39 lines
1.3 KiB
Java
39 lines
1.3 KiB
Java
public final class MagicConstant {
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public static void main(String[] aArgs) {
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System.out.println("The first 20 magic constants:");
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for ( int i = 1; i <= 20; i++ ) {
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System.out.print(" " + magicConstant(order(i)));
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}
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System.out.println(System.lineSeparator());
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System.out.println("The 1,000th magic constant: " + magicConstant(order(1_000)) + System.lineSeparator());
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System.out.println("Order of the smallest magic square whose constant is greater than:");
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for ( int i = 1; i <= 20; i++ ) {
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String powerOf10 = "10^" + i + ":";
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System.out.println(String.format("%6s%8s", powerOf10, minimumOrder(i)));
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}
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}
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// Return the magic constant for a magic square of the given order
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private static int magicConstant(int aN) {
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return aN * ( aN * aN + 1 ) / 2;
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}
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// Return the smallest order of a magic square such that its magic constant is greater than 10 to the given power
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private static int minimumOrder(int aN) {
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return (int) Math.exp( ( LN2 + aN * LN10 ) / 3 ) + 1;
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}
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// Return the order of the magic square at the given index
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private static int order(int aIndex) {
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return ORDER_FIRST_MAGIC_SQUARE + aIndex - 1;
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}
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private static final int ORDER_FIRST_MAGIC_SQUARE = 3;
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private static final double LN2 = Math.log(2.0);
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private static final double LN10 = Math.log(10.0);
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}
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