1+ def search (arr , target ):
2+ left , right = 0 , len (arr ) - 1
3+ 4+ while left <= right :
5+ mid = left + (right - left ) // 2
6+ 7+ # Check if the target is at mid
8+ if arr [mid ] == target :
9+ return True
10+ 11+ # Handle duplicates by shrinking the search space
12+ if arr [left ] == arr [mid ] == arr [right ]:
13+ left += 1
14+ right -= 1
15+ # Left half is sorted
16+ elif arr [left ] <= arr [mid ]:
17+ # Check if target is in the left sorted portion
18+ if arr [left ] <= target < arr [mid ]:
19+ right = mid - 1
20+ else :
21+ left = mid + 1
22+ # Right half is sorted
23+ else :
24+ # Check if target is in the right sorted portion
25+ if arr [mid ] < target <= arr [right ]:
26+ left = mid + 1
27+ else :
28+ right = mid - 1
29+ 30+ # If target is not found
31+ return False
32+ 33+ 34+ 35+ # Time Complexity = O(n)
36+ # Space Complexity = O(1)
37+ 38+ 39+ 40+ ##################################################################
41+ 42+ 43+ 44+ # Driver code
45+ def test_search ():
46+ test_cases = [
47+ ([47 , 78 , 90 , 901 , 10 , 30 , 40 , 42 , 42 ], 30 , True ),
48+ ([47 , 78 , 90 , 901 , 10 , 30 , 40 , 42 , 42 ], 100 , False ),
49+ ([4 , 5 , 6 , 7 , 0 , 1 , 2 ], 0 , True ),
50+ ([4 , 5 , 6 , 7 , 0 , 1 , 2 ], 3 , False ),
51+ ([1 , 1 , 3 , 3 , 3 , 3 , 1 ], 1 , True ),
52+ ([1 , 1 , 1 , 3 , 3 , 3 ], 3 , True ),
53+ ([5 , 6 , 7 , 1 , 2 , 3 , 4 ], 6 , True ),
54+ ([5 , 6 , 7 , 1 , 2 , 3 , 4 ], 8 , False ),
55+ ([1 ], 1 , True ),
56+ ([2 ], 1 , False )
57+ ]
58+ 59+ for i , (arr , target , expected ) in enumerate (test_cases ):
60+ result = search (arr , target )
61+ assert result == expected , f"Test case { i + 1 } { expected } { result }
62+ print (f"Test case { i + 1 } )
63+ 64+ # Run the test cases
65+ test_search ()
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