There are 2 strings , how can we check if one is a rotated version of another ?
For Example : hello --- lohel
One simple solution is by concatenating first string with itself and checking if the other one is a substring of the concatenated version.
Is there any other solution to it ?
I was wondering if we could use circular linked list maybe ? But I am not able to arrive at the solution.
One simple solution is by concatenating them and checking if the other one is a substring of the concatenated version.
I assume you mean concatenate the first string with itself, then check if the other one is a substring of that concatenation.
That will work, and in fact can be done without any concatenation at all. Just use any string searching algorithm to search for the second string in the first, and when you reach the end, loop back to the beginning.
For instance, using Boyer-Moore the overall algorithm would be O(n).
There's no need to concatenate at all.
First, check the lengths. If they're different then return false.
Second, use an index that increments from the first character to the last of the source. Check if the destination starts with all the letters from the index to the end, and ends with all the letters before the index. If at any time this is true, return true.
Otherwise, return false.
EDIT:
An implementation in Python:
def isrot(src, dest):
# Make sure they have the same size
if len(src) != len(dest):
return False
# Rotate through the letters in src
for ix in range(len(src)):
# Compare the end of src with the beginning of dest
# and the beginning of src with the end of dest
if dest.startswith(src[ix:]) and dest.endswith(src[:ix]):
return True
return False
print isrot('hello', 'lohel')
print isrot('hello', 'lohell')
print isrot('hello', 'hello')
print isrot('hello', 'lohe')
You could compute the lexicographically minimal string rotation of each string and then test if they were equal.
Computing the minimal rotation is O(n).
This would be good if you had lots of strings to test as the minimal rotation could be applied as a preprocessing step and then you could use a standard hash table to store the rotated strings.
Trivial O(min(n,m)^2) algorithm: (n - length of S1, m - length of S2)
isRotated(S1 , S2):
if (S1.length != S2.length)
return false
for i : 0 to n-1
res = true
index = i
for j : 0 to n-1
if S1[j] != S2[index]
res = false
break
index = (index+1)%n
if res == true
return true
return false
EDIT:
Explanation -
Two strings S1 and S2 of lengths m and n respectively are cyclic identical if and only if m == n and exist index 0 <= j <= n-1 such S1 = S[j]S[j+1]...S[n-1]S[0]...S[j-1].
So in the above algorithm we check if the length is equal and if exist such an index.
A very straightforward solution is to rotate one of the words n times, where n is the length of the word. For each of those rotations, check to see if the result is the same as the other word.
You can do it in O(n) time and O(1) space:
def is_rot(u, v):
n, i, j = len(u), 0, 0
if n != len(v):
return False
while i < n and j < n:
k = 1
while k <= n and u[(i + k) % n] == v[(j + k) % n]:
k += 1
if k > n:
return True
if u[(i + k) % n] > v[(j + k) % n]:
i += k
else:
j += k
return False
See my answer here for more details.
Simple solution in Java. No need of iteration or concatenation.
private static boolean isSubString(String first, String second){
int firstIndex = second.indexOf(first.charAt(0));
if(first.length() == second.length() && firstIndex > -1){
if(first.equalsIgnoreCase(second))
return true;
int finalPos = second.length() - firstIndex ;
return second.charAt(0) == first.charAt(finalPos)
&& first.substring(finalPos).equals(second.subSequence(0, firstIndex));
}
return false;
}
Test case:
String first = "bottle";
String second = "tlebot";
Logic:
Take the first string's first character, find the index in the second string. Subtract the length of the second with the index found, check if first character of the second at 0 is same as character at the difference of length of the second and index found and substrings between those 2 characters are the same.
Another python implementation (without concatenation) although not efficient but it's O(n), looking forward for comments if any.
Assume that there are two strings s1 and s2.
Obviously, if s1 and s2 are rotations, there exists two sub strings of s2 in s1, the sum of them will total to the length of the string.
