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# 6A. Sorting

Sorting means the rearrangement of an array into an order based on some key, which may be either implicit or explicit. The implicit keys are the integer or real number fields, and the standard alphabet. Explicit keys may be any arbitrary set. Note that sorting applies equally well to character data and to Boolean, integer, real numbers, complex numbers, or to boxed data. When applied to real numbers, comparisons are exact. No tolerance is used. Verbs defined to sort in ascending order can be converted to give descending order by changing `/:` to`\:`, as in `m0` and `m1`. Note also that these verbs apply (unless they use the rank operator to prevent it) to arrays of arbitrary ranks, where the items are treated as if they were raveled.

`m0=: /:~` | Sort the array y in ascending order
`m1=: \:~` | Sort the array y in descending order
`m2=: /:~"_1` | Sort the items of array y ascending
`d3=: /:@:{ { [` | Sort indices x according to y
`d4=: ]/:{"1` | Sort table y according to column x
`d5=: \:@[`(/:@[) @. ]` | Grade x up if y is 1 and down if y is 0
`d6=: \:~@[`(/:~@[) @. ]` | Sort up or down (Try literal argument)
`d7=: /:~` | Sort y according to x

       y=:'leap','note',:'file'
       m1 y
    note
    leap
    file

       m1"1 y
    plea
    tone
    life

       z=:> ;: 'to be or not to be that is the question'

       (] ; m0 ; m1 ; m2) z
    +-----------------------------------+
    ¦to      ¦be      ¦to      ¦      ot¦
    ¦be      ¦be      ¦to      ¦      be¦
    ¦or      ¦is      ¦the     ¦      or¦
    ¦not     ¦not     ¦that    ¦     not¦
    ¦to      ¦or      ¦question¦      ot¦
    ¦be      ¦question¦or      ¦      be¦
    ¦that    ¦that    ¦not     ¦    ahtt¦
    ¦is      ¦the     ¦is      ¦      is¦
    ¦the     ¦to      ¦be      ¦     eht¦
    ¦question¦to      ¦be      ¦einoqstu¦
    +-----------------------------------+

       q=: ?.15#9
       (] , m0 ,: m1) q
    1 6 4 4 1 0 6 6 8 3 4 7 0 0 4
    0 0 0 1 1 3 4 4 4 4 6 6 6 7 8
    8 7 6 6 6 4 4 4 4 3 1 1 0 0 0

       x=: 2 3 4 5 0 1 9 8 7 6
       y=:100+10 4 8 6 7 9 5 3 2 1
       x ([ , ] ,: d3) y
      2   3   4   5   0   1   9   8   7   6
    110 104 108 106 107 109 105 103 102 101
      9   8   7   1   6   3   4   2   5   0

       y=: ?.5 6$100
       d4=: ]/:{"1
       (0&d4 ; 2&d4 ; 5&d4) y
    +-----------------------------------------------------+
    ¦ 3  5 52 67  0 38¦13 75 45 53 21  4¦13 75 45 53 21  4¦
    ¦ 6 41 68 58 93 84¦ 3  5 52 67  0 38¦ 3  5 52 67  0 38¦
    ¦13 75 45 53 21  4¦52  9 65 41 70 91¦67 67 93 38 51 83¦
    ¦52  9 65 41 70 91¦ 6 41 68 58 93 84¦ 6 41 68 58 93 84¦
    ¦67 67 93 38 51 83¦67 67 93 38 51 83¦52  9 65 41 70 91¦
    +-----------------------------------------------------+

The random number generator`?.` used here produces repeatable experiments, but`?` can also be used. For example:

       ? 9 # 9
    1 6 4 4 1 0 6 6 8
       ?. 9 # 9
    1 6 4 4 1 0 6 6 8

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