* then all permutation table is logically defined (not physically to save memory). if pass in value is 5 chose 3, and say the symbol string is "12345" * table and all entries are defined, including an index. * Note that, once the Permutation object is initialized, or after the constructor is called, the permutation * if there are 5 symbols to chose from, I'll have 5 bin slot to indicate which symbol is taken. * Just like a human or simply myself to generate a permutation. * The algorithm I used is base on a bin slot. * Say if n = 5, r = 3, and the string is "12345", it will generate sll 60 different permutation of the set * the program will generate all possible permutation for the condition. * and a string of single character symbols * the user can input n = the number of items, * This Permutation Class can be use to generate a complete list of all different permutation of a set of symbols. Therefore, my code is very much like C/C++. * Algorithm is invented and implemented by Fred Pang Created by Fred Pang on. * Copyright 2015 Fred Pang A complete list of Permutation base on an index. You can base on an index to get a symbol permutation, or give a symbol permutation then get the index. However, I am not sure you still need the solution after these years. If you need to apply a permutation several times, first convert it to the common representation. Note that all the algorithms for dealing with permutations in the common form are O(n), while applying a permutation in our form is O(n²). e ends up at the only remaining position, indexed at 0.d ends up at the last remaining position, which (out of only two remaining positions) is 1.c ends up at the first remaining position, which is always 0.b ends up at the fourth position, which would be index 3, but it's the third remaining one, so we assign it 2.a, the first element, ends up at the second position, so we assign it index 1.For the position that the next element ends up at, you have n-1 remaining possibilities, so you can describe this with a number between 0 and n-2.Īs an example for n = 5, consider the permutation that brings abcde to caebd. To describe a permutation of n elements, you see that for the position that the first element ends up at, you have n possibilities, so you can describe this with a number between 0 and n-1.
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