The question is to find that partition for which I increment an index in s2 whenever a char of s2 matches with that of s1.
def is_rotation(s1, s2):
if len(s1) != len(s2):
return False
n = len(s1)
if n == 0: return True
j = 0
for i in range(n):
if s2[j] == s1[i]:
j += 1
return (j > 0 and s1[:n - j] == s2[j:] and s1[n - j:] == s2[:j])
The second and condition is just to ensure that the counter incremented for s2 are a sub string match.
input1= "hello" input2="llohe" input3="lohel"(input3 is special case)
if length's of input 1 & input2 are not same return 0.Let i and j be two indexes pointing to input1 and input2 respectively and initialize count to input1.length. Have a flag called isRotated which is set to false
while(count != 0){
When the character's of input1 matches input2
increment i & j
decrement count
If the character's donot match
if isRotated = true(it means even after rotation there's mismatch) so break;
else Reset j to 0 as there's a mismatch. Eg:
Please find the code below and let me know if it fails for some other combination I may not have considered.
public boolean isRotation(String input1, String input2) {
boolean isRotated = false;
int i = 0, j = 0, count = input1.length();
if (input1.length() != input2.length())
return false;
while (count != 0) {
if (i == input1.length() && !isRotated) {
isRotated = true;
i = 0;
}
if (input1.charAt(i) == input2.charAt(j)) {
i++;
j++;
count--;
}
else {
if (isRotated) {
break;
}
if (i == input1.length() - 1 && !isRotated) {
isRotated = true;
}
if (i < input1.length()) {
j = 0;
count = input1.length();
}
/* To handle the duplicates. This is the special case.
* This occurs when input1 contains two duplicate elements placed side-by-side as "ll" in "hello" while
* they may not be side-by-side in input2 such as "lohel" but are still valid rotations.
Eg: "hello" "lohel"
*/
if (input1.charAt(i) == input2.charAt(j)) {
i--;
}
i++;
}
}
if (count == 0)
return true;
return false;
}
public static void main(String[] args) {
// TODO Auto-generated method stub
System.out.println(new StringRotation().isRotation("harry potter",
"terharry pot"));
System.out.println(new StringRotation().isRotation("hello", "llohe"));
System.out.println(new StringRotation().isRotation("hello", "lohell"));
System.out.println(new StringRotation().isRotation("hello", "hello"));
System.out.println(new StringRotation().isRotation("hello", "lohe"));
}
Solving the problem in O(n)
void isSubstring(string& s1, string& s2)
{
if(s1.length() != s2.length())
cout<<"Not rotation string"<<endl;
else
{
int firstI=0, secondI=0;
int len = s1.length();
while( firstI < len )
{
if(s1[firstI%len] == s2[0] && s1[(firstI+1) %len] == s2[1])
break;
firstI = (firstI+1)%len;
}
int len2 = s2.length();
int i=0;
bool isSubString = true;
while(i < len2)
{
if(s1[firstI%len] != s2[i])
{
isSubString = false;
break;
}
i++;
}
if(isSubString)
cout<<"Is Rotation String"<<endl;
else
cout<<"Is not a rotation string"<<endl;
}
}
String source = "avaraavar";
String dest = "ravaraava";
System.out.println();
if(source.length()!=dest.length())
try {
throw (new IOException());
} catch (Exception e) {
// TODO Auto-generated catch block
e.printStackTrace();
}
int i = 0;
int j = 0;
int totalcount=0;
while(true)
{
i=i%source.length();
if(source.charAt(i)==dest.charAt(j))
{
System.out.println("i="+i+" , j = "+j);
System.out.println(source.charAt(i)+"=="+dest.charAt(j));
i++;
j++;
totalcount++;
}
else
{
System.out.println("i="+i+" , j = "+j);
System.out.println(source.charAt(i)+"!="+dest.charAt(j));
i++;
totalcount++;
j=0;
}
if(j==source.length())
{
System.out.println("Yes its a rotation");
break;
}
if(totalcount >(2*source.length())-1)
{
System.out.println("No its a rotation");
break;
}
}
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Definition:
A palindrome is a word, phrase, number or other sequence of units that has the property of reading the same in either direction
How to check if the given string is a palindrome?
This was one of the FAIQ [Frequently Asked Interview Question] a while ago but that mostly using C.
Looking for solutions in any and all languages possible.
PHP sample:
$string = "A man, a plan, a canal, Panama";
function is_palindrome($string)
{
$a = strtolower(preg_replace("/[^A-Za-z0-9]/","",$string));
return $a==strrev($a);
}
Removes any non-alphanumeric characters (spaces, commas, exclamation points, etc.) to allow for full sentences as above, as well as simple words.
