Taxicab numbers: Difference between revisions
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=={{header|VBA}}==
<lang vb>Public Type tuple
i As Variant
j As Variant
sum As Variant
End Type
Public Type tuple3
i1 As Variant
j1 As Variant
i2 As Variant
j2 As Variant
i3 As Variant
j3 As Variant
sum As Variant
End Type
Sub taxicab_numbers()
Dim i As Variant, j As Variant
Dim k As Long
Const MAX = 2019
Dim p(MAX) As Variant
Const bigMAX = (MAX + 1) * (MAX / 2)
Dim big(1 To bigMAX) As tuple
Const resMAX = 4400
Dim res(1 To resMAX) As tuple3
For i = 1 To MAX
p(i) = CDec(i * i * i) 'convert Variant to Decimal
Next i 'wich hold numbers upto 10^28
k = 1
For i = 1 To MAX
For j = i To MAX
big(k).i = CDec(i)
big(k).j = CDec(j)
big(k).sum = CDec(p(i) + p(j))
k = k + 1
Next j
Next i
n = 1
Quicksort big, LBound(big), UBound(big)
For i = 1 To bigMAX - 1
If big(i).sum = big(i + 1).sum Then
res(n).i1 = CStr(big(i).i)
res(n).j1 = CStr(big(i).j)
res(n).i2 = CStr(big(i + 1).i)
res(n).j2 = CStr(big(i + 1).j)
If big(i + 1).sum = big(i + 2).sum Then
res(n).i3 = CStr(big(i + 2).i)
res(n).j3 = CStr(big(i + 2).j)
i = i + 1
End If
res(n).sum = CStr(big(i).sum)
n = n + 1
i = i + 1
End If
Next i
Debug.Print n - 1; " taxis"
For i = 1 To 25
With res(i)
Debug.Print String$(4 - Len(CStr(i)), " "); i;
Debug.Print String$(11 - Len(.sum), " "); .sum; " = ";
Debug.Print String$(4 - Len(.i1), " "); .i1; "^3 +";
Debug.Print String$(4 - Len(.j1), " "); .j1; "^3 = ";
Debug.Print String$(4 - Len(.i2), " "); .i2; "^3 +";
Debug.Print String$(4 - Len(.j2), " "); .j2; "^3"
End With
Next i
Debug.Print
For i = 2000 To 2006
With res(i)
Debug.Print String$(4 - Len(CStr(i)), " "); i;
Debug.Print String$(11 - Len(.sum), " "); .sum; " = ";
Debug.Print String$(4 - Len(.i1), " "); .i1; "^3 +";
Debug.Print String$(4 - Len(.j1), " "); .j1; "^3 = ";
Debug.Print String$(4 - Len(.i2), " "); .i2; "^3 +";
Debug.Print String$(4 - Len(.j2), " "); .j2; "^3"
End With
Next i
Debug.Print
For i = 1 To resMAX
If res(i).i3 <> "" Then
With res(i)
Debug.Print String$(4 - Len(CStr(i)), " "); i;
Debug.Print String$(11 - Len(.sum), " "); .sum; " = ";
Debug.Print String$(4 - Len(.i1), " "); .i1; "^3 +";
Debug.Print String$(4 - Len(.j1), " "); .j1; "^3 = ";
Debug.Print String$(4 - Len(.i2), " "); .i2; "^3 +";
Debug.Print String$(4 - Len(.j2), " "); .j2; "^3";
Debug.Print String$(4 - Len(.i3), " "); .i3; "^3 +";
Debug.Print String$(4 - Len(.j3), " "); .j3; "^3"
End With
End If
Next i
End Sub
Sub Quicksort(vArray() As tuple, arrLbound As Long, arrUbound As Long)
'https://wellsr.com/vba/2018/excel/vba-quicksort-macro-to-sort-arrays-fast/
'Sorts a one-dimensional VBA array from smallest to largest
'using a very fast quicksort algorithm variant.
