SPRING

Optimal scenario of weighted reversals and block-interchanges:

The minimum cost of series for transforming S2 into S1 is 1 which is composed of 1 reversal and 0 block-interchange.

S2	(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
S1	(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)

The optimal scenario of weighted reversals and block interchanges is as follows:
S2 =
(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
=S1

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The minimum cost of series for transforming S3 into S1 is 1 which is composed of 1 reversal and 0 block-interchange.
S3 (1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
S1 (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S3 =
(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
=S1

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The minimum cost of series for transforming S4 into S1 is 1 which is composed of 1 reversal and 0 block-interchange.
S4 (1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
S1 (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S4 =
(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
=S1

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The minimum cost of series for transforming S7 into S1 is 2 which is composed of 2 reversals and 0 block-interchange.
S7 (1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
S1 (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S7 =
(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 -14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
=S1

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The minimum cost of series for transforming S8 into S1 is 6 which is composed of 6 reversals and 0 block-interchange.
S8 (1 2 3 4 5 6 7 8 9 10 12 13 -14 15 16 17 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
S1 (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S8 =
(1 2 3 4 5 6 7 8 9 10 12 13 -14 15 16 17 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 -14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 41 42 43 44 45 46 47 48 50 51 52 53 54 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -48 -47 -46 -45 -44 -43 -42 -41 50 51 52 53 54 55 56 57 58)
=S1

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The minimum cost of series for transforming S9 into S1 is 7 which is composed of 7 reversals and 0 block-interchange.
S9 (1 2 3 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 11 -17 -16 -15 14 -13 -12 -10 -9 -8 -7 -6 -5 -4 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
S1 (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S9 =
(1 2 3 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 11 -17 -16 -15 14 -13 -12 -10 -9 -8 -7 -6 -5 -4 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 11 -17 -16 -15 -14 -13 -12 -10 -9 -8 -7 -6 -5 -4 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 11 12 13 14 15 16 17 -10 -9 -8 -7 -6 -5 -4 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 41 42 43 44 45 46 47 48 50 51 52 53 54 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -48 -47 -46 -45 -44 -43 -42 -41 50 51 52 53 54 55 56 57 58)
=S1

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The permutation S3 has been transformed into S2.
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The permutation S4 has been transformed into S2.
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The minimum cost of series for transforming S5 into S2 is 7 which is composed of 7 reversals and 0 block-interchange.
S5 (1 2 3 4 5 -7 -6 8 9 10 11 12 13 -14 -19 -18 -17 -16 15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
S2 (1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S5 =
(1 2 3 4 5 -7 -6 8 9 10 11 12 13 -14 -19 -18 -17 -16 15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 -19 -18 -17 -16 15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 -19 -18 -17 -16 -15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 -57 -56 -55 58)
=S2

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The minimum cost of series for transforming S7 into S2 is 1 which is composed of 1 reversal and 0 block-interchange.
S7 (1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
S2 (1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S7 =
(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
=S2

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The minimum cost of series for transforming S8 into S2 is 5 which is composed of 5 reversals and 0 block-interchange.
S8 (1 2 3 4 5 6 7 8 9 10 12 13 -14 15 16 17 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
S2 (1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S8 =
(1 2 3 4 5 6 7 8 9 10 12 13 -14 15 16 17 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 41 42 43 44 45 46 47 48 50 51 52 53 54 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -48 -47 -46 -45 -44 -43 -42 -41 50 51 52 53 54 55 56 57 58)
=S2

The permutation S4 has been transformed into S3.
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The minimum cost of series for transforming S5 into S3 is 7 which is composed of 7 reversals and 0 block-interchange.
S5 (1 2 3 4 5 -7 -6 8 9 10 11 12 13 -14 -19 -18 -17 -16 15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
S3 (1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S5 =
(1 2 3 4 5 -7 -6 8 9 10 11 12 13 -14 -19 -18 -17 -16 15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 -19 -18 -17 -16 15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 -19 -18 -17 -16 -15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 -57 -56 -55 58)
=S3

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The minimum cost of series for transforming S7 into S3 is 1 which is composed of 1 reversal and 0 block-interchange.
S7 (1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
S3 (1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S7 =
(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
=S3

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The minimum cost of series for transforming S8 into S3 is 5 which is composed of 5 reversals and 0 block-interchange.
S8 (1 2 3 4 5 6 7 8 9 10 12 13 -14 15 16 17 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
S3 (1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S8 =
(1 2 3 4 5 6 7 8 9 10 12 13 -14 15 16 17 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 41 42 43 44 45 46 47 48 50 51 52 53 54 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -48 -47 -46 -45 -44 -43 -42 -41 50 51 52 53 54 55 56 57 58)
=S3

The minimum cost of series for transforming S5 into S4 is 7 which is composed of 7 reversals and 0 block-interchange.
S5 (1 2 3 4 5 -7 -6 8 9 10 11 12 13 -14 -19 -18 -17 -16 15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
S4 (1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S5 =
(1 2 3 4 5 -7 -6 8 9 10 11 12 13 -14 -19 -18 -17 -16 15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 -19 -18 -17 -16 15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 -19 -18 -17 -16 -15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 -57 55 56 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 -57 -56 -55 58)
=S4

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The minimum cost of series for transforming S7 into S4 is 1 which is composed of 1 reversal and 0 block-interchange.
S7 (1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
S4 (1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S7 =
(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
=S4

