Time for an 2014 update…

This commit is contained in:
Ingy döt Net 2014-01-17 05:32:22 +00:00
parent 372c577f83
commit 09687c4926
2520 changed files with 34227 additions and 7318 deletions

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@ -0,0 +1,32 @@
10 HOME
100 N = 27
110 GOSUB 400"HAILSTONE
120 DEF FN L(I) = E(I + 4 * (I < 0))
130IFL=112AND(S(0)=27ANDS(1)=82ANDS(2)=41ANDS(3)=124)AND(FNL(M-3)=8ANDFNL(M-2)=4ANDFNL(M-1)=2ANDFNL(M)=1)THENPRINT"THE HAILSTONE SEQUENCE FOR THE NUMBER 27 HAS 112 ELEMENTS STARTING WITH 27, 82, 41, 124 AND ENDING WITH 8, 4, 2, 1"
140 PRINT
150 V = PEEK(37) + 1
200 N = 1
210 GOSUB 400"HAILSTONE
220 MN = 1
230 ML = L
240 FOR I = 2 TO 99999
250 N = I
260 GOSUB 400"HAILSTONE
270 IFL>MLTHENMN=I:ML=L:VTABV:HTAB1:PRINT "THE NUMBER " MN " HAS A HAILSTONE SEQUENCE LENGTH OF "L" WHICH IS THE LONGEST HAILSTONE SEQUENCE OF NUMBERS LESS THAN ";:Y=PEEK(37)+1:X=PEEK(36)+1
280 IF Y THEN VTAB Y : HTAB X : PRINTI+1;
290 NEXT I
300 END
400 M = 0
410 FOR L = 1 TO 1E38
420 IF L < 5 THEN S(L-1) = N
430 M = (M + 1) * (M < 3)
440 E(M) = N
450 IF N = 1 THEN RETURN
460 EVEN = INT(N/2)=N/2
470 IF EVEN THEN N=N/2
480 IF NOT EVEN THEN N = (3 * N) + 1
490 NEXT L : STOP

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@ -0,0 +1,23 @@
seqlen% = FNhailstone(27, TRUE)
PRINT '"Sequence length = "; seqlen%
maxlen% = 0
FOR number% = 2 TO 100000
seqlen% = FNhailstone(number%, FALSE)
IF seqlen% > maxlen% THEN
maxlen% = seqlen%
maxnum% = number%
ENDIF
NEXT
PRINT "The number with the longest hailstone sequence is " ; maxnum%
PRINT "Its sequence length is " ; maxlen%
END
DEF FNhailstone(N%, S%)
LOCAL L%
IF S% THEN PRINT N%;
WHILE N% <> 1
IF N% AND 1 THEN N% = 3 * N% + 1 ELSE N% DIV= 2
IF S% THEN PRINT N%;
L% += 1
ENDWHILE
= L% + 1

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@ -0,0 +1,52 @@
print "Part 1: Create a routine to generate the hailstone sequence for a number."
print ""
while hailstone < 1 or hailstone <> int(hailstone)
input "Please enter a positive integer: "; hailstone
wend
print ""
print "The following is the 'Hailstone Sequence' for your number..."
print ""
print hailstone
while hailstone <> 1
if hailstone / 2 = int(hailstone / 2) then hailstone = hailstone / 2 else hailstone = (3 * hailstone) + 1
print hailstone
wend
print ""
input "Hit 'Enter' to continue to part 2...";dummy$
cls
print "Part 2: Use the routine to show that the hailstone sequence for the number 27 has 112 elements starting with 27, 82, 41, 124 and ending with 8, 4, 2, 1."
print ""
print "No. in Seq.","Hailstone Sequence Number for 27"
print ""
c = 1: hailstone = 27
print c, hailstone
while hailstone <> 1
c = c + 1
if hailstone / 2 = int(hailstone / 2) then hailstone = hailstone / 2 else hailstone = (3 * hailstone) + 1
print c, hailstone
wend
print ""
input "Hit 'Enter' to continue to part 3...";dummy$
cls
print "Part 3: Show the number less than 100,000 which has the longest hailstone sequence together with that sequence's length.(But don't show the actual sequence)!"
print ""
print "Calculating result... Please wait... This could take a little while..."
print ""
print "Percent Done", "Start Number", "Seq. Length", "Maximum Sequence So Far"
print ""
for cc = 1 to 99999
hailstone = cc: c = 1
while hailstone <> 1
c = c + 1
if hailstone / 2 = int(hailstone / 2) then hailstone = hailstone / 2 else hailstone = (3 * hailstone) + 1
wend
if c > max then max = c: largesthailstone = cc
locate 1, 7
print " "
locate 1, 7
print using("###.###", cc / 99999 * 100);"%", cc, c, max
scan
next cc
print ""
print "The number less than 100,000 with the longest 'Hailstone Sequence' is "; largesthailstone;". It's sequence length is "; max;"."
end

