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i dont know the answers can anybody explain this in Detail

The above method is Binary Search. Its worse case is log(n).

@khoa, yep its binary search but the array input from user need not be monotonously increasing, instead it can be quite unordered!
though the program might exit after log(n) steps, yet it might not be able to find an element in the array even though that element is present in it since it searches in the wrong half, since the program is designed for monotonously increasing sequences.

worst case is o(n) as it would be like linear search each time array is breaking into two halves with size 1 and other n-1;

worst case is o(n) as it would be like linear search each time array is breaking into two halves with size 1 and other n-1;

The array is sorted in ascending order and it is clearly ln(n) worst case order.