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PO
primarykey
Id
9292517
data
AcceptedAnswerId
0
AnswerCount
0
ClosedDate
CommentCount
0
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CreationDate
2012-02-15T11:30:12.500
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LastActivityDate
2012-02-15T11:36:39.457
LastEditDate
2012-02-15T11:36:39.457
LastEditorUserId
604128
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604128
ParentId
8885723
PostTypeId
2
Score
4
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0
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text
Body
For the special case where set Y = [1..9] and n > 0: <ul> <li>n <= 9 : 0 operations</li> <li>n <=18 : 1 operation (+)</li> <li>otherwise : Remove any divisor found in Y. If this is not enough, do a recursion on the remainder for all offsets -9 .. +9. Offset 0 can be skipped as it has already been tried.</li> </ul> Notice how division is not needed in this case. For other Y this does not hold. This algorithm is exponential in log(n). The exact analysis is a job for somebody with more knowledge about algebra than I. For more speed, add pruning to eliminate some of the search for larger numbers. Sample code: <pre><code>def findop(n, maxlen=9999): # Return a short postfix list of numbers and operations # Simple solution to small numbers if n<=9: return [n] if n<=18: return [9,n-9,'+'] # Find direct multiply x = divlist(n) if len(x) > 1: mults = len(x)-1 x[-1:] = findop(x[-1], maxlen-2*mults) x.extend(['*'] * mults) return x shortest = 0 for o in range(1,10) + range(-1,-10,-1): x = divlist(n-o) if len(x) == 1: continue mults = len(x)-1 # We spent len(divlist) + mults + 2 fields for offset. # The last number is expanded by the recursion, so it doesn't count. recursion_maxlen = maxlen - len(x) - mults - 2 + 1 if recursion_maxlen < 1: continue x[-1:] = findop(x[-1], recursion_maxlen) x.extend(['*'] * mults) if o > 0: x.extend([o, '+']) else: x.extend([-o, '-']) if shortest == 0 or len(x) < shortest: shortest = len(x) maxlen = shortest - 1 solution = x[:] if shortest == 0: # Fake solution, it will be discarded return '#' * (maxlen+1) return solution def divlist(n): l = [] for d in range(9,1,-1): while n%d == 0: l.append(d) n = n/d if n>1: l.append(n) return l </code></pre>
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singulars
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1. POFind the minimum number of operations required to compute a number using a specified range of numbers
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1. PTAnswer
UserLastEditorUserId
1. USPeer Sommerlund
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1. USPeer Sommerlund
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1. POFind the minimum number of operations required to compute a number using a specified range of numbers
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