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].
Restricciones
1 ≤ square ≤ 64. Output strings contain decimal digits only, with no commas, spaces, or leading zeros.
Ejemplos
Entrada:
square = 6
Salida esperada:
expected = ["32", "18446744073709551615"]Entrada:
long long square = 6;
Salida esperada:
std::vector<std::string> expected = {"32", "18446744073709551615"};Entrada:
long square = 6;
Salida esperada:
string[] expected = new string[] {"32", "18446744073709551615"};Explicación
The first six counts are 1, 2, 4, 8, 16, 32. The board total is 1 + 2 + … + 2⁶³ = 2⁶⁴ − 1.
Entrada:
square = 1
Salida esperada:
expected = ["1", "18446744073709551615"]Entrada:
long long square = 1;
Salida esperada:
std::vector<std::string> expected = {"1", "18446744073709551615"};Entrada:
long square = 1;
Salida esperada:
string[] expected = new string[] {"1", "18446744073709551615"};Explicación
The first square holds 1 grain. The second output always refers to all 64 squares, not just the requested prefix.
Cómo abordarlo
Inténtalo primero por tu cuenta y luego abre las pistas una a una.
Pista 1
Each square doubles the previous square, so the requested count depends only on its position.
Pista 2
The total across all 64 squares is a geometric progression, and it grows far beyond normal integer limits.
Pista 3
Return both values as plain decimal text, and watch that the first square is one, not zero.
Complejidad esperada
O(1) time, O(1) extra space
Referencias
Este reto está adaptado para CodeUtility. Sigue el enunciado y las restricciones indicadas arriba.