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Ingy döt Net 2023-09-01 09:35:06 -07:00
parent 61b93a2cd1
commit 5af6d93694
858 changed files with 20572 additions and 2082 deletions
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Task/Magic-constant/Java/magic-constant.java Normal file
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public final class MagicConstant {
public static void main(String[] aArgs) {
System.out.println("The first 20 magic constants:");
for ( int i = 1; i <= 20; i++ ) {
System.out.print(" " + magicConstant(order(i)));
}
System.out.println(System.lineSeparator());
System.out.println("The 1,000th magic constant: " + magicConstant(order(1_000)) + System.lineSeparator());
System.out.println("Order of the smallest magic square whose constant is greater than:");
for ( int i = 1; i <= 20; i++ ) {
String powerOf10 = "10^" + i + ":";
System.out.println(String.format("%6s%8s", powerOf10, minimumOrder(i)));
}
}
// Return the magic constant for a magic square of the given order
private static int magicConstant(int aN) {
return aN * ( aN * aN + 1 ) / 2;
}
// Return the smallest order of a magic square such that its magic constant is greater than 10 to the given power
private static int minimumOrder(int aN) {
return (int) Math.exp( ( LN2 + aN * LN10 ) / 3 ) + 1;
}
// Return the order of the magic square at the given index
private static int order(int aIndex) {
return ORDER_FIRST_MAGIC_SQUARE + aIndex - 1;
}
private static final int ORDER_FIRST_MAGIC_SQUARE = 3;
private static final double LN2 = Math.log(2.0);
private static final double LN10 = Math.log(10.0);
}