Finding all possible permutations of a given string in python

Question

I have a string  I want to generate all permutations from that string  by changing the order of characters in it  For example  say   x  stack    what I want is a list like this   l   stack   satck   sackt            Currently I am iterating on the list cast of the string  picking 2 letters randomly and transposing them to form a new string  and adding it to set cast of l  Based on the length of the string  I am calculating the number of permutations possible and continuing iterations till set size reaches the limit  There must be a better way to do this

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With recursive approach  def permute word       if len word     1          return  word      permutations   permute word 1        character   word 0      result          for p in permutations          for i in range len p  1               result append p  i    character   p i        return result     running code    gt  gt  gt  permute  abc     abc    bac    bca    acb    cab    cba

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You can get all N  permutations without much code  def permutations string  step   0          if we ve gotten to the end  print the permutation     if step    len string           print    join string         everything to the right of step has not been swapped yet     for i in range step  len string               copy the string  store as array          string copy    character for character in string             swap the current index with the step         string copy step   string copy i    string copy i   string copy step             recurse on the portion of the string that has not been swapped yet  now it s index will begin with step   1          permutations string copy  step   1

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why do you not simple do   from itertools import permutations perms       join p  for p in permutations   s   t   a   c   k     print perms print len perms  print len set perms     you get no duplicate as you can see       stack    stakc    stcak    stcka    stkac    stkca    satck    satkc     sactk    sackt    saktc    sakct    sctak    sctka    scatk    scakt    sckta     sckat    sktac    sktca    skatc    skact    skcta    skcat    tsack     tsakc    tscak    tscka    tskac    tskca    tasck    taskc    tacsk    tacks     taksc    takcs    tcsak    tcska    tcask    tcaks    tcksa    tckas    tksac     tksca    tkasc    tkacs    tkcsa    tkcas    astck    astkc    asctk    asckt     asktc    askct    atsck    atskc    atcsk    atcks    atksc    atkcs    acstk     acskt    actsk    actks    ackst    ackts    akstc    aksct    aktsc    aktcs     akcst    akcts    cstak    cstka    csatk    csakt    cskta    cskat    ctsak     ctska    ctask    ctaks    ctksa    ctkas    castk    caskt    catsk    catks     cakst    cakts    cksta    cksat    cktsa    cktas    ckast    ckats    kstac     kstca    ksatc    ksact    kscta    kscat    ktsac    ktsca    ktasc    ktacs     ktcsa    ktcas    kastc    kasct    katsc    katcs    kacst    kacts    kcsta     kcsat    kctsa    kctas    kcast    kcats       120     120      Finished in 0 3s

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All Possible Word with stack  from itertools import permutations for i in permutations  stack        print    join i     permutations iterable  r None    Return successive r length permutations of elements in the iterable   If r is not specified or is None  then r defaults to the length of the iterable and all possible full-length permutations are generated   Permutations are emitted in lexicographic sort order  So  if the input iterable is sorted  the permutation tuples will be produced in sorted order   Elements are treated as unique based on their position  not on their value  So if the input elements are unique  there will be no repeat values in each permutation

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See itertools combinations or itertools permutations

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itertools permutations is good  but it doesn t deal nicely with sequences that contain repeated elements  That s because internally it permutes the sequence indices and is oblivious to the sequence item values   Sure  it s possible to filter the output of itertools permutations through a set to eliminate the duplicates  but it still wastes time generating those duplicates  and if there are several repeated elements in the base sequence there will be lots of duplicates  Also  using a collection to hold the results wastes RAM  negating the benefit of using an iterator in the first place   Fortunately  there are more efficient approaches  The code below uses the algorithm of the 14th century Indian mathematician Narayana Pandita  which can be found in the Wikipedia article on Permutation  This ancient algorithm is still one of the fastest known ways to generate permutations in order  and it is quite robust  in that it properly handles permutations that contain repeated elements   def lexico permute string s           Generate all permutations in lexicographic order of string  s           This algorithm  due to Narayana Pandita  is from         https   en wikipedia org wiki Permutation Generation in lexicographic order          To produce the next permutation in lexicographic order of sequence  a           1  Find the largest index j such that a j   lt  a j   1   If no such index exists           the permutation is the last permutation          2  Find the largest index k greater than j such that a j   lt  a k           3  Swap the value of a j  with that of a k           4  Reverse the sequence from a j   1  up to and including the final element a n                a   sorted s      n   len a  - 1     while True          yield    join a            1  Find the largest index j such that a j   lt  a j   1          for j in range n-1  -1  -1               if a j   lt  a j   1                   break         else              return           2  Find the largest index k greater than j such that a j   lt  a k          v   a j          for k in range n  j  -1               if v  lt  a k                   break           3  Swap the value of a j  with that of a k           a j   a k    a k   a j            4  Reverse the tail of the sequence         a j 1     a j 1     -1   for s in lexico permute string  data        print s    output  aadt aatd adat adta atad atda daat data dtaa taad tada tdaa   Of course  if you want to collect the yielded strings into a list you can do  list lexico permute string  data      or in recent Python versions     lexico permute string  data

