Are there any better methods to do permutation of string?

Question

void permute(string elems, int mid, int end)
{
    static int count;
    if (mid == end) {
        cout << ++count << " : " << elems << endl;
        return ;
    }
    else {
    for (int i = mid; i <= end; i++) {
            swap(elems, mid, i);
            permute(elems, mid + 1, end);
            swap(elems, mid, i);
        }
    }
}

The above function shows the permutations of str(with str[0..mid-1] as a steady prefix, and str[mid..end] as a permutable suffix). So we can use permute(str, 0, str.size() - 1) to show all the permutations of one string.

But the function uses a recursive algorithm; maybe its performance could be improved?

Are there any better methods to permute a string?

Answer 1

Here is a non-recursive algorithm in C++ from the Wikipedia entry for unordered generation of permutations. For the string s of length n, for any k from 0 to n! - 1 inclusive, the following modifies s to provide a unique permutation (that is, different from those generated for any other k value on that range). To generate all permutations, run it for all n! k values on the original value of s.

#include <algorithm>

void permutation(int k, string &s) 
{
    for(int j = 1; j < s.size(); ++j) 
    {
        std::swap(s[k % (j + 1)], s[j]); 
        k = k / (j + 1);
    }
}

Here swap(s, i, j) swaps position i and j of the string s.

Answer 2

Why dont you try std::next_permutation() or std::prev_permutation() ?

Links:

std::next_permutation()
std::prev_permutation()

A simple example:

#include<string>
#include<iostream>
#include<algorithm>

int main()
{
   std::string s="123";
   do
   {

      std::cout<<s<<std::endl;

   }while(std::next_permutation(s.begin(),s.end()));
}

Output:

123
132
213
231
312
321

Answer 3

I'd like to second Permaquid's answer. The algorithm he cites works in a fundamentally different way from the various permutation enumeration algorithms that have been offered. It doesn't generate all of the permutations of n objects, it generates a distinct specific permutation, given an integer between 0 and n!-1. If you need only a specific permutation, it's much faster than enumerating them all and then selecting one.

Even if you do need all permutations, it provides options that a single permutation enumeration algorithm does not. I once wrote a brute-force cryptarithm cracker, that tried every possible assignment of letters to digits. For base-10 problems, it was adequate, since there are only 10! permutations to try. But for base-11 problems took a couple of minutes and base-12 problems took nearly an hour.

I replaced the permutation enumeration algorithm that I had been using with a simple i=0--to--N-1 for-loop, using the algorithm Permaquid cited. The result was only slightly slower. But then I split the integer range in quarters, and ran four for-loops simultaneously, each in a separate thread. On my quad-core processor, the resulting program ran nearly four times as fast.

Just as finding an individual permutation using the permutation enumeration algorithms is difficult, generating delineated subsets of the set of all permutations is also difficult. The algorithm that Permaquid cited makes both of these very easy

Answer 4

In particular, you want std::next_permutation.

void permute(string elems, int mid, int end)
{
  int count = 0;
  while(next_permutation(elems.begin()+mid, elems.end()))
    cout << << ++count << " : " << elems << endl;
}

... or something like that...

Answer 5

Any algorithm for generating permutations is going to run in polynomial time, because the number of permutations for characters within an n-length string is (n!). That said, there are some pretty simple in-place algorithms for generating permutations. Check out the Johnson-Trotter algorithm.

Answer 6

The Knuth random shuffle algorithm is worth looking into.

// In-place shuffle of char array
void shuffle(char array[], int n)
{
    for ( ; n > 1; n--)
    {
        // Pick a random element to move to the end
        int k = rand() % n;  // 0 <= k <= n-1  

        // Simple swap of variables
        char tmp = array[k];
        array[k] = array[n-1];
        array[n-1] = tmp;
    }
}

Answer 7

Any algorithm that makes use of or generates all permutations will take O(N!*N) time, O(N!) at the least to generate all permutations and O(N) to use the result, and that's really slow. Note that printing the string is also O(N) afaik.