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function Hailstone(sys *n)
'=========================
if n and 1
n=n*3+1
else
n=n>>1
end if
end function
function HailstoneSequence(sys n) as sys
'=======================================
count=1
do
Hailstone n
Count++
if n=1 then exit do
end do
return count
end function
'MAIN
'====
maxc=0
maxn=0
e=100000
for n=1 to e
c=HailstoneSequence n
if c>maxc
maxc=c
maxn=n
end if
next
print e ", " maxn ", " maxc
'result 100000, 77031, 351

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@ -0,0 +1,48 @@
NewList Hailstones.i() ; Make a linked list to use as we do not know the numbers of elements needed for an Array
Procedure.i FillHailstones(n) ; Fills the list & returns the amount of elements in the list
Shared Hailstones() ; Get access to the Hailstones-List
ClearList(Hailstones()) ; Remove old data
Repeat
AddElement(Hailstones()) ; Add an element to the list
Hailstones()=n ; Fill current value in the new list element
If n=1
ProcedureReturn ListSize(Hailstones())
ElseIf n%2=0
n/2
Else
n=(3*n)+1
EndIf
ForEver
EndProcedure
If OpenConsole()
Define i, l, maxl, maxi
l=FillHailstones(27)
Print("#27 has "+Str(l)+" elements and the sequence is: "+#CRLF$)
ForEach Hailstones()
If i=6
Print(#CRLF$)
i=0
EndIf
i+1
Print(RSet(Str(Hailstones()),5))
If Hailstones()<>1
Print(", ")
EndIf
Next
i=1
Repeat
l=FillHailstones(i)
If l>maxl
maxl=l
maxi=i
EndIf
i+1
Until i>=100000
Print(#CRLF$+#CRLF$+"The longest sequence below 100000 is #"+Str(maxi)+", and it has "+Str(maxl)+" elements.")
Print(#CRLF$+#CRLF$+"Press ENTER to exit."): Input()
CloseConsole()
EndIf

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@ -0,0 +1,40 @@
print "Part 1: Create a routine to generate the hailstone sequence for a number."
print ""
while hailstone < 1 or hailstone <> int(hailstone)
input "Please enter a positive integer: "; hailstone
wend
count = doHailstone(hailstone,"Y")
print: print "Part 2: Use the routine to show that the hailstone sequence for the number 27 has 112 elements starting with 27, 82, 41, 124 and ending with 8, 4, 2, 1."
count = doHailstone(27,"Y")
print: print "Part 3: Show the number less than 100,000 which has the longest hailstone sequence together with that sequence's length.(But don't show the actual sequence)!"
print "Calculating result... Please wait... This could take a little while..."
print "Stone Percent Count"
for i = 1 to 99999
count = doHailstone(i,"N")
if count > maxCount then
theBigStone = i
maxCount = count
print using("#####",i);" ";using("###.#", i / 99999 * 100);"% ";using("####",count)
end if
next i
end
'---------------------------------------------
' pass number and print (Y/N)
FUNCTION doHailstone(hailstone,prnt$)
if prnt$ = "Y" then
print
print "The following is the 'Hailstone Sequence' for number:";hailstone
end if
while hailstone <> 1
if (hailstone and 1) then hailstone = (hailstone * 3) + 1 else hailstone = hailstone / 2
doHailstone = doHailstone + 1
if prnt$ = "Y" then
print hailstone;chr$(9);
if (doHailstone mod 10) = 0 then print
end if
wend
END FUNCTION

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@ -0,0 +1,42 @@
Module HailstoneSequence
Sub Main()
' Checking sequence of 27.
Dim l As List(Of Long) = HailstoneSequence(27)
Console.WriteLine("27 has {0} elements in sequence:", l.Count())
For i As Integer = 0 To 3 : Console.Write("{0}, ", l(i)) : Next
Console.Write("... ")
For i As Integer = l.Count - 4 To l.Count - 1 : Console.Write(", {0}", l(i)) : Next
Console.WriteLine()
' Finding longest sequence for numbers below 100000.
Dim max As Integer = 0
Dim maxCount As Integer = 0
For i = 1 To 99999
l = HailstoneSequence(i)
If l.Count > maxCount Then
max = i
maxCount = l.Count
End If
Next
Console.WriteLine("Max elements in sequence for number below 100k: {0} with {1} elements.", max, maxCount)
Console.ReadLine()
End Sub
Private Function HailstoneSequence(ByVal n As Long) As List(Of Long)
Dim valList As New List(Of Long)()
valList.Add(n)
Do Until n = 1
n = IIf(n Mod 2 = 0, n / 2, (3 * n) + 1)
valList.Add(n)
Loop
Return valList
End Function
End Module

