Re: Seaching in Pi a sequence. Looking for a faster method

*To*: mathgroup at smc.vnet.net*Subject*: [mg119651] Re: Seaching in Pi a sequence. Looking for a faster method*From*: Anthony Hodsdon <ajhodsd at hotmail.com>*Date*: Thu, 16 Jun 2011 04:00:32 -0400 (EDT)*References*: <201106151119.HAA22777@smc.vnet.net>

Very interesting! I'm surprised that the regular expression path is actually faster than the simple string. I guess Mathematica doesn't bother to preprocess the string to use a more efficient searching algorithm like KMP or Boyer-Moore. It looks like you get the same optimization by making a regular expression out of the explicit string: In[91]:= piesimoSPlus[m_String] := First /@ StringPosition[pi, RegularExpression[m]] In[92]:= piesimoSPlus["9999999"] // Timing Out[92]= {0.234, {1722776, 3389380, 4313727, 5466169}} In[82]:= piesimoS["9999999"] // Timing Out[82]= {0.53, {1722776, 3389380, 4313727, 5466169}} In[84]:= DigitSequence[pi, 9, 7] // Timing Out[84]= {0.28, {{7, 1722776}, {7, 3389380}, {7, 4313727}, {7, 5466169}}} --Anthony -----Original Message----- From: Dana DeLouis [mailto:dana.del at gmail.com] Sent: Wednesday, June 15, 2011 4:20 AM To: mathgroup at smc.vnet.net Subject: [mg119651] Re: Seaching in Pi a sequence. Looking for a faster method Hi. Just something a little different. Given piesimo[10^7, 9, 7], You are looking for a specific digit (9) repeated a number of times (7). Here's what we have so far. Our String: pi=StringDrop[ToString[N[Pi,10^7]],2]; Function: piesimoS[m_String]:=First/@StringPosition[pi,m] Check Timing: piesimoS["9999999"]//Timing {0.2513,{1722776,3389380,4313727,5466169}} This idea finds all sequences of the digit 9 repeated 7 or more times. DigitSequence[pi,9,7]//Timing {0.08725,{{7,1722776},{7,3389380},{7,4313727},{7,5466169}}} It appears to be about 3 times faster. That code returned the length of the sequence, and the starting position. (* s - String, d - digit to check, start - Minimum length *) DigitSequence[s_,d_,start_]:=Module[ {re,z,t}, z=StringReplace["n{s,}",{"n"->ToString[d],"s"->ToString[start]}]; re=RegularExpression[z]; t=StringPosition[s,re,Overlaps->False]; t=t/.{x_Integer,y_Integer}:>{y-x+1,x}; SortBy[SortBy[t,Last],First] ] If you only wanted a specific length, then change rule to "n{s,s}" If you didn't know how many consecutive 9's there are in a string, then this finds 6 or more: DigitSequence[pi,9,6]//Timing {0.08989, {{6,762},{6,193034},{6,1985813},{6,2878443},{6,3062881}, {6,3529731},{6,6951812},{6,7298585},{6,8498459},{7,1722776}, {7,3389380},{7,4313727},{7,5466169}}} So, the digit 9 occurs at most 7 times in a row. This is more in line with your specific length example. This does not look at overlap: DigitSequence2[s_,d_,length_]:=Module[ {z,t}, z=StringReplace["n{s,s}",{"n"->ToString[d],"s"->ToString[length]}]; t=StringPosition[s,RegularExpression[z],Overlaps->False]; t/.{x_Integer,y_Integer}:>x ] DigitSequence2[pi,9,7]//Timing {0.08325,{1722776,3389380,4313727,5466169}} = = = = = = = = = = HTH : >) Dana DeLouis $Version 8.0 for Mac OS X x86 (64-bit) (November 6, 2010) On Jun 10, 6:38 am, Guillermo Sanchez <guillermo.sanc... at hotmail.com> wrote: > Dear Group > > I have developed this function > > piesimo[n_, m_, r_] := Module[{a}, a = Split[RealDigits[Pi - 3, 10, n] > [[1]]]; Part[Accumulate[Length /@ a], Flatten[Position[a, Table[m, > {r}]]] - 1] + 1] > > n is the digits of Pi, after 3, where to search a sequence of m digit > r times consecutives. > For instance: > > piesimo[10^7, 9, 7] > > Gives that the sequence 9999999 happens in positions: > > {1722776, 3389380, 4313727, 5466169} > > I know that in this group I will find faster methods. Any idea? > > Guillermo

**References**:**Re: Seaching in Pi a sequence. Looking for a faster method***From:*Dana DeLouis <dana.del@gmail.com>