'Adapted to multidimensions/typedef
Dim pivotVal As Variant
Dim vSwap As tuple
Dim tmpLow As Long
Dim tmpHi As Long
tmpLow = arrLbound
tmpHi = arrUbound
pivotVal = vArray((arrLbound + arrUbound) \ 2).sum
While (tmpLow <= tmpHi) 'divide
While (vArray(tmpLow).sum < pivotVal And tmpLow < arrUbound)
tmpLow = tmpLow + 1
Wend
While (pivotVal < vArray(tmpHi).sum And tmpHi > arrLbound)
tmpHi = tmpHi - 1
Wend
If (tmpLow <= tmpHi) Then
vSwap.i = vArray(tmpLow).i
vSwap.j = vArray(tmpLow).j
vSwap.sum = vArray(tmpLow).sum
vArray(tmpLow).i = vArray(tmpHi).i
vArray(tmpLow).j = vArray(tmpHi).j
vArray(tmpLow).sum = vArray(tmpHi).sum
vArray(tmpHi).i = vSwap.i
vArray(tmpHi).j = vSwap.j
vArray(tmpHi).sum = vSwap.sum
tmpLow = tmpLow + 1
tmpHi = tmpHi - 1
End If
Wend
If (arrLbound < tmpHi) Then Quicksort vArray, arrLbound, tmpHi 'conquer
If (tmpLow < arrUbound) Then Quicksort vArray, tmpLow, arrUbound 'conquer
End Sub</lang>{{out}}
<pre> 4399 taxis
1 1729 = 9^3 + 10^3 = 1^3 + 12^3
2 4104 = 2^3 + 16^3 = 9^3 + 15^3
3 13832 = 2^3 + 24^3 = 18^3 + 20^3
4 20683 = 19^3 + 24^3 = 10^3 + 27^3
5 32832 = 18^3 + 30^3 = 4^3 + 32^3
6 39312 = 15^3 + 33^3 = 2^3 + 34^3
7 40033 = 16^3 + 33^3 = 9^3 + 34^3
8 46683 = 27^3 + 30^3 = 3^3 + 36^3
9 64232 = 26^3 + 36^3 = 17^3 + 39^3
10 65728 = 31^3 + 33^3 = 12^3 + 40^3
11 110656 = 4^3 + 48^3 = 36^3 + 40^3
12 110808 = 27^3 + 45^3 = 6^3 + 48^3
13 134379 = 12^3 + 51^3 = 38^3 + 43^3
14 149389 = 29^3 + 50^3 = 8^3 + 53^3
15 165464 = 38^3 + 48^3 = 20^3 + 54^3
16 171288 = 24^3 + 54^3 = 17^3 + 55^3
17 195841 = 9^3 + 58^3 = 22^3 + 57^3
18 216027 = 22^3 + 59^3 = 3^3 + 60^3
19 216125 = 45^3 + 50^3 = 5^3 + 60^3
20 262656 = 36^3 + 60^3 = 8^3 + 64^3
21 314496 = 4^3 + 68^3 = 30^3 + 66^3
22 320264 = 32^3 + 66^3 = 18^3 + 68^3
23 327763 = 51^3 + 58^3 = 30^3 + 67^3
24 373464 = 54^3 + 60^3 = 6^3 + 72^3
25 402597 = 56^3 + 61^3 = 42^3 + 69^3
2000 1671816384 = 940^3 + 944^3 = 428^3 +1168^3
2001 1672470592 = 29^3 +1187^3 = 632^3 +1124^3
2002 1673170856 = 828^3 +1034^3 = 458^3 +1164^3
2003 1675045225 = 744^3 +1081^3 = 522^3 +1153^3
2004 1675958167 = 492^3 +1159^3 = 711^3 +1096^3
2005 1676926719 = 714^3 +1095^3 = 63^3 +1188^3
2006 1677646971 = 99^3 +1188^3 = 891^3 + 990^3
455 87539319 = 167^3 + 436^3 = 228^3 + 423^3 255^3 + 414^3
535 119824488 = 90^3 + 492^3 = 346^3 + 428^3 11^3 + 493^3
588 143604279 = 408^3 + 423^3 = 359^3 + 460^3 111^3 + 522^3
655 175959000 = 70^3 + 560^3 = 315^3 + 525^3 198^3 + 552^3
888 327763000 = 300^3 + 670^3 = 339^3 + 661^3 510^3 + 580^3
1299 700314552 = 334^3 + 872^3 = 456^3 + 846^3 510^3 + 828^3
1398 804360375 = 15^3 + 930^3 = 295^3 + 920^3 198^3 + 927^3
1515 958595904 = 22^3 + 986^3 = 180^3 + 984^3 692^3 + 856^3
1660 1148834232 = 718^3 + 920^3 = 816^3 + 846^3 222^3 +1044^3
1837 1407672000 = 140^3 +1120^3 = 396^3 +1104^3 630^3 +1050^3
2100 1840667192 = 681^3 +1151^3 = 372^3 +1214^3 225^3 +1223^3
2143 1915865217 = 9^3 +1242^3 = 484^3 +1217^3 969^3 +1002^3
2365 2363561613 = 501^3 +1308^3 = 684^3 +1269^3 765^3 +1242^3
2480 2622104000 = 1020^3 +1160^3 = 600^3 +1340^3 678^3 +1322^3
2670 3080802816 = 904^3 +1328^3 = 81^3 +1455^3 456^3 +1440^3
2732 3235261176 = 33^3 +1479^3 = 270^3 +1476^31038^3 +1284^3
2845 3499524728 = 116^3 +1518^3 = 350^3 +1512^31169^3 +1239^3
2895 3623721192 = 348^3 +1530^3 = 761^3 +1471^31098^3 +1320^3
2979 3877315533 = 1224^3 +1269^3 = 1077^3 +1380^3 333^3 +1566^3
3293 4750893000 = 210^3 +1680^3 = 945^3 +1575^3 594^3 +1656^3
3562 5544709352 = 207^3 +1769^3 = 1076^3 +1626^3 842^3 +1704^3
3589 5602516416 = 912^3 +1692^3 = 1020^3 +1656^3 668^3 +1744^3
3826 6434883000 = 590^3 +1840^3 = 30^3 +1860^3 396^3 +1854^3
4162 7668767232 = 44^3 +1972^3 = 1384^3 +1712^3 360^3 +1968^3
4359 8849601000 = 1017^3 +1983^3 = 1530^3 +1740^3 900^3 +2010^3</pre>
=={{header|zkl}}==
{{trans|D}}
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