Finding Permutations´┐ŻEasier and Faster

Introduction

This article explains the technique of finding permutations in a simple and fast manner. It also provides the source code for the same.

Explanation

For a given string of length N, there are actually N! Permutations. The technique we apply here is to find the unique of those permutations and display them.

Let's take this string: 123. If we rotate this string in a circular manner, we get 231 and 312. The point here is, if we find 1 string of the N! Permutations, we can produce N permutations by rotating it circularly. This reduces the time, which is proportional to N. The greater the value of N, the more the algorithm is optimized.

In short, the algorithm finds a number and rotates the number circularly N times to get N numbers.

Lets apply the algorithm. Lets take string {12} of length 2 (N=2). The unique pattern is 12 and if we rotate we get 21.

Let's take the string {123} of length 3 (N=3). The unique patterns are as follows:

1(23): 123 is unique pattern resulting in (123)
1(32): Rotate the pattern (23) u get another pattern (32) resulting in a pattern (132)
(231): By rotating the pattern (123)
(312): By rotating the pattern (123)
(321): By rotating the pattern (132)
(213): By rotating the pattern (132)

The output patterns are:

Level 1     Level 2     Permutations    
123
1(23) 123
231
312
1(32) 132
321
213

If we apply the same algorithm for the string {1234} of length 4 (N=4), the patterns are as below:

Level 1     Level 2     Level 3     Permutations
1234
12(34)
1(234) 1234
2341
3412
4123
1(342) 1342
3421
4213
2134
1(423) 1423
4231
2314
3142
12(43)
1(243) 1243
2431
4312
3124
1(432) 1432
4321
3214
2143
1(324) 1324
3241
2413
4132

Comparison

The traditional algorithm goes and finds all the permutations where, as in this algorithm, we find only the unique permutation and produce the other permutations by rotating the original permutation in a circular manner.

Conclusion

The algorithm finds only the unique numbers and finds the other (N) permutations by rotating the original permutation circularly. Hence, it increases the performance.



About the Author

Srinivasan Muthuswamy Sivaraman

Working on Java/C++/C/Windows/Linux technologies Hobbies: playing with numbers.

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