Kotlin: Calculate Disjoint Pythagoras Numbers

Table of Contents

I calculated disjoint Pythgoras numbers with Kotlin.

Environment

Kotlin 1.1.2-2

How to do

Think about disjoint pythagorus number trio, ( a, b, c ( a leq b lt c ) ) . As I wrote at Diophantus Formula for Pythagorean Numbers, ( c ) is odd and ( a ) and ( b ) are odd and even.

Then, ( c ) を奇数のループにします。 ( b ) を ( frac{c}{sqrt{2}} lt [frac{c}{sqrt{2}}] + 1 leq b lt c ) の範囲でループさせます。そして ( a = sqrt{ b ^ 2 – c ^ 2 } ) が整数になる場合にそれをピタゴラス数とします。ただし互いに素である必要があるため、共通因数を持つ場合は排除します。

In such way, calculate Pythagoras number trios under ( c leq 1000 ) .

Code

共通因数が存在するか否かは Euclidean Algorithm in Kotlin のコードを流用します。

I created the class of Pythagoras number trio, at first. It’s also OK to use List or Array instead.

package com.improve_future.math
data class PythagorasNumber(
var a: Long,
var b: Long,
var c: Long
) {
override fun toString(): String {
return "($a, $b, $c)"
}
}

package com.improve_future.math

data class PythagorasNumber(

var a: Long,

var b: Long,

var c: Long

) {

override fun toString(): String {

return "($a, $b, $c)"

}

Here is the main function. After the calculation, print all Pythagoras numbers and the numbers of them.

package com.improve_future.math
object Main {
@JvmStatic
fun main(args: Array<String>) {
val pythagorasList =
mutableListOf<PythagorasNumber>()
val m = 1000L
for (c in 5L..m step 2) {
for (b in c - 1 downTo
(c.toDouble() / Math.sqrt(2.0) + 1).
toLong()) {
val a = Math.sqrt(
Math.pow(c.toDouble(), 2.0) -
Math.pow(b.toDouble(), 2.0))
if (a % 1 == 0.0 &&
calcGcm(mutableListOf<Long>(
a.toLong(), b, c)) == 1L) {
pythagorasList.add(
PythagorasNumber(a.toLong(), b, c))
}
}
}
pythagorasList.forEach{ println(it) }
println(pythagorasList.count())
}
fun calcGcm(numList: MutableList<Long>): Long {
var newList =
numList.distinct().sorted() as MutableList
var r: Long = 0
while (newList.count() > 1) {
r = newList[0]
newList = newList.
takeLast(newList.count() - 1).map {
it % newList[0]} as MutableList
newList.add(r)
newList = newList.distinct().sorted().
filter { it != 0L } as MutableList<Long>
}
return r
}
}

package com.improve_future.math

object Main {

@JvmStatic

fun main(args: Array<String>) {

val pythagorasList =

mutableListOf<PythagorasNumber>()

val m = 1000L

for (c in 5L..m step 2) {

for (b in c - 1 downTo

(c.toDouble() / Math.sqrt(2.0) + 1).

toLong()) {

val a = Math.sqrt(

Math.pow(c.toDouble(), 2.0) -

Math.pow(b.toDouble(), 2.0))

if (a % 1 == 0.0 &&

calcGcm(mutableListOf<Long>(

a.toLong(), b, c)) == 1L) {

pythagorasList.add(

PythagorasNumber(a.toLong(), b, c))

}

pythagorasList.forEach{ println(it) }

println(pythagorasList.count())

}

fun calcGcm(numList: MutableList<Long>): Long {

var newList =

numList.distinct().sorted() as MutableList

var r: Long = 0

while (newList.count() > 1) {

r = newList[0]

newList = newList.

takeLast(newList.count() - 1).map {

it % newList[0]} as MutableList

newList.add(r)

newList = newList.distinct().sorted().

