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Suppose there are n number of full water bottles, we can exchange m empty water bottles for only one full water bottle. Now drinking a full water bottle makes it an empty bottle. We have to find the maximum number of water bottles we can drink.

So, if the input is like n = 9, m = 3, then the output will be 13 because initially we have 9 bottles, so after drinking all bottles, we can get 9/3 = 3 full bottles, after drinking them all we have three empty bottles and using them we can buy one and drink it, so we completed 9 + 3 + 1 = 13 bottles.

To solve this, we will follow these steps −

x:= n, s:= 0, k:= 0

while x >= m, do

k:= x mod m

x:= quotient of x / m

s:= s + x

x:= x + k

return n + s

Let us see the following implementation to get better understanding −

def solve(n, m): x=n s=0 k=0 while x >= m: k=x % m x=x // m s=s + x x=x + k return n + s n = 9 m = 3 print(solve(n, m))

9, 3

13

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