TheAlgorithms · MD-Suhad · May 23, 2026
@@ -3,32 +3,39 @@
 import com.thealgorithms.devutils.searches.SearchAlgorithm;
 
 /**
- * Binary Search Algorithm Implementation
+ * Binary Search Algorithm Implementation.
  *
- * <p>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.
+ * <p>Binary search is an efficient algorithm for finding a target element in a sorted array. It
+ * repeatedly divides the search range in half and compares the target value with the middle
+ * element.
  *
- * <p>IMPORTANT: This algorithm ONLY works correctly if the input array is sorted in ascending
- * order.
+ * <p>The algorithm works as follows:
+ * <ol>
+ * <li>Start with the entire sorted array.</li>
+ * <li>Find the middle element of the current search range.</li>
+ * <li>If the middle element is equal to the target, return its index.</li>
+ * <li>If the target is smaller than the middle element, continue searching the left half.</li>
+ * <li>If the target is greater than the middle element, continue searching the right half.</li>
+ * <li>If the search range becomes empty, return {@code -1}.</li>
+ * </ol>
  *
- * <p>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
+ * <p>Example:
+ * <pre>
+ * array = [1, 3, 5, 7, 9, 11]
+ * key = 7
+ * result = 3
+ * </pre>
  *
- * <p>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
+ * <p>Time Complexity:
+ * <ul>
+ * <li>Best case: O(1), when the key is found at the middle index.</li>
+ * <li>Average case: O(log n), because the search range is divided in half each time.</li>
+ * <li>Worst case: O(log n), when the key is not present or is found after repeated halving.</li>
+ * </ul>
  *
- * <p>Example Walkthrough: Array: [1, 3, 5, 7, 9, 11, 13, 15, 17, 19] Target: 7
+ * <p>Space Complexity: O(log n), due to the recursive call stack.
  *
- * <p>Step 1: left=0, right=9, mid=4, array[4]=9 (9 &gt; 7, search left half) Step 2: left=0,
- * right=3, mid=1, array[1]=3 (3 &lt; 7, search right half) Step 3: left=2, right=3, mid=2,
- * array[2]=5 (5 &lt; 7, search right half) Step 4: left=3, right=3, mid=3, array[3]=7 (Found!
- * Return index 3)
+ * <p>Note: The input array must be sorted in ascending order.
  *
  * @author Varun Upadhyay (https://github.com/varunu28)
  * @author Podshivalov Nikita (https://github.com/nikitap492)
@@ -38,89 +45,43 @@
 class BinarySearch implements SearchAlgorithm {
 
     /**
-     * Generic method to perform binary search on any comparable type. This is the main entry point
-     * for binary search operations.
+     * Searches for the given key in a sorted array.
      *
-     * <p>Example Usage:
-     * <pre>
-     * Integer[] numbers = {1, 3, 5, 7, 9, 11};
-     * int result = new BinarySearch().find(numbers, 7);
-     * // result will be 3 (index of element 7)
-     *
-     * int notFound = new BinarySearch().find(numbers, 4);
-     * // notFound will be -1 (element 4 does not exist)
-     * </pre>
-     *
-     * @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 or if array is null/empty
+     * @param <T> the type of elements in the array; must implement {@link Comparable}
+     * @param array the sorted array to search in
+     * @param key the element to search for
+     * @return the index of the key if found, or {@code -1} if the key is not found
      */
     @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);
     }
 
     /**
-     * Core recursive implementation of binary search algorithm. This method divides the problem
-     * into smaller subproblems recursively.
-     *
-     * <p>How it works:
-     * <ol>
-     * <li>Calculate the middle index to avoid integer overflow</li>
-     * <li>Check if middle element matches the target</li>
-     * <li>If not, recursively search either left or right half</li>
-     * <li>Base case: left &gt; right means element not found</li>
-     * </ol>
+     * Recursively searches for the key between the given left and right indexes.
      *
-     * <p>Time Complexity: O(log n) because we halve the search space each time.
-     * Space Complexity: O(log n) due to recursive call stack.
-     *
-     * @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
+     * @param <T> the type of elements in the array; must implement {@link Comparable}
+     * @param array the sorted array to search in
+     * @param key the element to search for
+     * @param left the left boundary of the current search range
+     * @param right the right boundary of the current search range
+     * @return the index of the key if found, or {@code -1} if the key is not found
      */
     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; // Key not found in the array
+            return -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 median = (left + right) >>> 1;
         int comp = key.compareTo(array[median]);
-
-        // Case 1: Found the target element at middle position
         if (comp == 0) {
-            return median; // Return the index where element was found
+            return median;
         }
-        // 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);
         }
-        // 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);
         }
     }