Windows XP (might also work on 2000) or later BATCH script:
#echo off
call :is_palindrome %1
if %ERRORLEVEL% == 0 (
echo %1 is a palindrome
) else (
echo %1 is NOT a palindrome
)
exit /B 0
:is_palindrome
set word=%~1
set reverse=
call :reverse_chars "%word%"
set return=1
if "$%word%" == "$%reverse%" (
set return=0
)
exit /B %return%
:reverse_chars
set chars=%~1
set reverse=%chars:~0,1%%reverse%
set chars=%chars:~1%
if "$%chars%" == "$" (
exit /B 0
) else (
call :reverse_chars "%chars%"
)
exit /B 0
Language agnostic meta-code then...
rev = StringReverse(originalString)
return ( rev == originalString );
C# in-place algorithm. Any preprocessing, like case insensitivity or stripping of whitespace and punctuation should be done before passing to this function.
boolean IsPalindrome(string s) {
for (int i = 0; i < s.Length / 2; i++)
{
if (s[i] != s[s.Length - 1 - i]) return false;
}
return true;
}
Edit: removed unnecessary "+1" in loop condition and spent the saved comparison on removing the redundant Length comparison. Thanks to the commenters!
C#: LINQ
var str = "a b a";
var test = Enumerable.SequenceEqual(str.ToCharArray(),
str.ToCharArray().Reverse());
A more Ruby-style rewrite of Hal's Ruby version:
class String
def palindrome?
(test = gsub(/[^A-Za-z]/, '').downcase) == test.reverse
end
end
Now you can call palindrome? on any string.
Unoptimized Python:
>>> def is_palindrome(s):
... return s == s[::-1]
Java solution:
public class QuickTest {
public static void main(String[] args) {
check("AmanaplanacanalPanama".toLowerCase());
check("Hello World".toLowerCase());
}
public static void check(String aString) {
System.out.print(aString + ": ");
char[] chars = aString.toCharArray();
for (int i = 0, j = (chars.length - 1); i < (chars.length / 2); i++, j--) {
if (chars[i] != chars[j]) {
System.out.println("Not a palindrome!");
return;
}
}
System.out.println("Found a palindrome!");
}
}
Using a good data structure usually helps impress the professor:
Push half the chars onto a stack (Length / 2).
Pop and compare each char until the first unmatch.
If the stack has zero elements: palindrome.
*in the case of a string with an odd Length, throw out the middle char.
C in the house. (not sure if you didn't want a C example here)
bool IsPalindrome(char *s)
{
int i,d;
int length = strlen(s);
char cf, cb;
for(i=0, d=length-1 ; i < length && d >= 0 ; i++ , d--)
{
while(cf= toupper(s[i]), (cf < 'A' || cf >'Z') && i < length-1)i++;
while(cb= toupper(s[d]), (cb < 'A' || cb >'Z') && d > 0 )d--;
if(cf != cb && cf >= 'A' && cf <= 'Z' && cb >= 'A' && cb <='Z')
return false;
}
return true;
}
That will return true for "racecar", "Racecar", "race car", "racecar ", and "RaCe cAr". It would be easy to modify to include symbols or spaces as well, but I figure it's more useful to only count letters(and ignore case). This works for all palindromes I've found in the answers here, and I've been unable to trick it into false negatives/positives.
Also, if you don't like bool in a "C" program, it could obviously return int, with return 1 and return 0 for true and false respectively.
Here's a python way. Note: this isn't really that "pythonic" but it demonstrates the algorithm.
def IsPalindromeString(n):
myLen = len(n)
i = 0
while i <= myLen/2:
if n[i] != n[myLen-1-i]:
return False
i += 1
return True
Delphi
function IsPalindrome(const s: string): boolean;
var
i, j: integer;
begin
Result := false;
j := Length(s);
for i := 1 to Length(s) div 2 do begin
if s[i] <> s[j] then
Exit;
Dec(j);
end;
Result := true;
end;
I'm seeing a lot of incorrect answers here. Any correct solution needs to ignore whitespace and punctuation (and any non-alphabetic characters actually) and needs to be case insensitive.
A few good example test cases are:
"A man, a plan, a canal, Panama."
"A Toyota's a Toyota."
"A"
""
As well as some non-palindromes.
Example solution in C# (note: empty and null strings are considered palindromes in this design, if this is not desired it's easy to change):
public static bool IsPalindrome(string palindromeCandidate)
{
if (string.IsNullOrEmpty(palindromeCandidate))
{
return true;
}
Regex nonAlphaChars = new Regex("[^a-z0-9]");
string alphaOnlyCandidate = nonAlphaChars.Replace(palindromeCandidate.ToLower(), "");
if (string.IsNullOrEmpty(alphaOnlyCandidate))
{
return true;
}
int leftIndex = 0;
int rightIndex = alphaOnlyCandidate.Length - 1;
while (rightIndex > leftIndex)
{
if (alphaOnlyCandidate[leftIndex] != alphaOnlyCandidate[rightIndex])
{
return false;
}
leftIndex++;
rightIndex--;
}
return true;
}
EDIT: from the comments:
bool palindrome(std::string const& s)
{
return std::equal(s.begin(), s.end(), s.rbegin());
}
The c++ way.