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@ -1,4 +1,4 @@
hailstone:
local hailstone:
swap [ over ]
while < 1 dup:
if % over 2:
@ -10,25 +10,27 @@ hailstone:
swap push-through rot dup
drop
local :h27 hailstone 27
. = 112 len h27
. = 27 h27! 0
. = 82 h27! 1
. = 41 h27! 2
. = 124 h27! 3
. = 8 h27! 108
. = 4 h27! 109
. = 2 h27! 110
. = 1 h27! 111
if = (name) :(main):
local :h27 hailstone 27
!. = 112 len h27
!. = 27 h27! 0
!. = 82 h27! 1
!. = 41 h27! 2
!. = 124 h27! 3
!. = 8 h27! 108
!. = 4 h27! 109
!. = 2 h27! 110
!. = 1 h27! 111
local :max 0
local :maxlen 0
for i range 1 99999:
dup len hailstone i
if < maxlen:
set :maxlen
set :max i
else:
drop
print( "number: " max ", length: " maxlen )
local :max 0
local :maxlen 0
for i range 1 99999:
dup len hailstone i
if < maxlen:
set :maxlen
set :max i
else:
drop
!print( "number: " to-str max ", length: " to-str maxlen )
else:
@hailstone

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@ -2,8 +2,10 @@ package main
import "fmt"
func hs(n int, seq *[]int) {
s := append((*seq)[:0], n)
// 1st arg is the number to generate the sequence for.
// 2nd arg is a slice to recycle, to reduce garbage.
func hs(n int, recycle []int) []int {
s := append(recycle[:0], n)
for n > 1 {
if n&1 == 0 {
n = n / 2
@ -12,21 +14,18 @@ func hs(n int, seq *[]int) {
}
s = append(s, n)
}
*seq = s
return s
}
func main() {
var seq []int
hs(27, &seq)
seq := hs(27, nil)
fmt.Printf("hs(27): %d elements: [%d %d %d %d ... %d %d %d %d]\n",
len(seq), seq[0], seq[1], seq[2], seq[3],
seq[len(seq)-4], seq[len(seq)-3], seq[len(seq)-2], seq[len(seq)-1])
var maxN, maxLen int
for n := 1; n < 100000; n++ {
// reusing seq reduces garbage
hs(n, &seq)
seq = hs(n, seq)
if len(seq) > maxLen {
maxN = n
maxLen = len(seq)

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@ -1,7 +1,7 @@
function hailstone(n)
seq = [n]
while n>1
n = n % 2 == 0 ? n/2 : 3n + 1
n = n % 2 == 0 ? n >> 1 : 3n + 1
push!(seq,n)
end
return seq

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@ -0,0 +1,52 @@
implement Hailstone;
include "sys.m"; sys: Sys;
include "draw.m";
Hailstone: module {
init: fn(ctxt: ref Draw->Context, args: list of string);
};
init(nil: ref Draw->Context, nil: list of string)
{
sys = load Sys Sys->PATH;
seq := hailstone(big 27);
l := len seq;
sys->print("hailstone(27): ");
for(i := 0; i < 4; i++) {
sys->print("%bd, ", hd seq);
seq = tl seq;
}
sys->print("⋯");
while(len seq > 4)
seq = tl seq;
while(seq != nil) {
sys->print(", %bd", hd seq);
seq = tl seq;
}
sys->print(" (length %d)\n", l);
max := 1;
maxn := big 1;
for(n := big 2; n < big 100000; n++) {
cur := len hailstone(n);
if(cur > max) {
max = cur;
maxn = n;
}
}
sys->print("hailstone(%bd) has length %d\n", maxn, max);
}
hailstone(i: big): list of big
{
if(i == big 1)
return big 1 :: nil;
if(i % big 2 == big 0)
return i :: hailstone(i / big 2);
return i :: hailstone((big 3 * i) + big 1);
}

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@ -26,6 +26,5 @@ hailstone: procedure expose @.; parse arg n 1 s 1 o /*N,S,O = 1st arg.*/
else n=n%2 /* " " " even, perform fast ÷ */
s=s n /*build a sequence list (append).*/
end /*forever*/
@.o=s /*memoization for this hailstone.*/
@.o=subword(s,2)
@.o=subword(s,2) /*memoization for this hailstone.*/
return s