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I have a List of elements and I need to pick the element which have the maximum or minimum for the third element and the first and second must be equal e.g.

list={{0,2,1}, {0,2,2},{0,2,3},{0,3,0},{1,2,0},{2,2,0},{2,2,1}}

to ouput 

min={{0,2,1}, {2,2,0},{0,3,0},{1,2,0}} or max={{0,2,3},{2,2,1},{0,3,0},{1,2,0}}

Thanks

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  • $\begingroup$ Your output doesn't seem to be consistent with your criteria: in 'min', {0, 2, 1} doesn't have equal first and second elements, and 1 is not the minimum of the three; in 'max', {0, 2, 3} doesn't have he first two elements the same. Can you clarify? $\endgroup$ Commented Jan 29, 2020 at 17:02
  • $\begingroup$ I actually meant the first element of the nth element and the second element of the mth element.. so {x,y,z} and {x,y,p} share the the same first two sub-elements. Apologies for the unclear exposition $\endgroup$ Commented Jan 29, 2020 at 17:06
  • $\begingroup$ should {0, 2, 3} appear in min? And the second {0, 2, 3} in max is a typo? $\endgroup$ Commented Jan 29, 2020 at 18:14
  • $\begingroup$ Just corrected it $\endgroup$ Commented Jan 29, 2020 at 18:16

1 Answer 1

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You can use GatherBy, SplitBy or GroupBy as follows:

min1 = First /@ GatherBy[Sort@list, Most]

{{0, 2, 1}, {0, 3, 0}, {1, 2, 0}, {2, 2, 0}}

max1 = Last /@ GatherBy[Sort@list, Most]

{{0, 2, 3}, {0, 3, 0}, {1, 2, 0}, {2, 2, 1}}

Alternatively,

min2 = First /@ SplitBy[Sort@list, Most]; max2 = Last /@ SplitBy[Sort@list, Most]; min3 = First@*MinimalBy[Last] /@ GatherBy[list, Most]; max3 = First@*MaximalBy[Last] /@ GatherBy[list, Most]; min4 = Values@GroupBy[Sort@list, Most, First]; max4 = Values@GroupBy[Sort@list, Most, Last]; min5 = Values@GroupBy[list, Most, First@*MinimalBy[Last]]; max5 = Values@GroupBy[list, Most, First@*MaximalBy[Last]]; Equal[min1, min2, min3, min4, min5]

True

Equal[max1, max2, max3, max4, max5]

True

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  • $\begingroup$ Thanks, but does not actually do what I want. My question is not really clear. What I mean is that if there are {x,y,z}, {x,y,p}, so x and y are common, I need to output either the min(z,p) or the max (z,p). If there are no multiplicities I just need to print the sub element. Apologies for the unclearness - I edited the original question to make it clearer $\endgroup$ Commented Jan 29, 2020 at 17:59
  • $\begingroup$ @dadelutz, please see the updated version. $\endgroup$ Commented Jan 29, 2020 at 18:23
  • $\begingroup$ It works just fine. Thanks! $\endgroup$ Commented Jan 29, 2020 at 18:27

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