Add MedianOfTwoSortedArrays algorithm (#5554)

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

@@ -0,0 +1,53 @@
+package com.thealgorithms.divideandconquer;
+
+public final class MedianOfTwoSortedArrays {
+
+    private MedianOfTwoSortedArrays() {
+    }
+
+    /**
+     * Finds the median of two sorted arrays in logarithmic time.
+     *
+     * @param nums1 the first sorted array
+     * @param nums2 the second sorted array
+     * @return the median of the combined sorted array
+     * @throws IllegalArgumentException if the input arrays are not sorted
+     */
+    public static double findMedianSortedArrays(int[] nums1, int[] nums2) {
+        if (nums1.length > nums2.length) {
+            return findMedianSortedArrays(nums2, nums1); // Ensure nums1 is the smaller array
+        }
+
+        int m = nums1.length;
+        int n = nums2.length;
+        int low = 0;
+        int high = m;
+        while (low <= high) {
+            int partition1 = (low + high) / 2; // Partition in the first array
+            int partition2 = (m + n + 1) / 2 - partition1; // Partition in the second array
+
+            int maxLeft1 = (partition1 == 0) ? Integer.MIN_VALUE : nums1[partition1 - 1];
+            int minRight1 = (partition1 == m) ? Integer.MAX_VALUE : nums1[partition1];
+            int maxLeft2 = (partition2 == 0) ? Integer.MIN_VALUE : nums2[partition2 - 1];
+            int minRight2 = (partition2 == n) ? Integer.MAX_VALUE : nums2[partition2];
+
+            // Check if partition is valid
+            if (maxLeft1 <= minRight2 && maxLeft2 <= minRight1) {
+                // If combined array length is odd
+                if (((m + n) & 1) == 1) {
+                    return Math.max(maxLeft1, maxLeft2);
+                }
+                // If combined array length is even
+                else {
+                    return (Math.max(maxLeft1, maxLeft2) + Math.min(minRight1, minRight2)) / 2.0;
+                }
+            } else if (maxLeft1 > minRight2) {
+                high = partition1 - 1;
+            } else {
+                low = partition1 + 1;
+            }
+        }
+
+        throw new IllegalArgumentException("Input arrays are not sorted");
+    }
+}

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

@@ -0,0 +1,41 @@
+package com.thealgorithms.divideandconquer;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import java.util.stream.Stream;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.Arguments;
+import org.junit.jupiter.params.provider.MethodSource;
+
+public class MedianOfTwoSortedArraysTest {
+
+    @ParameterizedTest
+    @MethodSource("provideTestCases")
+    void testFindMedianSortedArrays(int[] nums1, int[] nums2, double expectedMedian) {
+        assertEquals(expectedMedian, MedianOfTwoSortedArrays.findMedianSortedArrays(nums1, nums2));
+    }
+
+    private static Stream<Arguments> provideTestCases() {
+        return Stream.of(
+            // Test case 1: Arrays of equal length
+            Arguments.of(new int[] {1, 3}, new int[] {2, 4}, 2.5),
+
+            // Test case 2: Arrays of different lengths
+            Arguments.of(new int[] {1, 3}, new int[] {2}, 2.0),
+
+            // Test case 3: Arrays with even total length
+            Arguments.of(new int[] {1, 2, 8}, new int[] {3, 4, 5, 6, 7}, 4.5),
+
+            // Test case 4: Arrays with odd total length
+            Arguments.of(new int[] {1, 2, 8}, new int[] {3, 4, 5}, 3.5),
+
+            // Test case 5: Single element arrays
+            Arguments.of(new int[] {1}, new int[] {3}, 2.0),
+
+            // Test case 6: Empty arrays
+            Arguments.of(new int[] {}, new int[] {0}, 0.0),
+
+            // Test case 7: Same element arrays
+            Arguments.of(new int[] {2, 2, 2}, new int[] {2, 2, 2}, 2.0));
+    }
+}