In a second you can realistically only handle strings up to a maximum of 10 or 11 characters, no matter what method you use. Since 11!*11 = 439084800 iterations (doing this many in a second on most machines is pushing it) and 12!*12 = 5748019200 iterations. So even the fastest implementation would take about 30 to 60 seconds on 12 characters.

Factorial just grows too fast for you to hope to gain anything by writing a faster implementation, you'd at most gain one character. So I'd suggest Prasoon's recommendation. It's easy to code and it's quite fast. Though sticking with your code is completely fine as well.

I'd just recommend that you take care that you don't inadvertantly have extra characters in your string such as the null character. Since that will make your code a factor of N slower.

Answer 8

Actually you can do it using Knuth shuffling algo!

// find all the permutations of a string
// using Knuth radnom shuffling algorithm!

#include <iostream>
#include <string>

template <typename T, class Func>
void permutation(T array, std::size_t N, Func func)
{
    func(array);
    for (std::size_t n = N-1; n > 0; --n)
    {
        for (std::size_t k = 0; k <= n; ++k)
        {
            if (array[k] == array[n]) continue;
            using std::swap;
            swap(array[k], array[n]);
            func(array);
        }
    }
}

int main()
{
    while (std::cin.good())
    {
        std::string str;
        std::cin >> str;
        permutation(str, str.length(), [](std::string const &s){ 
            std::cout << s << std::endl; });
    }
}

Answer 9

I've written a permutation algorithm recently. It uses a vector of type T (template) instead of a string, and it's not super-fast because it uses recursion and there's a lot of copying. But perhaps you can draw some inspiration for the code. You can find the code here.

Answer 10

The only way to significantly improve performance is to find a way to avoid iterating through all the permutations in the first place!

Permuting is an unavoidably slow operation (O(n!), or worse, depending on what you do with each permutation), unfortunately nothing you can do will change this fact.

Also, note that any modern compiler will flatten out your recursion when optimisations are enabled, so the (small) performance gains from hand-optimising are reduced even further.

Answer 11

Do you want to run through all the permutations, or count the number of permutations?

For the former, use std::next_permutation as suggested by others. Each permutation takes O(N) time (but less amortized time) and no memory except its callframe, vs O(N) time and O(N) memory for your recursive function. The whole process is O(N!) and you can't do better than this, as others said, because you can't get more than O(X) results from a program in less than O(X) time! Without a quantum computer, anyway.

For the latter, you just need to know how many unique elements are in the string.

big_int count_permutations( string s ) {
    big_int divisor = 1;
    sort( s.begin(), s.end() );
    for ( string::iterator pen = s.begin(); pen != s.end(); ) {
        size_t cnt = 0;
        char value = * pen;
        while ( pen != s.end() && * pen == value ) ++ cnt, ++ pen;
        divisor *= big_int::factorial( cnt );
    }
    return big_int::factorial( s.size() ) / divisor;
}

Speed is bounded by the operation of finding duplicate elements, which for chars can be done in O(N) time with a lookup table.

Answer 12

I don't think this is better, but it does work and does not use recursion:

#include <iostream>
#include <stdexcept>
#include <tr1/cstdint>

::std::uint64_t fact(unsigned int v)
{
   ::std::uint64_t output = 1;
   for (unsigned int i = 2; i <= v; ++i) {
      output *= i;
   }
   return output;
}

void permute(const ::std::string &s)
{
   using ::std::cout;
   using ::std::uint64_t;
   typedef ::std::string::size_type size_t;

   static unsigned int max_size = 20;  // 21! > 2^64

   const size_t strsize = s.size();

   if (strsize > max_size) {
      throw ::std::overflow_error("This function can only permute strings of size 20 or less.");
   } else if (strsize < 1) {
      return;
   } else if (strsize == 1) {
      cout << "0 : " << s << '\n';
   } else {
      const uint64_t num_perms = fact(s.size());
      // Go through each permutation one-by-one
      for (uint64_t perm = 0; perm < num_perms; ++perm) {
         // The indexes of the original characters in the new permutation
         size_t idxs[max_size];

         // The indexes of the original characters in the new permutation in
         // terms of the list remaining after the first n characters are pulled
         // out.
         size_t residuals[max_size];