My naive implementation using the elegant iterators. In reality, you would probably check
and stop once your forward iterator has past the halfway mark to your string.
#include <string>
#include <iostream>
using namespace std;
bool palindrome(string foo)
{
string::iterator front;
string::reverse_iterator back;
bool is_palindrome = true;
for(front = foo.begin(), back = foo.rbegin();
is_palindrome && front!= foo.end() && back != foo.rend();
++front, ++back
)
{
if(*front != *back)
is_palindrome = false;
}
return is_palindrome;
}
int main()
{
string a = "hi there", b = "laval";
cout << "String a: \"" << a << "\" is " << ((palindrome(a))? "" : "not ") << "a palindrome." <<endl;
cout << "String b: \"" << b << "\" is " << ((palindrome(b))? "" : "not ") << "a palindrome." <<endl;
}
boolean isPalindrome(String str1) {
//first strip out punctuation and spaces
String stripped = str1.replaceAll("[^a-zA-Z0-9]", "");
return stripped.equalsIgnoreCase((new StringBuilder(stripped)).reverse().toString());
}
Java version
Here's my solution, without using a strrev. Written in C#, but it will work in any language that has a string length function.
private static bool Pal(string s) {
for (int i = 0; i < s.Length; i++) {
if (s[i] != s[s.Length - 1 - i]) {
return false;
}
}
return true;
}
Here's my solution in c#
static bool isPalindrome(string s)
{
string allowedChars = "abcdefghijklmnopqrstuvwxyz"+
"1234567890ABCDEFGHIJKLMNOPQRSTUVWXYZ";
string compareString = String.Empty;
string rev = string.Empty;
for (int i = 0; i <= s.Length - 1; i++)
{
char c = s[i];
if (allowedChars.IndexOf(c) > -1)
{
compareString += c;
}
}
for (int i = compareString.Length - 1; i >= 0; i--)
{
char c = compareString[i];
rev += c;
}
return rev.Equals(compareString,
StringComparison.CurrentCultureIgnoreCase);
}
Here's a Python version that deals with different cases, punctuation and whitespace.
import string
def is_palindrome(palindrome):
letters = palindrome.translate(string.maketrans("",""),
string.whitespace + string.punctuation).lower()
return letters == letters[::-1]
Edit: Shamelessly stole from Blair Conrad's neater answer to remove the slightly clumsy list processing from my previous version.
C++
std::string a = "god";
std::string b = "lol";
std::cout << (std::string(a.rbegin(), a.rend()) == a) << " "
<< (std::string(b.rbegin(), b.rend()) == b);
Bash
function ispalin { [ "$( echo -n $1 | tac -rs . )" = "$1" ]; }
echo "$(ispalin god && echo yes || echo no), $(ispalin lol && echo yes || echo no)"
Gnu Awk
/* obvious solution */
function ispalin(cand, i) {
for(i=0; i<length(cand)/2; i++)
if(substr(cand, length(cand)-i, 1) != substr(cand, i+1, 1))
return 0;
return 1;
}
/* not so obvious solution. cough cough */
{
orig = $0;
while($0) {
stuff = stuff gensub(/^.*(.)$/, "\\1", 1);
$0 = gensub(/^(.*).$/, "\\1", 1);
}
print (stuff == orig);
}
Haskell
Some brain dead way doing it in Haskell
ispalin :: [Char] -> Bool
ispalin a = a == (let xi (y:my) = (xi my) ++ [y]; xi [] = [] in \x -> xi x) a
Plain English
"Just reverse the string and if it is the same as before, it's a palindrome"
Ruby:
class String
def is_palindrome?
