Problem
Consider positive integers strictly below limit. Include a value if it is divisible by at least one nonzero factor. Count each included value once even if several factors divide it. Ignore zero factors. Factors [3, 5] give the familiar multiples-of-3-or-5 task.
Implement sum_of_multiples(limit, factors).
Input
limit: The exclusive upper bound.
factors: The factors whose multiples are eligible.
Output
Return the sum of distinct eligible positive integers.
Constraints
0 ≤ limit ≤ 100,000. There may be 0 through 20 factors, each between 0 and 100,000. Duplicate factors are allowed.
Examples
Input:
limit = 12
factors = [3, 5]
Expected output:
expected = 33Input:
long long limit = 12;
std::vector<long long> factors = {3, 5};
Expected output:
long long expected = 33;Input:
long limit = 12;
long[] factors = new long[] {3, 5};
Expected output:
long expected = 33;Explanation
The included values are 3, 5, 6, 9, and 10. Their sum is 33.
Input:
limit = 10
factors = [2, 4]
Expected output:
expected = 20Input:
long long limit = 10;
std::vector<long long> factors = {2, 4};
Expected output:
long long expected = 20;Input:
long limit = 10;
long[] factors = new long[] {2, 4};
Expected output:
long expected = 20;Explanation
Include 2, 4, 6, and 8. Values 4 and 8 are counted once despite matching both factors.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
Only values divisible by at least one usable factor should contribute once.
Hint 2
Use inclusion-exclusion to combine overlapping factor multiples without double counting.
Hint 3
Ignore zero factors and duplicates before doing any arithmetic.
Expected complexity
O(2^m) time, O(1) extra space
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.