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# 6C. Grading

Grading is the assignment of an ordinal number to each item of an array, with all numbers distinct, and with the earliest of equal values being assigned a lower ordinal number. Grading can be used to produce the permutation that will put an array in order. Since sorting is a primitive operation in J, grading is more commonly used to put a companion array into an order derived from another array. For example, a table of addresses may be put into an order derived from a table of last names.

`m0=: /:` | Grade y up
`m1=: \:` | Grade y down
`d2=: /:@i.` | Grade y up according to key x
`d3=: \:@i.` | Grade y down according to key x

       y=:'leap','note',:'file'
       (] ; m0 ; (m0 { ]) ; m1 ; (m1 { ])) y
    +----+-----+----+-----+----+
    |leap|2 0 1|file|1 0 2|note|
    |note|     |leap|     |leap|
    |file|     |note|     |file|
    +----+-----+----+-----+----+

       x=: ' abcdefghijklmnopqrstuvwxyz' [ y=: 'senator'
       x (d2 ; (d2{]) ; d3 ; (d3{])) y
    +-------------+-------+-------------+-------+
    |3 1 2 5 6 0 4|aenorst|4 0 6 5 2 1 3|tsronea|
    +-------------+-------+-------------+-------+

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