letters_only = gsub(/\W/,'').downcase
letters_only == letters_only.reverse
end
end
puts 'abc'.is_palindrome? # => false
puts 'aba'.is_palindrome? # => true
puts "Madam, I'm Adam.".is_palindrome? # => true
An obfuscated C version:
int IsPalindrome (char *s)
{
char*a,*b,c=0;
for(a=b=s;a<=b;c=(c?c==1?c=(*a&~32)-65>25u?*++a,1:2:c==2?(*--b&~32)-65<26u?3:2:c==3?(*b-65&~32)-(*a-65&~32)?*(b=s=0,a),4:*++a,1:0:*++b?0:1));
return s!=0;
}
This Java code should work inside a boolean method:
Note: You only need to check the first half of the characters with the back half, otherwise you are overlapping and doubling the amount of checks that need to be made.
private static boolean doPal(String test) {
for(int i = 0; i < test.length() / 2; i++) {
if(test.charAt(i) != test.charAt(test.length() - 1 - i)) {
return false;
}
}
return true;
}
Another C++ one. Optimized for speed and size.
bool is_palindrome(const std::string& candidate) {
for(std::string::const_iterator left = candidate.begin(), right = candidate.end(); left < --right ; ++left)
if (*left != *right)
return false;
return true;
}
Lisp:
(defun palindrome(x) (string= x (reverse x)))
Three versions in Smalltalk, from dumbest to correct.
In Smalltalk, = is the comparison operator:
isPalindrome: aString
"Dumbest."
^ aString reverse = aString
The message #translateToLowercase returns the string as lowercase:
isPalindrome: aString
"Case insensitive"
|lowercase|
lowercase := aString translateToLowercase.
^ lowercase reverse = lowercase
And in Smalltalk, strings are part of the Collection framework, you can use the message #select:thenCollect:, so here's the last version:
isPalindrome: aString
"Case insensitive and keeping only alphabetic chars
(blanks & punctuation insensitive)."
|lowercaseLetters|
lowercaseLetters := aString
select: [:char | char isAlphabetic]
thenCollect: [:char | char asLowercase].
^ lowercaseLetters reverse = lowercaseLetters
Note that in the above C++ solutions, there was some problems.
One solution was inefficient because it passed an std::string by copy, and because it iterated over all the chars, instead of comparing only half the chars. Then, even when discovering the string was not a palindrome, it continued the loop, waiting its end before reporting "false".
The other was better, with a very small function, whose problem was that it was not able to test anything else than std::string. In C++, it is easy to extend an algorithm to a whole bunch of similar objects. By templating its std::string into "T", it would have worked on both std::string, std::wstring, std::vector and std::deque. But without major modification because of the use of the operator <, the std::list was out of its scope.
My own solutions try to show that a C++ solution won't stop at working on the exact current type, but will strive to work an anything that behaves the same way, no matter the type. For example, I could apply my palindrome tests on std::string, on vector of int or on list of "Anything" as long as Anything was comparable through its operator = (build in types, as well as classes).
Note that the template can even be extended with an optional type that can be used to compare the data. For example, if you want to compare in a case insensitive way, or even compare similar characters (like è, é, ë, ê and e).
Like king Leonidas would have said: "Templates ? This is C++ !!!"
So, in C++, there are at least 3 major ways to do it, each one leading to the other:
Solution A: In a c-like way
The problem is that until C++0X, we can't consider the std::string array of chars as contiguous, so we must "cheat" and retrieve the c_str() property. As we are using it in a read-only fashion, it should be ok...
bool isPalindromeA(const std::string & p_strText)
{
if(p_strText.length() < 2) return true ;
const char * pStart = p_strText.c_str() ;
const char * pEnd = pStart + p_strText.length() - 1 ;
for(; pStart < pEnd; ++pStart, --pEnd)
{
if(*pStart != *pEnd)
{
return false ;
}
}
return true ;
}
Solution B: A more "C++" version
Now, we'll try to apply the same solution, but to any C++ container with random access to its items through operator []. For example, any std::basic_string, std::vector, std::deque, etc. Operator [] is constant access for those containers, so we won't lose undue speed.
template <typename T>
bool isPalindromeB(const T & p_aText)
{
if(p_aText.empty()) return true ;
typename T::size_type iStart = 0 ;
typename T::size_type iEnd = p_aText.size() - 1 ;
for(; iStart < iEnd; ++iStart, --iEnd)
{
if(p_aText[iStart] != p_aText[iEnd])
{
return false ;
}
}
return true ;
}
Solution C: Template powah !
It will work with almost any unordered STL-like container with bidirectional iterators
For example, any std::basic_string, std::vector, std::deque, std::list, etc.
