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How can I numbering the elements in descending order of second elements of sublists? For example, if I have the list which is 

m={{1, 5}, {2, 8}, {3, 9}, {4, 2}, {5, 9}, {6, 7}, {7, 9}, {8, 10}, {9, 5}, {10, 2}};

The smallest second element is 2 of {10,2} so its number is 1.
Second smallest second element is also 2 of {4,2} so its number will be 2.
The output that I want is then: {4, 6, 9, 2, 8, 5, 7, 10, 3, 1}.
How can I do this?

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    $\begingroup$ Please have a look at SortBy. $\endgroup$ Commented Oct 30, 2012 at 10:36

2 Answers 2

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Why you rank {10, 2} before {4, 2} escapes me. Ignoring that:

m = {{1, 5}, {2, 8}, {3, 9}, {4, 2}, {5, 9}, {6, 7}, {7, 9}, {8, 10}, {9, 5}, {10, 2}}; m[[All, 2]] // Ordering // Ordering 
{3, 6, 7, 1, 8, 5, 9, 10, 4, 2}

Equivalent: Nest[Ordering, m[[All, 2]], 2]

See Ordering.

If we reverse m before and after we get:

Nest[Ordering, Reverse[m][[All, 2]], 2] // Reverse 
 {4, 6, 9, 2, 8, 5, 7, 10, 3, 1}
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  • $\begingroup$ oh, I miss that part. If second element is same, I want to rank the sublists in ascending order of first element. Can you help me one more time please? $\endgroup$ Commented Oct 30, 2012 at 11:02
  • $\begingroup$ Sometimes, I wish they'd added an OrderingBy[] in complete analogy to SortBy[]... $\endgroup$ Commented Oct 30, 2012 at 11:07
  • $\begingroup$ @Sungjin, Ordering[{{1, 5}, {2, 8}, {3, 9}, {4, 2}, {5, 9}, {6, 7}, {7, 9}, {8, 10}, {9, 5}, {10, 2}}, All, If[Last[#1] != Last[#2], Last[#1] > Last[#2], First[#1] <= First[#2]] &] $\endgroup$ Commented Oct 30, 2012 at 11:14
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    $\begingroup$ @J.M. orderingBy[list_, f_] := Ordering[{f@#, #} & /@ list] $\endgroup$ Commented Oct 30, 2012 at 12:37
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    $\begingroup$ Two or more, use a... Nest? Dijkstra would be proud! :) $\endgroup$ Commented Oct 30, 2012 at 14:02
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Since V 12.0 there is OrderingBy:

m = {{1, 5}, {2, 8}, {3, 9}, {4, 2}, {5, 9}, {6, 7}, {7, 9}, {8, 10}, {9, 5}, {10, 2}}; Ordering @ OrderingBy[Last] @ m

{3, 6, 7, 1, 8, 5, 9, 10, 4, 2}

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