How to find the nearest string to another string in a mixed array

Question

I am trying to find which string is nearest to another string in an array of numbers and strings. For example, say I have an array that is as follows

testarray={0,0,0,"apple",0,0,0,"pear",0,0,0,0,0,"pineapple"}

I want a general way to find that "apple" is nearest to "pear". Is there an efficient way to do this?

Thanks!

Answer 1

If you want to specify a string in advance and find the position of another string closest to the original, you could do something like this:

positionOfApple = Position[testarray, "apple"] 
(* {{4}} *)

closestToApple = 
  Nearest[Complement[Position[testarray, _String], positionOfApple], positionOfApple]
(* {{{8}}} *)

Extract[testarray, #] & /@ closestToApple
(* {{"pear"}} *)

If instead you are wanting to find a pair of strings with minimal distance between them...

closest = 
  MinimalBy[Partition[Position[testarray, _String], 2, 1], Abs@*Apply[Subtract]@*Flatten]
(* {{{4}, {8}}} *)

Extract[testarray, #] & /@ closest
(* {{"apple", "pear"}} *)

Answer 2

Just for fun, another option is to write your own distance function

t = {0, 0, 0, "apple", 0, 0, 0, "pear", 0, 0, 0, 0, 0, "pineapple"}
nearItem = "pear";
f[x_, y_] := Module[{dist = 10^6},
  If[StringQ[y] && y != nearItem, 
     dist = Abs[Position[t, x][[1, 1]] - Position[t, y][[1, 1]]]
  ];
  dist
 ]

Nearest[t, nearItem, DistanceFunction -> f]

{"apple"}

When

t = {"apple", 0, 0, 0, 0, 0, 0, "pear", 0, 0, 0, 0, 0, "pineapple"}

It gives

{"pineapple"}

And when there are two equal distance ones, it gives

t = {0, "apple", 0, 0, 0, 0, 0, "pear", 0, 0, 0, 0, 0, "pineapple"}
{"apple", "pineapple"}

You can modify your distance function as needed.

Answer 3

testarray = {0, 0, 0, "apple", 0, 0, 0, "pear", 0, 0, 0, 0, 0, "pineapple"}

Extract positions of strings:

pos = Position[testarray, _String]

{{4}, {8}, {14}}

strs = Extract[testarray, pos]

{"apple", "pear", "pineapple"}

Make subsets of pairs:

ssets = Subsets[strs, {2}]

{{"apple", "pear"}, {"apple", "pineapple"}, {"pear", "pineapple"}}

Define a distance function:

dist[{a_, b_}] := 
 Det@Position[testarray, b] - Det@Position[testarray, a]

Transpose[{Rule @@@ ssets, dist /@ ssets}] // TableForm

$$\left( \begin{array}{cc} \text{apple}\to \text{pear} & 4 \\ \text{apple}\to \text{pineapple} & 10 \\ \text{pear}\to \text{pineapple} & 6 \\ \end{array} \right)$$

This can be sorted based on distance or as required.