how it is O(NT) in both the approach
Time complexity of min coin change
IN BOTTOM UP APPROACH
There is two nested loop in the code. The first loop is iterating from 1 to n and the second is iterating from 1 to T. Time Complexity = O(A*m ) , where T is the number of coins
what about top down approach
similarly in top down
your recursive function run n times and in each function call loop runs T time
hence time Complexity will be O(NT)