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Re: Sum elements in a list with conditions

• To: mathgroup at smc.vnet.net
• Subject: [mg69861] Re: Sum elements in a list with conditions
• From: dimmechan at yahoo.com
• Date: Tue, 26 Sep 2006 00:59:17 -0400 (EDT)
• References: <ef5066$mm5$1@smc.vnet.net><ef82hh$e43$1@smc.vnet.net>

Hi.

In my solution of the previous post, I assumed that you want to
examine only successive elements of the list.

E.g. for the following list

lst = {{1, 2}, {4, 5}, {4, 10}, {1, 6}, {2, 9}, {2, 3}, {1, 10}, {4,
3}, {1, 5}};

the pattern matching rule I proposed gives

lst //. {a___, {x_, y_}, {x_, z_}, b___} -> {a, {x, y + z}, b}
{{1, 2}, {4, 15}, {1, 6}, {2, 12}, {1, 10}, {4, 3}, {1, 5}}

because only the successive elements {4, 5}, {4, 10} and {2, 9}, {2, 3}
have their first element the same.

If you want a rule that applied regardless of the position of the
elements in the list the following rule must be used

lst //. {a___, {x_, y_}, c___, {x_, z_}, b___} -> {a, {x, y + z}, c, b}
{{1, 23}, {4, 18}, {2, 12}}

Sincerely
Dimitris


Î?/Î? dimmechan at yahoo.com έγÏ?αÏ?ε:
> Your desired output can be achieved with proper
> pattern matching.
>
> lst = {{a1, b1}, {a2, b2}, {a2, b3}, {a2, b4}, {a3, b5}, {a3, b6}};
>
> lst //. {a___, {x_, y_}, {x_, z_}, b___} -> {a, {x, y + z}, b}
> {{a1, b1}, {a2, b2 + b3 + b4}, {a3, b5 + b6}}
>
> Information["___"]
> ___ (three _ characters) or BlankNullSequence[ ] is a pattern object
> that can stand for any sequence of zero or more Mathematica
> expressions.
> ___h or BlankNullSequence[h] can stand for any sequence of expressions,
>
> all of which have head h.
> Attributes[BlankNullSequence] = {Protected}
>
> Information["//."]
> expr //. rules repeatedly performs replacements until expr no longer
> changes.
> Attributes[ReplaceRepeated] = {Protected}
> Options[ReplaceRepeated] = {MaxIterations -> 65536}
>
> For example
>
> myrule = {a___, {x_, y_}, {x_, z_}, b___} -> {a, {x, y + z}, b};
>
> dat=Table[Random[Integer,{1,5}],{30},{2}]
> {{4,3},{4,5},{4,2},{5,4},{4,2},{5,2},{2,4},{5,1},{1,3},{4,4},{3,1},{3,5},
> {5,4},{3,1},{3,4},{2,5},{2,5},{3,5},{4,4},{2,4},{4,3},{4,5},{5,3},{5,4},
> {5,1},{1,4},{5,2},{1,3},{3,1},{4,1}}
>
> dat//.myrule
> {{4,10},{5,4},{4,2},{5,2},{2,4},{5,1},{1,3},{4,4},{3,6},{5,4},{3,5},{2,10},
> {3,5},{4,4},{2,4},{4,8},{5,8},{1,4},{5,2},{1,3},{3,1},{4,1}}
> 
> Regards
> Dimitris