Problema
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.
Vincoli
0 ≤ limit ≤ 100,000. There may be 0 through 20 factors, each between 0 and 100,000. Duplicate factors are allowed.
Esempi
Input:
limit = 12
factors = [3, 5]
Output atteso:
expected = 33Input:
long long limit = 12;
std::vector<long long> factors = {3, 5};
Output atteso:
long long expected = 33;Input:
long limit = 12;
long[] factors = new long[] {3, 5};
Output atteso:
long expected = 33;Spiegazione
The included values are 3, 5, 6, 9, and 10. Their sum is 33.
Input:
limit = 10
factors = [2, 4]
Output atteso:
expected = 20Input:
long long limit = 10;
std::vector<long long> factors = {2, 4};
Output atteso:
long long expected = 20;Input:
long limit = 10;
long[] factors = new long[] {2, 4};
Output atteso:
long expected = 20;Spiegazione
Include 2, 4, 6, and 8. Values 4 and 8 are counted once despite matching both factors.
Come affrontarlo
Prova prima da solo, poi apri un suggerimento alla volta.
Suggerimento 1
Only values divisible by at least one usable factor should contribute once.
Suggerimento 2
Use inclusion-exclusion to combine overlapping factor multiples without double counting.
Suggerimento 3
Ignore zero factors and duplicates before doing any arithmetic.
Complessità attesa
O(2^m) time, O(1) extra space
Riferimenti
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