Problem 293. Generalized sorting

Write generalized sort function sortg() that sorts array elements in “ascending” order with given comparison function. A comparison function takes two arguments and return true if the first argument goes before the second in the specific (strick weak) ordering.

The function have to be stable, that is, if A has elements are “equal” (strictly speaking, both comp(a1, a2) and comp(a2, a1) are false), then the ordering of these elements must be preserved. Since MATLAB's sort() function is stable, sort(A) and sortg(A, @lt) will be equivalent.

(Assume that the input argument A will be a vector, not a matrix, and the comparison function comp() will do scalar expansion like MATLAB's lt() ( < ), that is, comparing scalar with vector is possible.)

Example

    A = [1, 0, 0 + 1i];
    [B, IX] = sortg(A, @(a, b) abs(a) < abs(b));

    => B == [0, 1, 0 + 1i];
       IX == [2 1 3]

(1 and 0 + 1i have the same absolute value, but 1 has to appear before 0 + 1i, as the original ordering.)