Minimal steps down to 1: Difference between revisions
Minimal steps down to 1 in FreeBASIC
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There is one number below 2000 that requires 17 steps: 1699
There is one number below 20000 that requires 24 steps: 19681</pre>
=={{header|FreeBASIC}}==
{{trans|XPL0}}
<lang freebasic>Dim Shared As Integer minPasos 'minimal number of steps to get to 1
Dim Shared As Integer Subtractor '1 or 2
Dim Shared As Integer Ns(20000), Ops(20000), MinNs(20000), MinOps(20000)
Sub Reduce(N As Integer, Paso As Integer) 'Reduce N to 1, recording minimum steps
If N = 1 Then
If Paso < minPasos Then
For i As Integer = 0 To Paso-1
MinOps(i) = Ops(i)
MinNs(i) = Ns(i)
Next i
minPasos = Paso
End If
End If
If Paso >= minPasos Then Exit Sub 'don't search further
If N Mod 3 = 0 Then Ops(Paso) = 3 : Ns(Paso) = N/3 : Reduce(N/3, Paso+1)
If N Mod 2 = 0 Then Ops(Paso) = 2 : Ns(Paso) = N/2 : Reduce(N/2, Paso+1)
Ops(Paso) = -Subtractor
Ns(Paso) = N-Subtractor
Reduce(N-Subtractor, Paso+1)
End Sub
Sub ShowSteps(N As Integer) 'Show minimal steps and how N steps to 1
minPasos = 50000
Reduce(N, 0)
Print "N = " & N & " takes " & minPasos & " steps: N";
For i As Integer = 0 To minPasos-1
Print Iif(Sgn(MinOps(i)) < 0, " -", " /");
Print Abs(MinOps(i)) & "=>" & MinNs(i); '" "
Next i
Print
End Sub
Sub ShowCount(Range As Integer) 'Show count of maximum minimal steps and their Ns
Dim As Integer N, MaxSteps
MaxSteps = 0 'find maximum number of minimum steps
For N = 1 To Range
minPasos = 50000
Reduce(N, 0)
If minPasos > MaxSteps Then MaxSteps = minPasos
Next N
Print "Maximum steps:"; MaxSteps; " for N =";
For N = 1 To Range 'show numbers (Ns) for Maximum steps
minPasos = 50000
Reduce(N, 0)
If minPasos = MaxSteps Then Print N; '" ";
Next N
Print
End Sub
Dim As Integer N
Subtractor = 1 '1.
For N = 1 To 10
ShowSteps(N)
Next N
ShowCount(2000) '2.
ShowCount(20000) '2a.
Print
Subtractor = 2 '3.
For N = 1 To 10
ShowSteps(N)
Next N
ShowCount(2000) '4.
ShowCount(20000) '4a.
Sleep</lang>
{{out}}
<pre>Same as XPL0 entry.</pre>
=={{header|Go}}==
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