21
Ladders Optimal solution Ladders
What is a Ladder? A ladder is a graphical means
of depicting the adjacent transposition whose production is a given permutation
1
3
2
4
3
6
4
2
5
1
6
5
Top row
Bottom row / Sequence
Rungs
Optimal Solution
1
5
2
4
3
2
4
6
5
1
6
3
1 2 3 4 5 6
5 4 2 6 1 3
0 1 2 0 4 3
Solution I
1
5
2
4
3
2
4
6
5
1
6
3
1 2 3 4 5 6
5 4 2 6 1 3
Solution I
1 2 3 4 5 6
5 4 2 6 1 3
1
5
2
4
3
2
4
6
5
1
6
3
Solution I
1 2 3 4 5 6
5 4 2 6 1 31
5
2
4
3
2
4
6
5
1
6
3
Solution I
1 2 3 4 5 6
5 4 2 6 1 31
5
2
4
3
2
4
6
5
1
6
3
Solution I
1 2 3 4 5 6
5 4 2 6 1 31
5
2
4
3
2
4
6
5
1
6
3
Solution I
1 2 3 4 5 6
5 4 2 6 1 3
1
5
2
4
3
2
4
6
5
1
6
3
Solution I
1 2 3 4 5 6
5 4 2 6 1 3
1
5
2
4
3
2
4
6
5
1
6
3
Solution I
1 2 3 4 5 6
5 4 2 6 1 3
1
5
2
4
3
2
4
6
5
1
6
3
Solution I
1 2 3 4 5 6
5 4 2 6 1 3
1
5
2
4
3
2
4
6
5
1
6
3
Solution I
1 2 3 4 5 6
5 4 2 6 1 3
1
5
2
4
3
2
4
6
5
1
6
3
Solution I
1 2 3 4 5 6
5 4 2 6 1 3
1
5
2
4
3
2
4
6
5
1
6
3
Solution I
1 2 3 4 5 6
5 4 2 6 1 3
1
5
2
4
3
2
4
6
5
1
6
3
Solution I
1 2 3 4 5 6
5 4 2 6 1 3
1
5
2
4
3
2
4
6
5
1
6
3
Solution I
1 2 3 4 5 6
5 4 2 6 1 3
4 3 1 2 0 0
1
5
2
4
3
2
4
6
5
1
6
3
Solution I
1
5
2
2
3
1
4
6
5
4
6
3
1 2 3 4 5 6
5 2 1 6 4 3
0 1 2 0 2 3
Solution II
Parities
1
5
2
2
3
1
4
6
5
4
6
3
1 2 3 4 5 6
5 2 1 6 4 3
0 1 2 0 2 3
障眼法
1
5
2
4
3
2
4
6
5
1
6
3
1 2 3 4 5 6
5 4 2 6 1 3
0 3 2 3 4 2
Exercise
Solution ISolution I
Add strokes
