Permutate9/4/2023 ![]() ![]() Let's take a second and figure out what 24 actually represents, 24 is the number of ways you can arrange "pencil" with "pen" being a single letter, but we got 6 of those (pen, nep, epn. And "pencil" just became a 4 letters word, so it has 4! ways of being arranged, therefore 24 ways. Now we're doing it with 3 letters "p e and n" so there are 3! ways of arranging them, therefore 6 ways. Finally we added them together to get our answer. But really we looked at all the different ways to arrange 2 items, and there was 2! ways of doing it, so 2 ways and "pencil" was treated as a 5 letters word. With "e" and "n" we figured out that "en" and "ne" were the only two possible way to arrange them, and treated them as a single letter. Now to dig in a little deeper what if we wanted "p e and n" to always be together ? Have a go at it before looking below :) There we go ! There are 240 different ways to arrange "pencil" so that e and n are always next to each other. n, - and the ith element will be exchanged later - with some element of the tail Is_Last := True I := N - 1 loop if P ( I ) P ( I ) loop J := J - 1 end loop J := J + 1 - exchange them - this will give the next permutation in lexicographic order, - since every element from ith to the last is minimum Swap ( P ( I ), P ( J )) end Go_To_Next end Generic_Perm The procedure Print_Perms ĬO REQUIRED BY "prelude_permutations.First let's think about it a bit, to figure out how many ways you can arrange "Pencil" with N and E always next to one another it's going to be all the different ways to arrange "pencil" as if "en" was a single letter and the same thing with "ne"ġ) How many ways can we arrange Pencil as if "en" was a single letter?ĥ! = 120 ways, we have 5 things to arrange P c i l and "en"Ģ) Now how many ways can we arrange Pencil as if "ne" was a single letter? Package body Generic_Perm is procedure Set_To_First ( P : out Permutation Is_Last : out Boolean ) is begin for I in P ' Range loop P ( I ) := I end loop Is_Last := P ' Length = 1 - if P has a single element, the fist permutation is the last one end Set_To_First procedure Go_To_Next ( P : in out Permutation Is_Last : out Boolean ) is procedure Swap ( A, B : in out Integer ) is C : Integer := A begin A := B B := C end Swap I, J, K : Element begin - find longest tail decreasing sequence - after the loop, this sequence is I+1. When given N, this package defines the Element and Permutation types and exports procedures to set a permutation P to the first one, and to change P into the next one: The second part is to read the N from the command line, and to actually print all permutations over 1. This can be used elsewhere, e.g., for the Topswaps ] task. ![]() We split the task into two parts: The first part is to represent permutations, to initialize them and to go from one permutation to another one, until the last one has been reached. modify iv_set index lv_perm from lv_temp_2. read table iv_set index lv_len into lv_temp_2. read table iv_set index lv_perm into lv_temp. modify iv_set index lv_first from lv_temp. modify iv_set index lv_count from lv_temp_2. read table iv_set index lv_first into lv_temp_2. read table iv_set index lv_count into lv_temp. lv_first = lv_len + lv_perm - lv_count + 1. " Swap tail decresing to get a tail increasing. If we find one, break out of the table and set the " flag indicating a switch. " Loop backwards through the table, attempting to find elements which " can be permuted. data : lv_len type i, lv_first type i, lv_third type i, lv_count type i, lv_temp type i, lv_temp_2 type i, lv_second type i, lv_changed type c, lv_perm type i. form permute using iv_set like lt_numbers changing ev_last type c. " Permutation function - this is used to permute: " Can be used for an unbounded size set. write ( 1 ) lv_number no - gap left - justified. perform permute using lt_numbers changing lv_flag. ![]() include "./includeARM64.inc" Value : +1ĭata : lv_flag type c, lv_number type i, lt_numbers type table of i. Ldr x1,qAdrsZoneConv // insert conversion * permutation by heap iteratif (wikipedia) */Ĭsel x2,x2,x1,ne // the stack must be a multiple of 16 Ldr x0,qAdrTableNumber //address number table * for this file see task include a file in language AArch64 assembly */ * ARM assembly AARCH64 Raspberry PI 3B */ ![]()
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