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The minimum cost of series for transforming S8 into S4 is 5 which is composed of 5 reversals and 0 block-interchange.
S8 (1 2 3 4 5 6 7 8 9 10 12 13 -14 15 16 17 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
S4 (1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S8 =
(1 2 3 4 5 6 7 8 9 10 12 13 -14 15 16 17 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 41 42 43 44 45 46 47 48 50 51 52 53 54 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 11 12 13 -14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -48 -47 -46 -45 -44 -43 -42 -41 50 51 52 53 54 55 56 57 58)
=S4

The minimum cost of series for transforming S6 into S5 is 1 which is composed of 1 reversal and 0 block-interchange.
S6 (1 2 3 4 5 -7 -6 8 9 10 11 12 13 -14 -19 -18 -17 -16 15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 -54 -53 -52 -51 -50 -49 -48 47 -46 -45 -44 -43 -42 -41 -57 55 56 58)
S5 (1 2 3 4 5 -7 -6 8 9 10 11 12 13 -14 -19 -18 -17 -16 15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S6 =
(1 2 3 4 5 -7 -6 8 9 10 11 12 13 -14 -19 -18 -17 -16 15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 -54 -53 -52 -51 -50 -49 -48 47 -46 -45 -44 -43 -42 -41 -57 55 56 58)
=S5

The minimum cost of series for transforming S8 into S7 is 4 which is composed of 4 reversals and 0 block-interchange.
S8 (1 2 3 4 5 6 7 8 9 10 12 13 -14 15 16 17 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
S7 (1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S8 =
(1 2 3 4 5 6 7 8 9 10 12 13 -14 15 16 17 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 41 42 43 44 45 46 47 48 50 51 52 53 54 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -48 -47 -46 -45 -44 -43 -42 -41 50 51 52 53 54 55 56 57 58)
=S7

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The minimum cost of series for transforming S9 into S7 is 5 which is composed of 5 reversals and 0 block-interchange.
S9 (1 2 3 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 11 -17 -16 -15 14 -13 -12 -10 -9 -8 -7 -6 -5 -4 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
S7 (1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S9 =
(1 2 3 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 11 -17 -16 -15 14 -13 -12 -10 -9 -8 -7 -6 -5 -4 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 11 12 13 -14 15 16 17 -10 -9 -8 -7 -6 -5 -4 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 41 42 43 44 45 46 47 48 50 51 52 53 54 55 56 57 58)
->(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -48 -47 -46 -45 -44 -43 -42 -41 50 51 52 53 54 55 56 57 58)
=S7

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The minimum cost of series for transforming S9 into S8 is 1 which is composed of 1 reversal and 0 block-interchange.
S9 (1 2 3 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 11 -17 -16 -15 14 -13 -12 -10 -9 -8 -7 -6 -5 -4 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
S8 (1 2 3 4 5 6 7 8 9 10 12 13 -14 15 16 17 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
The optimal scenario of weighted reversals and block interchanges is as follows:
S9 =
(1 2 3 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 11 -17 -16 -15 14 -13 -12 -10 -9 -8 -7 -6 -5 -4 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
=S8

SPRING by Ying Chih Lin¹, Chin Lung Lu ², Ying-Chuan Liu¹ and Chuan Yi Tang ¹
¹Department of Computer Science, National Tsing Hua University, Taiwan, ROC.
²Department of Biological Science and Technology, National Chiao Tung University, Taiwan, ROC.
The identified LCBs are computed using a program from Mauve, Copyright © 2003-2005, Aaron Darling
The program for sorting permutation by reversals is derived from a Java applet, Copyright © 1999, Itsik Mantin and Ron Shamir

S5	(1 2 3 4 5 -7 -6 8 9 10 11 12 13 -14 -19 -18 -17 -16 15 20 21 22 23 24 25 26 27 28 29 -30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -47 48 49 50 51 52 53 54 -57 55 56 58)
S1	(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)

S7	(1 2 3 4 5 6 7 8 9 10 -17 -16 -15 14 -13 -12 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)
S1	(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)

S8	(1 2 3 4 5 6 7 8 9 10 12 13 -14 15 16 17 -11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
S1	(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)

S9	(1 2 3 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 11 -17 -16 -15 14 -13 -12 -10 -9 -8 -7 -6 -5 -4 30 31 32 33 34 35 36 37 38 39 40 -49 -54 -53 -52 -51 -50 -48 -47 -46 -45 -44 -43 -42 -41 55 56 57 58)
S1	(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)

S10	(50 -45 52 -41 55 58 1 -36 35 -34 3 4 -32 7 -23 9 -22 10 -19 -18 -21 11 -20 -17 12 13 -14 15 16 -8 24 6 -29 -25 28 -26 27 -5 30 31 33 -2 -57 38 -56 37 39 -40 -54 42 -49 -53 43 -46 51 44 47 48)
S1	(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)

S11	(45 37 39 40 52 53 49 -42 54 55 56 -38 57 2 -33 -31 -30 5 6 -29 -28 -27 26 -25 -24 8 10 -19 -16 -15 13 -14 -12 17 20 -11 21 18 22 -9 23 -7 32 -4 -3 34 35 36 -1 -58 -50 -43 -41 -46 51 44 47 48)
S1	(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)