Lottery Coupon Winners Calculation
Problem Description
You are given a range of consecutively numbered lottery coupons from 1 to n (inclusive). A coupon is considered a winner if the sum of its digits equals a specific value s.
Your task is to determine how many distinct s values produce the maximum number of winners. This means finding the s value(s) that appear most frequently as a digit-sum among coupons 1 through n, and then counting how many such s values exist.
Implement a function lotteryCoupons(n) that returns this count. You must also explain the algorithm's time and space complexity.
Constraints and Notes
- Assume
nis an integer andn ≥ 1. - All numbers are represented in base-10.
- The valid range for
svalues is from 1 to9 * d, wheredis the number of digits inn. - Values of
sthat are not achievable for any coupon in the range 1 tonsimply have zero winners and should not influence the determination of the maximum frequency.
AI interview prep
Core dilemma
The central engineering challenge is to efficiently calculate the frequency of digit sums for numbers within a potentially vast range (1 to n) without resorting to a brute-force iteration, which would be computationally prohibitive for large 'n'. This requires a combinatorial or dynamic programming approach.
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Interview prep
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Lottery Coupon Winners Calculation
Problem Description
You are given a range of consecutively numbered lottery coupons from 1 to n (inclusive). A coupon is considered a winner if the sum of its digits equals a specific value s.
Your task is to determine how many distinct s values produce the maximum number of winners. This means finding the s value(s) that appear most frequently as a digit-sum among coupons 1 through n, and then counting how many such s values exist.
Implement a function lotteryCoupons(n) that returns this count. You must also explain the algorithm's time and space complexity.
Constraints and Notes
- Assume
nis an integer andn ≥ 1. - All numbers are represented in base-10.
- The valid range for
svalues is from 1 to9 * d, wheredis the number of digits inn. - Values of
sthat are not achievable for any coupon in the range 1 tonsimply have zero winners and should not influence the determination of the maximum frequency.