         // We use div to pull our permutation number apart into a set of
         // indexes.  This holds what's left of the permutation number.
         uint64_t permleft = perm;

         // For a given permutation figure out which character from the original
         // goes in each slot in the new permutation.  We start assuming that
         // any character could go in any slot, then narrow it down to the
         // remaining characters with each step.
         for (unsigned int i = strsize; i > 0; permleft /= i, --i) {
            uint64_t taken_char = permleft % i;
            residuals[strsize - i] = taken_char;

            // Translate indexes in terms of the list of remaining characters
            // into indexes in terms of the original string.
            for (unsigned int o = (strsize - i); o > 0; --o) {
               if (taken_char >= residuals[o - 1]) {
                  ++taken_char;
               }
            }
            idxs[strsize - i] = taken_char;
         }
         cout << perm << " : ";
         for (unsigned int i = 0; i < strsize; ++i) {
            cout << s[idxs[i]];
         }
         cout << '\n';
      }
   }
}

The fun thing about this is that the only state it uses from permutation to permutation is the number of the permutation, the total number of permutations, and the original string. That means it can be easily encapsulated in an iterator or something like that without having to carefully preserve the exact correct state. It can even be a random access iterator.

Of course ::std::next_permutation stores the state in the relationships between elements, but that means it can't work on unordered things, and I would really wonder what it does if you have two equal things in the sequence. You can solve that by permuting indexes of course, but that adds slightly more complication.

Mine will work with any random access iterator range provided it's short enough. And if it isn't, you'll never get through all the permutations anyway.

The basic idea of this algorithm is that every permutation of N items can be enumerated. The total number is N! or fact(N). And any given permutation can be thought of as a mapping of source indices from the original sequence into a set of destination indices in the new sequence. Once you have an enumeration of all permutations the only thing left to do is map each permutation number into an actual permutation.

The first element in the permuted list can be any of the N elements from the original list. The second element can be any of the N - 1 remaining elements, and so on. The algorithm uses the % operator to pull apart the permutation number into a set of selections of this nature. First it modulo's the permutation number by N to get a number from [0,N). It discards the remainder by dividing by N, then it modulo's it by the size of the list - 1 to get a number from [0,N-1) and so on. That is what the for (i = loop is doing.

The second step is translating each number into an index into the original list. The first number is easy because it's just a straight index. The second number is an index into a list that contains every element but the one removed at the first index, and so on. That is what the for (o = loop is doing.

residuals is a list of indices into the successively smaller lists. idxs is a list of indices into the original list. There is a one-one mapping between values in residuals and idxs. They each represent the same value in different 'coordinate spaces'.

The answer pointed to by the answer you picked has the same basic idea, but has a much more elegant way of accomplishing the mapping than my rather literal and brute force method. That way will be slightly faster than my method, but they are both about the same speed and they both have the same advantage of random access into permutation space which makes a whole number of things easier, including (as the answer you picked pointed out) parallel algorithms.

Answer 13

Even I found it difficult to understand that recursive version of the first time and it took me some time to search for a berre way.Better method to find (that I can think of) is to use the algorithm proposed by Narayana Pandita. The basic idea is:

1. First sort the given string in no-decreasing order and then find the index of the first element from the end that is less than its next character lexicigraphically. Call this element index the 'firstIndex'.
2. Now find the smallest character which is greater thn the element at the 'firstIndex'. Call this element index the 'ceilIndex'.
3. Now swap the elements at 'firstIndex' and 'ceilIndex'.
4. Reverse the part of the string starting from index 'firstIndex+1' to the end of the string.
5. (Instead of point 4) You can also sort the part of the string from index 'firstIndex+1' to the end of the string.

Point 4 and 5 do the same thing but the time complexity in case of point 4 is O(n*n!) and that in case of point 5 is O(n^2*n!).

