How do you rearrange a list of strings based given certain conditions?

Question

I had looked at previous answers for this but was unable to find a solution. I have the following code:

dnames1={"A1","A2","A3","A4","A5","A6"}
dnumber={20,20,11,21,19,20}

newdnumber=TakeSmallest[dnumber,6]


AssociationThread[dnames,dnumber]

The positions of the strings given in "dnames1" correspond to the values in the same position given by list "dnumber" (this can be seen through the AssociationThread). I then rearranged the list "dnumber" to go from the smallest number to the largest, giving a new list designated "newdnumber." I'm trying to then produce a new corresponding list called "newdnames1" which reflects the new ordering given by "newdnumber." This would give an output of:

newdnames1={"A3","A5","A1","A2","A6","A4"}

I've tried the following to solve this question:

assoc=AssociationThread[dnumber,dnames1]
newdnumber/.assoc

but the main issue is that the AssociationThreaddoes not associate the correct list of strings if there are repeating values given in dnumber (I.e. The number 20 appears 3 times but the association only ever assigns "A6"`a value of 20 and it never assigns strings "A1" or "A2". Any help producing newdnames1 would be greatly appreciated.

Answer 1

You can get newdnames1 directly using

dnames1[[Ordering[dnumber]]]

If you you want to work with associations, for newdnumber, you can get the desired result simply using Sort:

assoc1 = AssociationThread[dnames1, dnumber]

<|"A1" -> 20, "A2" -> 20, "A3" -> 11, "A4" -> 21, "A5" -> 19,   "A6" -> 20|>

assoc2b = Sort[assoc1]

 <|"A3" -> 11, "A5" -> 19, "A1" -> 20, "A2" -> 20, "A6" -> 20,  "A4" -> 21|>

Keys @ assoc2

 {"A3", "A5", "A1", "A2", "A6", "A4"}

For general newdnumber, you can sort assoc1 using SortBy[PositionIndex[newdnumber]]:

assoc2 = SortBy[PositionIndex[newdnumber]]@assoc1

<|"A3" -> 11, "A5" -> 19, "A4" -> 21, "A1" -> 20, "A2" -> 20,  "A6" -> 20|>

Keys @ assoc2

 {"A3", "A5", "A1", "A2", "A6", "A4"}

SeedRandom[1]

shuffledDnumber = RandomSample[dnumber]

 {19, 11, 20, 20, 21, 20}

assoc3 = SortBy[PositionIndex[shuffledDnumber]]@assoc1

<|"A5" -> 19, "A3" -> 11, "A4" -> 21, "A1" -> 20, "A2" -> 20,  "A6" -> 20|>

Keys @ assoc3

{"A5", "A3", "A4", "A1", "A2", "A6"}