Johnsone Trotter Algorithm Permutations

1. Assignment No 01
Submitted By: Sunawar Khan
Reg No: 813/FBAS/MSCS/F14
Topic:JohnsonTrotterAlgorithm(Permutations)
Submitted To: Dr. R. Aewan
Subject: Advance Algorithm Analysis
Date: 5 October,2015
Department: ComputerScience
International Islamicuniversityislamabad

2. Algorithm:
//input: the numbernwhose permutationare tobe obtained.
//output:permutationof numbers“n”
 Initializethe firstpermutation with 1L
2L
3L
4L
 While (there existamobile number K) do{
 Findthe largestmobile numberk
 Swapmobile integerkandthe adjacentnumberitsarrow point
 Reverse the directionof all integersthatare the largestthenK
 }
Problem:obtainall possible permutationsusingJohnsonTrotterAlgorithmforn=4
Solution:Asn=4 we will consideraset{1,2, 3, 4} forgenerationpermutation
1:- 1L
2L
3L
4L
Initially4,arrowof 4 pointto 3, exchange 4 with3
2:- 1L
2L
4L
3L
Exchange 2 & 4
3:- 1L
4L
2L
3L
Exchange 4 & 1
4:- 4L
1L
2L
3L
4 isno longermobile asitison the left mostcolumn pointingtothe left.Swap3 & 2 and
change 4’s direction.
5:- 4R
1L
3L
2L
Exchange 4 & 1
6:- 1L
4R
3L
2L
Exchange 4 & 3
7:- 1L
3L
4R
2L
Exchange 4 & 2
8:- 1L
3L
2L
4R
4 isno longermobile asitison the rightmostcolumnpendingtothe right.Swap3 & 4.
Change 4’s direction.
9:- 3L
1L
2L
4L
Exchange 2 & 4
0:- 3L
1L
4L
2L
Exchange 1 & 4
1:- 3L
4L
1L
2L
Exchange 3 & 4

3. 2:- 4L
3L
1L
2L
4 isno longermobile asitison the leftmostcolumnpointingtoleft.3isno longer
mobile nowasthere isno numbersmallerthenitself onitsdirection.Swap 2 & 1.
Change 4 and3 direction.
3:- 4R
3R
2L
1L
Exchange 4 & 3
4:- 3R
4R
2L
1L
Exchange 4 & 2
5:- 3R
2L
4R
1L
Exchange 4 & 1
6:- 3R
2L
1L
4R
4 isno longermobile astoitson the rightmostcolumnpointingtothe right.Swap3 & 2.
Change 4’s direction.
7:- 2L
3R
1L
4L
Exchange 4 & 1
8:- 2L
3R
4L
1L
Exchange 4 & 3
9:- 2L
4R
3R
1L
Exchange 4 & 2
0:- 4L
2L
3R
1L
4 isno longermobile asitison the leftmostcolumnpointingtothe left.Swap3& 1. And
change 4’s direction.
1:- 4R
2L
1L
3R
Exchange 4 & 2
2:- 2L
4R
1L
3R
Exchange 4 & 1
3:- 2L
1L
4R
3R
4:- 2L
1L
3R
4R
No mobile numberare more.
Total Permutations:- 4 != 24