int k = 5, ops = 2;
+        int result = MaxFrequencyAfterOperations.maxFrequency(nums, k, ops);
+        assertEquals(4, result);
+    }
+
+    @Test
+    public void testLargeK() {
+        int[] nums = { 1, 100, 200 };
+        int k = 200, ops = 2;
+        int result = MaxFrequencyAfterOperations.maxFrequency(nums, k, ops);
+        assertEquals(3, result);
+    }
+
+    @Test
+    public void testEmptyArray() {
+        int[] nums = {};
+        int result = MaxFrequencyAfterOperations.maxFrequency(nums, 5, 2);
+        assertEquals(0, result);
+    }
+
+    @Test
+    public void testSingleElement() {
+        int[] nums = { 10 };
+        int result = MaxFrequencyAfterOperations.maxFrequency(nums, 3, 1);
+        assertEquals(1, result);
+    }
+
+    @Test
+    public void testNullInputThrowsException() {
+        assertThrows(NullPointerException.class, () -> MaxFrequencyAfterOperations.maxFrequency(null, 1, 2));
+    }
+}