Suspicious Bank Complete Solution

This article is part of the Scaler Topics Fortnightly Contest - 21

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Solution Approach

If the maximum limit of bank is not greater than the daily deposits. (A<=B)
Then it's obvious that at the end of each day for 1 <= day < A.
Amount in the bank will be A. But at the Ath day amount first after deposit bank will have Rs. A and after withdrawn it would have Rs. 0.
Now, we have to find the answer for the case when A > B.
How can we determine if the bank has no money?
It's reasonable that if there are Rs. q on the k-th day after deposit, then at the end of the (k-1)-th day there are q-B money in the bank.
So, if on the (k-1)-th day the bank becomes empty (q-B <= 0), then there must be q <= B rupees on the k-th day after amount is deposited.
So, we can apply binary search to find the first day with no money in bank.

Time Complexity - O(30) Time Complexity - O(1)