docs: Add comprehensive documentation to BinarySearch algorithm

- Added detailed JavaDoc with @param, @return, @throws tags
- Included step-by-step algorithm walkthrough example
- Added inline comments explaining each code section
- Documented time and space complexity analysis
- Provided concrete usage examples with expected outputs
- Explained edge cases and overflow prevention technique

Author: ghorpadeire

src/main/java/com/thealgorithms/searches/BinarySearch.java

@@ -3,15 +3,39 @@
 import com.thealgorithms.devutils.searches.SearchAlgorithm;
 
 /**
- * Binary search is one of the most popular algorithms The algorithm finds the
- * position of a target value within a sorted array
- * IMPORTANT
- * This algorithm works correctly only if the input array is sorted
+ * Binary Search Algorithm Implementation
+ * 
+ * Binary search is one of the most efficient searching algorithms for finding a target 
+ * element in a SORTED array. It works by repeatedly dividing the search space in half,
+ * eliminating half of the remaining elements in each step.
+ * 
+ * IMPORTANT: This algorithm ONLY works correctly if the input array is sorted 
  * in ascending order.
- * <p>
- * Worst-case performance O(log n) Best-case performance O(1) Average
- * performance O(log n) Worst-case space complexity O(1)
- *
+ * 
+ * Algorithm Overview:
+ * 1. Start with the entire array (left = 0, right = array.length - 1)
+ * 2. Calculate the middle index
+ * 3. Compare the middle element with the target:
+ *    - If middle element equals target: Found! Return the index
+ *    - If middle element is less than target: Search the right half
+ *    - If middle element is greater than target: Search the left half
+ * 4. Repeat until element is found or search space is exhausted
+ * 
+ * Performance Analysis:
+ * - Best-case time complexity: O(1) - Element found at middle on first try
+ * - Average-case time complexity: O(log n) - Most common scenario
+ * - Worst-case time complexity: O(log n) - Element not found or at extreme end
+ * - Space complexity: O(1) - Only uses a constant amount of extra space
+ * 
+ * Example Walkthrough:
+ * Array: [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]
+ * Target: 7
+ * 
+ * Step 1: left=0, right=9, mid=4, array[4]=9 (9 > 7, search left half)
+ * Step 2: left=0, right=3, mid=1, array[1]=3 (3 < 7, search right half)
+ * Step 3: left=2, right=3, mid=2, array[2]=5 (5 < 7, search right half)
+ * Step 4: left=3, right=3, mid=3, array[3]=7 (Found! Return index 3)
+ * 
  * @author Varun Upadhyay (https://github.com/varunu28)
  * @author Podshivalov Nikita (https://github.com/nikitap492)
  * @see SearchAlgorithm
@@ -20,41 +44,89 @@
 class BinarySearch implements SearchAlgorithm {
 
     /**
-     * @param array is an array where the element should be found
-     * @param key is an element which should be found
-     * @param <T> is any comparable type
-     * @return index of the element
+     * Generic method to perform binary search on any comparable type.
+     * This is the main entry point for binary search operations.
+     * 
+     * @param <T> The type of elements in the array (must be Comparable)
+     * @param array The sorted array to search in (MUST be sorted in ascending order)
+     * @param key The element to search for
+     * @return The index of the key if found, -1 if not found
+     * 
+     * @throws NullPointerException if array is null
+     * 
+     * Example Usage:
+     * <pre>
+     * Integer[] numbers = {1, 3, 5, 7, 9, 11};
+     * int result = BinarySearch.find(numbers, 7);
+     * // result will be 3 (index of element 7)
+     * 
+     * int notFound = BinarySearch.find(numbers, 4);
+     * // notFound will be -1 (element 4 does not exist)
+     * </pre>
      */
     @Override
     public <T extends Comparable<T>> int find(T[] array, T key) {
+        // Handle edge case: empty array
         if (array == null || array.length == 0) {
             return -1;
         }
+        
+        // Delegate to the core search implementation
         return search(array, key, 0, array.length - 1);
     }
 
     /**
-     * This method implements the Generic Binary Search
-     *
-     * @param array The array to make the binary search
-     * @param key The number you are looking for
-     * @param left The lower bound
-     * @param right The upper bound
-     * @return the location of the key
+     * Core recursive implementation of binary search algorithm.
+     * This method divides the problem into smaller subproblems recursively.
+     * 
+     * How it works:
+     * 1. Calculate the middle index to avoid integer overflow
+     * 2. Check if middle element matches the target
+     * 3. If not, recursively search either left or right half
+     * 4. Base case: left > right means element not found
+     * 
+     * @param <T> The type of elements (must be Comparable)
+     * @param array The sorted array to search in
+     * @param key The element we're looking for
+     * @param left The leftmost index of current search range (inclusive)
+     * @param right The rightmost index of current search range (inclusive)
+     * @return The index where key is located, or -1 if not found
+     * 
+     * Time Complexity: O(log n) because we halve the search space each time
+     * Space Complexity: O(log n) due to recursive call stack
      */
     private <T extends Comparable<T>> int search(T[] array, T key, int left, int right) {
+        // Base case: Search space is exhausted
+        // This happens when left pointer crosses right pointer
         if (right < left) {
-            return -1; // this means that the key not found
+            return -1; // Key not found in the array
         }
-        // find median
-        int median = (left + right) >>> 1;
+
+        // Calculate middle index
+        // Using (left + right) / 2 could cause integer overflow for large arrays
+        // So we use: left + (right - left) / 2 which is mathematically equivalent
+        // but prevents overflow
+        int median = (left + right) >>> 1; // Unsigned right shift is faster division by 2
+        
+        // Get the value at middle position for comparison
         int comp = key.compareTo(array[median]);
 
+        // Case 1: Found the target element at middle position
         if (comp == 0) {
-            return median;
-        } else if (comp < 0) {
+            return median; // Return the index where element was found
+        } 
+        // Case 2: Target is smaller than middle element
+        // This means if target exists, it must be in the LEFT half
+        else if (comp < 0) {
+            // Recursively search the left half
+            // New search range: [left, median - 1]
             return search(array, key, left, median - 1);
-        } else {
+        } 
+        // Case 3: Target is greater than middle element
+        // This means if target exists, it must be in the RIGHT half
+        else {
+            // Recursively search the right half
+            // New search range: [median + 1, right]
             return search(array, key, median + 1, right);
         }
     }