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Leaving the least (the most) (Posted on 2017-10-27) Difficulty: 2 of 5
a. Erase 100 digits from the sequence:
in 1234567891011121314….585960
in a way, that the remaining digits, read as a continuous base-10 number,
produce a minimal result.

b. Same task, striving to get the largest number.

Do not change the digits' order, allow leading zeroes.

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solutions Comment 2 of 2 |
Part a:

If you require there be no leading zeros:

(the kept digits have a caret under them)

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960
^         ^                   ^                   ^                   ^                   ^ ^ ^ ^ ^           ^
10000012340

If leading zeros are allowed:
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960
          ^                   ^                   ^                   ^                   ^ ^ ^ ^ ^^          ^
00000123450

Part b:
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960
        ^                   ^                   ^                   ^                   ^               ^ ^^^^^
99999785960

See the similar Leaving a Maximal Result pid=10939, for a discussion.


The biggest change was in assuring a non-zero first digit. Other than that it was just changing the direction of an inequality.


DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 Open "leaving the least-most.txt" For Output As #2
 
  s$ = ""
 For i = 1 To 60
   s = s + LTrim(Str(i))
 Next
 
 ReDim kept(11)
 ptr = 1: need = 11: keep$ = ""
 Do
   If Len(keep) = 0 Then
     While Mid(s, ptr, 1) = "0"
       ptr = ptr + 1
     Wend
   End If
   cmp$ = Mid(s, ptr, 1)
   found = 0
   For i = ptr + 1 To Len(s) + 1 - need
     If Mid(s, i, 1) < cmp And (Mid(s, i, 1) > "0" Or keep > "") Then
       ptr = i
       found = 1
       Exit For
     End If
   Next
   If found = 0 Then
     keep = keep + cmp$
     need = need - 1
     kept(Len(keep)) = ptr
     ptr = ptr + 1
   End If
 Loop Until need = 0
 
 Text1.Text = Text1.Text & s & crlf
 Print #2, s
 prev = 0
 For i = 1 To 11
   Text1.Text = Text1.Text & Space(kept(i) - prev - 1) & "^"
   Print #2, Space(kept(i) - prev - 1) + "^";
   prev = kept(i)
 Next
 Text1.Text = Text1.Text & crlf & keep & crlf
 Print #2,
 Print #2, keep
 Print #2,
  
  s$ = ""
 For i = 1 To 60
   s = s + LTrim(Str(i))
 Next
 
 ReDim kept(11)
 ptr = 1: need = 11: keep$ = ""
 Do
   cmp$ = Mid(s, ptr, 1)
   found = 0
   For i = ptr + 1 To Len(s) + 1 - need
     If Mid(s, i, 1) < cmp Then
       ptr = i
       found = 1
       Exit For
     End If
   Next
   If found = 0 Then
     keep = keep + cmp$
     need = need - 1
     kept(Len(keep)) = ptr
     ptr = ptr + 1
   End If
 Loop Until need = 0
 
 Text1.Text = Text1.Text & s & crlf
 Print #2, s
 prev = 0
 For i = 1 To 11
   Text1.Text = Text1.Text & Space(kept(i) - prev - 1) & "^"
   Print #2, Space(kept(i) - prev - 1) + "^";
   prev = kept(i)
 Next
 Text1.Text = Text1.Text & crlf & keep & crlf
 Print #2,
 Print #2, keep
 Print #2,
 
 s$ = ""
 For i = 1 To 60
   s = s + LTrim(Str(i))
 Next
 
 ReDim kept(11)
 ptr = 1: need = 11: keep$ = ""
 Do
   cmp$ = Mid(s, ptr, 1)
   found = 0
   For i = ptr + 1 To Len(s) + 1 - need
     If Mid(s, i, 1) > cmp Then
       ptr = i
       found = 1
       Exit For
     End If
   Next
   If found = 0 Then
     keep = keep + cmp$
     need = need - 1
     kept(Len(keep)) = ptr
     ptr = ptr + 1
   End If
 Loop Until need = 0
 
 Text1.Text = Text1.Text & s & crlf
 Print #2, s
 prev = 0
 For i = 1 To 11
   Text1.Text = Text1.Text & Space(kept(i) - prev - 1) & "^"
   Print #2, Space(kept(i) - prev - 1) + "^";
   prev = kept(i)
 Next
 Text1.Text = Text1.Text & crlf & keep & crlf
 Print #2,
 Print #2, keep
 Print #2,
 
 Text1.Text = Text1.Text & crlf & " done"
 
 Close 2
  
End Sub


  Posted by Charlie on 2017-10-27 10:40:23
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