filter { it != 0L } as MutableList<Long>

}

return r

}

実行結果

( c leq 1000 ) では 158件みつかりました。

(3, 4, 5)
(5, 12, 13)
(8, 15, 17)
(7, 24, 25)
(20, 21, 29)
(12, 35, 37)
(9, 40, 41)
(28, 45, 53)
(11, 60, 61)
(16, 63, 65)
(33, 56, 65)
(48, 55, 73)
(13, 84, 85)
(36, 77, 85)
(39, 80, 89)
(65, 72, 97)
(20, 99, 101)
(60, 91, 109)
(15, 112, 113)
(44, 117, 125)
(88, 105, 137)
(17, 144, 145)
(24, 143, 145)
(51, 140, 149)
(85, 132, 157)
(119, 120, 169)
(52, 165, 173)
(19, 180, 181)
(57, 176, 185)
(104, 153, 185)
(95, 168, 193)
(28, 195, 197)
(84, 187, 205)
(133, 156, 205)
(21, 220, 221)
(140, 171, 221)
(60, 221, 229)
(105, 208, 233)
(120, 209, 241)
(32, 255, 257)
(23, 264, 265)
(96, 247, 265)
(69, 260, 269)
(115, 252, 277)
(160, 231, 281)
(161, 240, 289)
(68, 285, 293)
(136, 273, 305)
(207, 224, 305)
(25, 312, 313)
(75, 308, 317)
(36, 323, 325)
(204, 253, 325)
(175, 288, 337)
(180, 299, 349)
(225, 272, 353)
(27, 364, 365)
(76, 357, 365)
(252, 275, 373)
(135, 352, 377)
(152, 345, 377)
(189, 340, 389)
(228, 325, 397)
(40, 399, 401)
(120, 391, 409)
(29, 420, 421)
(87, 416, 425)
(297, 304, 425)
(145, 408, 433)
(84, 437, 445)
(203, 396, 445)
(280, 351, 449)
(168, 425, 457)
(261, 380, 461)
(31, 480, 481)
(319, 360, 481)
(44, 483, 485)
(93, 476, 485)
(132, 475, 493)
(155, 468, 493)
(217, 456, 505)
(336, 377, 505)
(220, 459, 509)
(279, 440, 521)
(92, 525, 533)
(308, 435, 533)
(341, 420, 541)
(33, 544, 545)
(184, 513, 545)
(165, 532, 557)
(276, 493, 565)
(396, 403, 565)
(231, 520, 569)
(48, 575, 577)
(368, 465, 593)
(240, 551, 601)
(35, 612, 613)
(105, 608, 617)
(336, 527, 625)
(100, 621, 629)
(429, 460, 629)
(200, 609, 641)
(315, 572, 653)
(300, 589, 661)
(385, 552, 673)
(52, 675, 677)
(37, 684, 685)
(156, 667, 685)
(111, 680, 689)
(400, 561, 689)
(185, 672, 697)
(455, 528, 697)
(260, 651, 701)
(259, 660, 709)
(333, 644, 725)
(364, 627, 725)
(108, 725, 733)
(216, 713, 745)
(407, 624, 745)
(468, 595, 757)
(39, 760, 761)
(481, 600, 769)
(195, 748, 773)
(56, 783, 785)
(273, 736, 785)
(168, 775, 793)
(432, 665, 793)
(555, 572, 797)
(280, 759, 809)
(429, 700, 821)
(540, 629, 829)
(41, 840, 841)
(116, 837, 845)
(123, 836, 845)
(205, 828, 853)
(232, 825, 857)
(287, 816, 865)
(504, 703, 865)
(348, 805, 877)
(369, 800, 881)
(60, 899, 901)
(451, 780, 901)
(464, 777, 905)
(616, 663, 905)
(43, 924, 925)
(533, 756, 925)
(129, 920, 929)
(215, 912, 937)
(580, 741, 941)
(301, 900, 949)
(420, 851, 949)
(615, 728, 953)
(124, 957, 965)
(387, 884, 965)
(248, 945, 977)
(473, 864, 985)
(696, 697, 985)
(372, 925, 997)
158

