Script for working out exponential limit within a set range

问题

In the image above column B is multiples of A1 and column C is C = C + B (working down the rows)

I worked out that in order for C for be 50 in 20 rows A1 has to be 0.2631579 but I'd like to be able to simplify that to a function that will return a list: list = exp(50, 20).

I'm not sure about the terminology of such a script so researching beforehand didn't really bring anything up sorry.

回答1:

Well based on your problem statement, we know that:

B_n=(n-1)×a; and C_n=(n-1)×n×a/2 (here a is the value for A₁).

So we only have to solve a for C₂₀=50. Or more genic: C_n=m. This is simply: a = 2×m/(n×(n-1)).

So the function is simply:

def find_threshold(m,n):
    return 2.0*m/(n*(n-1))

For your sample input, the lower bound is:

>>> find_threshold(50,20)
0.2631578947368421

If you plug in this value in the Excel sheet, you will obtain 50 (although there can be small rounding errors). Given we assume calculations on the numbers are done in constant time, this script works in constant time as well (O(1)) so it is quite fast (even if the row number, etc. would be huge).

来源：https://stackoverflow.com/questions/43140213/script-for-working-out-exponential-limit-within-a-set-range