LeetCode 3870 & 3871: from a simple to a general solution

LeetCode problems 3870 and 3871 clearly demonstrate the progression from a straightforward case to a more generalized solution based on problem constraints. While both problems share the same description - given an integer n, return the total number of commas used when writing all integers from [1, n] in standard number formatting - the constraints lead to vastly different solutions.

Problem 3870 has a constraint of 1 ≤ n ≤ 10^5, which allows us to leverage the fact that each number can have at most one comma. In this range, numbers from 1 to 999 have 0 commas, while numbers from 1000 to n have 1 comma. Thus, the solution is simply max(0, n - 999).

However, problem 3871 presents a much larger constraint of 1 ≤ n ≤ 10^15. This means numbers can now contain 2, 3, 4, or even 5 commas. The approach from problem 3870 is no longer sufficient because we must account for numbers with multiple commas. The general solution involves iterating through powers of 1000, adding the number of commas for each range to a result variable.

Within the given constraints, the loop in problem 3871 runs only a few times at most, making it effectively constant-time bounded work. The number of additional commas for each range of numbers increases as the number of digits increases. We can optimize the solution by multiplying the starting number by 1000 in each iteration to move to the next range where a new comma would appear.