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def permute seq       if not seq          yield seq     else          for i in range len seq                rest   seq  i  seq i 1               for x in permute rest                   yield seq i i 1  x  print list permute  stack

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The itertools module has a useful method called permutations    The documentation says      itertools permutations iterable   r        Return successive r length permutations of elements in the iterable       If r is not specified or is None  then r defaults to the length of the   iterable and all possible full-length permutations are generated       Permutations are emitted in lexicographic sort order  So  if the input   iterable is sorted  the permutation tuples will be produced in sorted   order    You ll have to join your permuted letters as strings though    gt  gt  gt  from itertools import permutations  gt  gt  gt  perms       join p  for p in permutations  stack     gt  gt  gt  perms        stack    stakc    stcak    stcka    stkac    stkca    satck      satkc    sactk    sackt    saktc    sakct    sctak    sctka      scatk    scakt    sckta    sckat    sktac    sktca    skatc      skact    skcta    skcat    tsack    tsakc    tscak    tscka      tskac    tskca    tasck    taskc    tacsk    tacks    taksc      takcs    tcsak    tcska    tcask    tcaks    tcksa    tckas      tksac    tksca    tkasc    tkacs    tkcsa    tkcas    astck      astkc    asctk    asckt    asktc    askct    atsck    atskc      atcsk    atcks    atksc    atkcs    acstk    acskt    actsk      actks    ackst    ackts    akstc    aksct    aktsc    aktcs      akcst    akcts    cstak    cstka    csatk    csakt    cskta      cskat    ctsak    ctska    ctask    ctaks    ctksa    ctkas      castk    caskt    catsk    catks    cakst    cakts    cksta      cksat    cktsa    cktas    ckast    ckats    kstac    kstca      ksatc    ksact    kscta    kscat    ktsac    ktsca    ktasc      ktacs    ktcsa    ktcas    kastc    kasct    katsc    katcs      kacst    kacts    kcsta    kcsat    kctsa    kctas    kcast      kcats     If you find yourself troubled by duplicates  try fitting your data into a structure with no duplicates like a set    gt  gt  gt  perms       join p  for p in permutations  stacks     gt  gt  gt  len perms  720  gt  gt  gt  len set perms   360   Thanks to  pst for pointing out that this is not what we d traditionally think of as a type cast  but more of a call to the set   constructor

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With Recursion     swap ith and jth character of string def swap s  i  j       q   list s      q i   q j    q j   q i      return    join q      recursive function  def  permute p  s  permutes       if p  gt   len s  - 1          permutes append s          return      for i in range p  len s             permute p   1  swap s  p  i   permutes      helper function def permute s       permutes           permute 0  s  permutes      return permutes     TEST IT s    1234  all permute   permute s  print all permute       With Iterative approach  Using Stack      swap ith and jth character of string def swap s  i  j       q   list s      q i   q j    q j   q i      return    join q      iterative function def permute using stack s       stk     0  s        permutes           while len stk   gt  0          p  s   stk pop 0           if p  gt   len s  - 1              permutes append s              continue          for i in range p  len s                stk append  p   1  swap s  p  i         return permutes     TEST IT s    1234  all permute   permute using stack s  print all permute       With Lexicographically sorted     swap ith and jth character of string def swap s  i  j       q   list s      q i   q j    q j   q i      return    join q      finds next lexicographic string if exist otherwise returns -1 def next lexicographical s       for i in range len s  - 2  -1  -1           if s i   lt  s i   1               m   s i   1              swap pos   i   1              for j in range i   1  len s                    if m  gt  s j   gt  s i                       m   s j                      swap pos   j              if swap pos    -1                  s   swap s  i  swap pos                  s   s  i   1       join sorted s i   1                     return s      return -1     helper function def permute lexicographically s       s      join sorted s       permutes          while True          permutes append s          s   next lexicographical s          if s    -1              break     return permutes     TEST IT s    1234  all permute   permute lexicographically s  print all permute

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This program does not eliminate the duplicates  but I think it is one of the most efficient approaches   s raw input  Enter a string     print  Permutations   n  s size len s  lis list range 0 size   while True       k -1     while k gt -size and lis k-1  gt lis k            k- 1     if k gt -size          p sorted lis k-1            e p p index lis k-1   1          lis insert k-1  A           lis remove e          lis lis index  A    e         lis k   sorted lis k            list2            for k in lis                  list2 append s k           print    join list2      else                  break

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Yet another initiative and recursive solution  The idea is to select a letter as a pivot and then create a word     for a string with length n  there is a factorial n  permutations alphabet    abc  starting perm        with recursion def premuate perm  alphabet       if not alphabet    we created one word by using all letters in the alphabet         print perm   alphabet      else          for i in range len alphabet      iterate over all letters in the alphabet             premuate perm   alphabet i   alphabet 0 i    alphabet i 1      chose one letter from the alphabet    call it             premuate starting perm  alphabet    Output   abc acb bac bca cab cba

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Here s a simple function to return unique permutations   def permutations string       if len string     1          return string      recursive perms          for c in string          for perm in permutations string replace c    1                revursive perms append c perm       return set revursive perms