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

(3, 4, 5)

(5, 12, 13)

(8, 15, 17)

(7, 24, 25)

(20, 21, 29)

(12, 35, 37)

(9, 40, 41)

(28, 45, 53)

(11, 60, 61)

(16, 63, 65)

(33, 56, 65)

(48, 55, 73)

(13, 84, 85)

(36, 77, 85)

(39, 80, 89)

(65, 72, 97)

(20, 99, 101)

(60, 91, 109)

(15, 112, 113)

(44, 117, 125)

(88, 105, 137)

(17, 144, 145)

(24, 143, 145)

(51, 140, 149)

(85, 132, 157)

(119, 120, 169)

(52, 165, 173)

(19, 180, 181)

(57, 176, 185)

(104, 153, 185)

(95, 168, 193)

(28, 195, 197)

(84, 187, 205)

(133, 156, 205)

(21, 220, 221)

(140, 171, 221)

(60, 221, 229)

(105, 208, 233)

(120, 209, 241)

(32, 255, 257)

(23, 264, 265)

(96, 247, 265)

(69, 260, 269)

(115, 252, 277)

(160, 231, 281)

(161, 240, 289)

(68, 285, 293)

(136, 273, 305)

(207, 224, 305)

(25, 312, 313)

(75, 308, 317)

(36, 323, 325)

(204, 253, 325)

(175, 288, 337)

(180, 299, 349)

(225, 272, 353)

(27, 364, 365)

(76, 357, 365)

(252, 275, 373)

(135, 352, 377)

(152, 345, 377)

(189, 340, 389)

(228, 325, 397)

(40, 399, 401)

(120, 391, 409)

(29, 420, 421)

(87, 416, 425)

(297, 304, 425)

(145, 408, 433)

(84, 437, 445)

(203, 396, 445)

(280, 351, 449)

(168, 425, 457)

(261, 380, 461)

(31, 480, 481)

(319, 360, 481)

(44, 483, 485)

(93, 476, 485)

(132, 475, 493)

(155, 468, 493)

(217, 456, 505)

(336, 377, 505)

(220, 459, 509)

(279, 440, 521)

(92, 525, 533)

(308, 435, 533)

(341, 420, 541)

(33, 544, 545)

(184, 513, 545)

(165, 532, 557)

(276, 493, 565)

(396, 403, 565)

(231, 520, 569)

(48, 575, 577)

(368, 465, 593)

(240, 551, 601)

(35, 612, 613)

(105, 608, 617)

(336, 527, 625)

(100, 621, 629)

(429, 460, 629)

(200, 609, 641)

(315, 572, 653)

(300, 589, 661)

(385, 552, 673)

(52, 675, 677)

(37, 684, 685)

(156, 667, 685)

(111, 680, 689)

(400, 561, 689)

(185, 672, 697)

(455, 528, 697)

(260, 651, 701)

(259, 660, 709)

(333, 644, 725)

(364, 627, 725)

(108, 725, 733)

(216, 713, 745)

(407, 624, 745)

(468, 595, 757)

(39, 760, 761)

(481, 600, 769)

(195, 748, 773)

(56, 783, 785)

(273, 736, 785)

(168, 775, 793)

(432, 665, 793)

(555, 572, 797)

(280, 759, 809)

(429, 700, 821)

(540, 629, 829)

(41, 840, 841)

(116, 837, 845)

(123, 836, 845)

(205, 828, 853)

(232, 825, 857)

(287, 816, 865)

(504, 703, 865)

(348, 805, 877)

(369, 800, 881)

(60, 899, 901)

(451, 780, 901)

(464, 777, 905)

(616, 663, 905)

(43, 924, 925)

(533, 756, 925)

(129, 920, 929)

(215, 912, 937)

(580, 741, 941)

(301, 900, 949)

(420, 851, 949)

(615, 728, 953)

(124, 957, 965)

(387, 884, 965)

(248, 945, 977)

(473, 864, 985)

(696, 697, 985)

(372, 925, 997)

158

The Life