fix binary search to handle duplicates correctly

Author: rahini

searches/binary_search_with_duplicates.py

@@ -0,0 +1,18 @@
+def binary_search_first_occurrence(arr, target):
+    left, right = 0, len(arr) - 1
+    result = -1
+    while left <= right:
+        mid = (left + right) // 2
+        if arr[mid] == target:
+            result = mid
+            right = mid - 1  # keep searching left
+        elif arr[mid] < target:
+            left = mid + 1
+        else:
+            right = mid - 1
+    return result
+
+if __name__ == "__main__":
+    arr = [1, 2, 4, 4, 4, 5, 6]
+    target = 4
+    print(binary_search_first_occurrence(arr, target))  # Expected output: 2