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Here s a simple and straightforward recursive implementation   def stringPermutations s       if len s   lt  2          yield s         return     for pos in range 0  len s            char   s pos          permForRemaining   list stringPermutations s 0 pos    s pos 1             for perm in permForRemaining              yield char   perm

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Everyone loves the smell of their own code   Just sharing the one I find the simplest   def get permutations word       if len word     1          yield word      for i  letter in enumerate word           for perm in get permutations word  i    word i 1                 yield letter   perm

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Here s a really simple generator version   def find all permutations s  curr          if len s     0          yield curr     else          for i  c in enumerate s               for combo in find all permutations s  i  s i 1    curr    c                    yield    join combo    I think it s not so bad

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from itertools import permutations perms       join p  for p in permutations  ABC     perms       join p  for p in permutations  stack

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def permute all chars list  begin  end        if  begin    end           print list          return      for current position in range begin  end   1           list begin   list current position    list current position   list begin          permute all chars list  begin   1  end          list begin   list current position    list current position   list begin    given str    ABC  list      for char in given str      list append char  permute all chars list  0  len list  -1

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Here is another way of doing the permutation of string with minimal code  We basically create a loop and then we keep swapping two characters at a time  Inside the loop we ll have the recursion  Notice we only print when indexers reaches the length of our string  Example  ABC i for our starting point and our recursion param j for our loop    here is a visual help how it works from left to right top to bottom  is the order of permutation     the code    def permute data  i  length        if i  length           print    join data        else           for j in range i length                 swap             data i   data j    data j   data i               permute data  i 1  length               data i   data j    data j   data i      string    ABC  n   len string   data   list string   permute data  0  n

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def perm string      res       for j in range 0 len string           if len string  gt 1              for i in perm string 1                    res append string 0  i         else             return  string          string string 1   string 0      return res  l set perm  abcde      This is one way to generate permutations with recursion  you can understand the code easily by taking strings  a   ab   amp   abc  as input   You get all N  permutations with this  without duplicates

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def f s     if len s     2      X    s   s 1    s 0          return X else      list1          for i in range 0  len s            Y   f s 0 i    s i 1  len s            for j in Y              list1 append s i    j      return list1 s   raw input   z   f s  print z

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Simpler solution using permutations   from itertools import permutations  def stringPermutate s1       length len s1      if length  lt  2          return s1      perm       join p  for p in permutations s1        return set perm

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Here is another approach different from what  Adriano and  illerucis posted  This has a better runtime  you can check that yourself by measuring the time   def removeCharFromStr str  index       endIndex   index if index    len str  else index   1     return str  index    str endIndex       ab  - gt  a    b   b    a     abc  - gt   a   bc  b   ac  c   ab             a   cb  b   ca  c   ba def perm str       if len str   lt   1          return  str      permSet   set       for i  c in enumerate str           newStr   removeCharFromStr str  i          retSet   perm newStr          for elem in retSet              permSet add c   elem      return permSet   For an arbitrary string  dadffddxcf  it took 1 1336 sec for the permutation library  9 125 sec for this implementation and 16 357 secs for  Adriano s and  illerucis  version  Of course you can still optimize it

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This is a recursive solution with n  which accepts duplicate elements in the string import math  def getFactors root num       sol            return condition     if len num     1              return  root num        looping in next iteration     for i in range len num                Creating a substring with all remaining char but the taken in this iteration         if i  gt  0              rem   num  i  num i 1           else              rem   num i 1             Concatenating existing solutions with the solution of this iteration         sol   sol   getFactors root   num i   rem      return sol  I validated the solution taking into account two elements  the number of combinations is n  and the result can not contain duplicates  So  inpt    quot 1234 quot  results   getFactors  quot  quot  inpt   if len results     math factorial len inpt     len results     len set results        print  quot Wrong approach quot   else      print  quot Correct Approach quot

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Stack Overflow users have already posted some strong solutions but I wanted to show yet another solution  This one I find to be more intuitive  The idea is that for a given string  we can recurse by the algorithm  pseudo-code       permutations   char   permutations string - char  for char in string   I hope it helps someone   def permutations string               Create all permutations of a string with non-repeating characters             permutation list          if len string     1          return  string      else          for char in string               permutation list append char   a  for a in permutations string replace char      1        return permutation list

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Here s a slightly improved version of illerucis s code for returning a list of all permutations of a string s with distinct characters  not necessarily in lexicographic sort order   without using itertools   def get perms s  i 0               Returns a list of all  len s  - i   permutations t of s where t  i    s  i                 To avoid memory allocations for intermediate strings  use a list of chars      if isinstance s  str           s   list s         Base Case  0    1    1        Store the only permutation as an immutable string  not a mutable list      if i  gt   len s  - 1          return     join s          Inductive Step   len s  - i      len s  - i     len s  - i - 1         Swap in each suffix character to be at the beginning of the suffix      perms   get perms s  i   1      for j in range i   1  len s            s i   s j    s j   s i          perms extend get perms s  i   1           s i   s j    s j   s i      return perms

[python] Finding all possible permutations of a given string in python

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