The above algorithm can even be applied to the case when we have duplicate characters in the string. :

The code for displaying all the permutation of a string :

#include <iostream>

using namespace std;

void swap(char *a, char *b)
{
    char tmp = *a;
    *a = *b;
    *b = tmp;
}


int partition(char arr[], int start, int end)
{
    int x = arr[end];
    int i = start - 1;
    for(int j = start; j <= end-1; j++)
    {
        if(arr[j] <= x)
        {
            i = i + 1;
            swap(&arr[i], &arr[j]);
        }
    }
    swap(&arr[i+1], &arr[end]);
    return i+1;
}

void quickSort(char arr[], int start, int end)
{
    if(start<end)
    {
        int q = partition(arr, start, end);
        quickSort(arr, start, q-1);
        quickSort(arr, q+1, end);
    }
}

int findCeilIndex(char *str, int firstIndex, int n)
{
    int ceilIndex;
    ceilIndex = firstIndex+1;

    for (int i = ceilIndex+1; i < n; i++)
    {
        if(str[i] >= str[firstIndex] && str[i] <= str[ceilIndex])
            ceilIndex = i;
    }
    return ceilIndex;
}

void reverse(char *str, int start, int end)
{
    while(start<=end)
    {
        char tmp = str[start];
        str[start] = str[end];
        str[end] = tmp;
        start++;
        end--;
    }
}

void permutate(char *str, int n)
{
    quickSort(str, 0, n-1);
    cout << str << endl;
    bool done = false;
    while(!done)
    {
        int firstIndex;
        for(firstIndex = n-2; firstIndex >=0; firstIndex--)
        {
            if(str[firstIndex] < str[firstIndex+1])
                break;
        }
        if(firstIndex<0)
            done = true;
        if(!done)
        {
            int ceilIndex;
            ceilIndex = findCeilIndex(str, firstIndex, n);
            swap(&str[firstIndex], &str[ceilIndex]);
            reverse(str, firstIndex+1, n-1);
            cout << str << endl;
        }
    }
}


int main()
{
    char str[] = "mmd";
    permutate(str, 3);
    return 0;
}

Answer 14

This post: http://cplusplus.co.il/2009/11/14/enumerating-permutations/ deals with permuting just about anything, not only strings. The post itself and the comments below are pretty informative and I wouldn't want to copy&paste..

Answer 15

Here's one I just rustled up!!

void permute(const char* str, int level=0, bool print=true) {

    if (print) std::cout << str << std::endl;

    char temp[30];
    for (int i = level; i<strlen(str); i++) {

        strcpy(temp, str);

        temp[level] = str[i];
        temp[i] = str[level];

        permute(temp, level+1, level!=i);
    }
}

int main() {
    permute("1234");

    return 0;
}

Answer 16

If you are interested in permutation generation I did a research paper on it a while back : http://www.oriontransfer.co.nz/research/permutation-generation

It comes complete with source code, and there are 5 or so different methods implemented.

Answer 17

This is not the best logic, but then, i am a beginner. I'll be quite happy and obliged if anyone gives me suggestions on this code

#include<iostream.h>
#include<conio.h>
#include<string.h>
int c=1,j=1;


int fact(int p,int l)
{
int f=1;
for(j=1;j<=l;j++)
{
f=f*j;
if(f==p)
return 1;

}
return 0;
}


void rev(char *a,int q)
{
int l=strlen(a);
int m=l-q;
char t;
for(int x=m,y=0;x<q/2+m;x++,y++)
{
t=a[x];
a[x]=a[l-y-1];
a[l-y-1]=t;
}
c++;
cout<<a<<"  ";
}

int perm(char *a,int f,int cd)
{
if(c!=f)
{
int l=strlen(a);
rev(a,2);
cd++;
if(c==f)return 0;
if(cd*2==6)
{
for(int i=1;i<=c;i++)
{
if(fact(c/i,l)==1)
{
rev(a,j+1);
rev(a,2);
break;
}
}
cd=1;
}
rev(a,3);
perm(a,f,cd);
}
return 0;
}

void main()
{
clrscr();
char *a;
cout<<"\n\tEnter a Word";
cin>>a;
int f=1;

for(int o=1;o<=strlen(a);o++)
f=f*o;

perm(a,f,0);
getch();
}

Answer 18

**// Prints all permutation of a string**

    #include<bits/stdc++.h>
    using namespace std;


    void printPermutations(string input, string output){
        if(input.length() == 0){
            cout<<output <<endl;
            return;
        }

        for(int i=0; i<=output.length(); i++){
            printPermutations(input.substr(1),  output.substr(0,i) + input[0] + output.substr(i));
        }
    }

    int main(){
        string s = "ABC";
        printPermutations(s, "");
        return 0;
    }

