Re: Seaching in Pi a sequence. Looking for a faster method
- To: mathgroup at smc.vnet.net
- Subject: [mg119604] Re: Seaching in Pi a sequence. Looking for a faster method
- From: rafapa <rafapa at us.es>
- Date: Sun, 12 Jun 2011 05:06:52 -0400 (EDT)
- References: <isss68$jdf$1@smc.vnet.net>
On Jun 10, 12:38 pm, 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
What about
piesimoR[n_, m_String] := First /@
StringPosition[StringDrop[ToString[N[Pi, n]], 2], m]
piesimoR[10^7, "9999999"]//Timing
{4.04938, {1722776, 3389380, 4313727, 5466169}}
The original gave
piesimo[10^7, 9, 7]
{9.56055, {1722776, 3389380, 4313727, 5466169}}
If you intend to search several sequences it's better to save the
stringfied pi
pistring = StringDrop[ToString[N[Pi, 10^7]], 2];
piesimoS[m_String] := First /@ StringPosition[pistring, m]
piesimoS["9999999"]//Timing
{0.203969, {1722776, 3389380, 4313727, 5466169}}
piesimoS["1234567"]//Timing
{0.203969, {9470344}}
Rafael