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67 lines
1.5 KiB
67 lines
1.5 KiB
/* sorting.mod - how to sort arrays in MathProg */
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/* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
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# Sometimes it is necessary to print parameters or variables in the
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# order of ascending or descending their values. Suppose, for example,
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# that we have the following subscripted parameter:
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set I := 1..12;
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param a{i in I} := Uniform(2, 7);
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# If we print all its members:
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printf{i in I} "a[%d] = %g\n", i, a[i];
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# the output may look like follows:
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#
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# a[1] = 2.64156
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# a[2] = 2.04798
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# a[3] = 2.14843
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# a[4] = 4.76896
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# a[5] = 6.09132
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# a[6] = 3.27780
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# a[7] = 4.06113
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# a[8] = 4.05898
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# a[9] = 6.63120
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# a[10] = 6.50318
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# a[11] = 3.46065
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# a[12] = 4.69845
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#
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# However, we would like the parameter members to appear in the order
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# of ascending their values.
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#
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# Introduce the following auxiliary parameter:
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param pos{i in I} :=
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1 + card({j in I: a[j] < a[i] or a[j] = a[i] and j < i});
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# where pos[i] = k means that in the sorted list member a[i] would
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# have k-th position, 1 <= k <= |I|. Then introduce another auxiliary
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# parameter:
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param ind{k in 1..card(I)} := sum{i in I: pos[i] = k} i;
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# where ind[k] = i iff pos[k] = i.
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#
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# Now, the following statement:
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printf{k in 1..card(I)} "a[%d] = %g\n", ind[k], a[ind[k]];
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# prints the parameter members in the desired order:
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#
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# a[2] = 2.04798
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# a[3] = 2.14843
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# a[1] = 2.64156
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# a[6] = 3.27780
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# a[11] = 3.46065
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# a[8] = 4.05898
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# a[7] = 4.06113
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# a[12] = 4.69845
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# a[4] = 4.76896
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# a[5] = 6.09132
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# a[10] = 6.50318
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# a[9] = 6.63120
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end;
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