Answer 19

Here yet another recursive function for string permutations:

void permute(string prefix, string suffix, vector<string> &res) {
    if (suffix.size() < 1) {
        res.push_back(prefix);
        return;
    }
    for (size_t i = 0; i < suffix.size(); i++) {
        permute(prefix + suffix[i], suffix.substr(0,i) + suffix.substr(i + 1), res);
    }
}


int main(){
    string str = "123";
    vector<string> res;
    permute("", str, res);
}

The function collects all permutations in vector res. The idea can be generalized for different type of containers using templates and iterators:

template <typename Cont1_t, typename Cont2_t>
void permute(typename Cont1_t prefix,
    typename Cont1_t::iterator beg, typename Cont1_t::iterator end,
    Cont2_t &result)
{
    if (beg == end) {
        result.insert(result.end(), prefix);
        return;
    }
    for (auto it = beg; it != end; ++it) {
        prefix.insert(prefix.end(), *it);
        Cont1_t tmp;
        for (auto i = beg; i != end; ++i)
            if (i != it)
                tmp.insert(tmp.end(), *i);

        permute(prefix, tmp.begin(), tmp.end(), result);
        prefix.erase(std::prev(prefix.end()));
    }
}

int main()
{
    string str = "123";
    vector<string> rStr;
    permute<string, vector<string>>("", str.begin(), str.end(), rStr);

    vector<int>vint = { 1,2,3 };
    vector<vector<int>> rInt;
    permute<vector<int>, vector<vector<int>>>({}, vint.begin(), vint.end(), rInt);

    list<long> ll = { 1,2,3 };
    vector<list<long>> vlist;
    permute<list<long>, vector<list<long>>>({}, ll.begin(), ll.end(), vlist);
}

This may be an interesting programming exercise, but in production code you should use a non recusrive version of permutation , like next_permutation.

Answer 20

  //***************anagrams**************//


  //************************************** this code works only when there are no   
  repeatations in the original string*************//
  #include<iostream>
  using namespace std;

  int counter=0;

  void print(char empty[],int size)
  {

  for(int i=0;i<size;i++)
  {
    cout<<empty[i];
  }
  cout<<endl;
  }


  void makecombination(char original[],char empty[],char comb[],int k,int& nc,int size)
{
nc=0;

int flag=0;
for(int i=0;i<size;i++)
{
    flag=0;                                                                   // {
    for(int j=0;j<k;j++)
    {
        if(empty[j]==original[i])                                                                // remove this code fragment
        {                                                                                        // to print permutations with repeatation
            flag=1;
            break;
        }
    }
    if(flag==0)                                                                // }
    {
        comb[nc++]=original[i];
    }
}
//cout<<"checks  ";
//    print(comb,nc);
}


void recurse(char original[],char empty[],int k,int size)
{
char *comb=new char[size];


int nc;


if(k==size)
{
    counter++;
    print(empty,size);
    //cout<<counter<<endl;

}
else
{
    makecombination(original,empty,comb,k,nc,size);
    k=k+1;
    for(int i=0;i<nc;i++)
    {
        empty[k-1]=comb[i];

        cout<<"k = "<<k<<" nc = "<<nc<<" empty[k-1] = "<<empty[k-1]<<endl;//checks the  value of k , nc, empty[k-1] for proper understanding
        recurse(original,empty,k,size);
    }
}

}

int main()
{
const int size=3;
int k=0;
char original[]="ABC";

char empty[size];
for(int f=0;f<size;f++)
empty[f]='*';

recurse(original,empty,k,size);

cout<<endl<<counter<<endl;
return 0;
}