Problema
Square 1 holds one grain. Each later square holds twice as many grains as the previous square. Return both the count on the requested square and the total on squares 1 through 64. Write each count as decimal text, because the board total is too large for a signed 64-bit integer.
Implement chessboard_grains(square).
Input
square: The requested square, numbered from 1.
Output
Return two decimal strings: [count on the requested square, total on all 64 squares].
Restrições
1 ≤ square ≤ 64. Output strings contain decimal digits only, with no commas, spaces, or leading zeros.
Exemplos
Entrada:
square = 6
Saída esperada:
expected = ["32", "18446744073709551615"]Entrada:
long long square = 6;
Saída esperada:
std::vector<std::string> expected = {"32", "18446744073709551615"};Entrada:
long square = 6;
Saída esperada:
string[] expected = new string[] {"32", "18446744073709551615"};Explicação
The first six counts are 1, 2, 4, 8, 16, 32. The board total is 1 + 2 + … + 2⁶³ = 2⁶⁴ − 1.
Entrada:
square = 1
Saída esperada:
expected = ["1", "18446744073709551615"]Entrada:
long long square = 1;
Saída esperada:
std::vector<std::string> expected = {"1", "18446744073709551615"};Entrada:
long square = 1;
Saída esperada:
string[] expected = new string[] {"1", "18446744073709551615"};Explicação
The first square holds 1 grain. The second output always refers to all 64 squares, not just the requested prefix.
Como abordar
Tente sozinho primeiro e depois abra uma dica de cada vez.
Dica 1
Each square doubles the previous square, so the requested count depends only on its position.
Dica 2
The total across all 64 squares is a geometric progression, and it grows far beyond normal integer limits.
Dica 3
Return both values as plain decimal text, and watch that the first square is one, not zero.
Complexidade esperada
O(1) time, O(1) extra space
Referências
Este desafio foi adaptado para o CodeUtility. Siga o enunciado e as restrições acima.