So, this function can be applied on all STL-like containers with the following conditions:
1 - T is a container with bidirectional iterator
2 - T's iterator points to a comparable type (through operator =)
template <typename T>
bool isPalindromeC(const T & p_aText)
{
if(p_aText.empty()) return true ;
typename T::const_iterator pStart = p_aText.begin() ;
typename T::const_iterator pEnd = p_aText.end() ;
--pEnd ;
while(true)
{
if(*pStart != *pEnd)
{
return false ;
}
if((pStart == pEnd) || (++pStart == pEnd))
{
return true ;
}
--pEnd ;
}
}
A simple Java solution:
public boolean isPalindrome(String testString) {
StringBuffer sb = new StringBuffer(testString);
String reverseString = sb.reverse().toString();
if(testString.equalsIgnoreCase(reverseString)) {
return true;
else {
return false;
}
}
Many ways to do it. I guess the key is to do it in the most efficient way possible (without looping the string). I would do it as a char array which can be reversed easily (using C#).
string mystring = "abracadabra";
char[] str = mystring.ToCharArray();
Array.Reverse(str);
string revstring = new string(str);
if (mystring.equals(revstring))
{
Console.WriteLine("String is a Palindrome");
}
In Ruby, converting to lowercase and stripping everything not alphabetic:
def isPalindrome( string )
( test = string.downcase.gsub( /[^a-z]/, '' ) ) == test.reverse
end
But that feels like cheating, right? No pointers or anything! So here's a C version too, but without the lowercase and character stripping goodness:
#include <stdio.h>
int isPalindrome( char * string )
{
char * i = string;
char * p = string;
while ( *++i ); while ( i > p && *p++ == *--i );
return i <= p && *i++ == *--p;
}
int main( int argc, char **argv )
{
if ( argc != 2 )
{
fprintf( stderr, "Usage: %s <word>\n", argv[0] );
return -1;
}
fprintf( stdout, "%s\n", isPalindrome( argv[1] ) ? "yes" : "no" );
return 0;
}
Well, that was fun - do I get the job ;^)
Using Java, using Apache Commons String Utils:
public boolean isPalindrome(String phrase) {
phrase = phrase.toLowerCase().replaceAll("[^a-z]", "");
return StringUtils.reverse(phrase).equals(phrase);
}
How would I go about generating a list of all possible permutations of a string between x and y characters in length, containing a variable list of characters.
Any language would work, but it should be portable.
There are several ways to do this. Common methods use recursion, memoization, or dynamic programming. The basic idea is that you produce a list of all strings of length 1, then in each iteration, for all strings produced in the last iteration, add that string concatenated with each character in the string individually. (the variable index in the code below keeps track of the start of the last and the next iteration)
Some pseudocode:
list = originalString.split('')
index = (0,0)
list = [""]
for iteration n in 1 to y:
index = (index[1], len(list))
for string s in list.subset(index[0] to end):
for character c in originalString:
list.add(s + c)
you'd then need to remove all strings less than x in length, they'll be the first (x-1) * len(originalString) entries in the list.
It's better to use backtracking
#include <stdio.h>
#include <string.h>
void swap(char *a, char *b) {
char temp;
temp = *a;
*a = *b;
*b = temp;
}
void print(char *a, int i, int n) {
int j;
if(i == n) {
printf("%s\n", a);
} else {
for(j = i; j <= n; j++) {
swap(a + i, a + j);
print(a, i + 1, n);
swap(a + i, a + j);
}
}
}
int main(void) {
char a[100];
gets(a);
print(a, 0, strlen(a) - 1);
return 0;
}
You are going to get a lot of strings, that's for sure...
Where x and y is how you define them and r is the number of characters we are selecting from --if I am understanding you correctly. You should definitely generate these as needed and not get sloppy and say, generate a powerset and then filter the length of strings.
The following definitely isn't the best way to generate these, but it's an interesting aside, none-the-less.
Knuth (volume 4, fascicle 2, 7.2.1.3) tells us that (s,t)-combination is equivalent to s+1 things taken t at a time with repetition -- an (s,t)-combination is notation used by Knuth that is equal to . We can figure this out by first generating each (s,t)-combination in binary form (so, of length (s+t)) and counting the number of 0's to the left of each 1.
10001000011101 --> becomes the permutation: {0, 3, 4, 4, 4, 1}
Non recursive solution according to Knuth, Python example:
def nextPermutation(perm):
k0 = None
for i in range(len(perm)-1):
if perm[i]<perm[i+1]:
k0=i
if k0 == None:
return None
l0 = k0+1
for i in range(k0+1, len(perm)):
if perm[k0] < perm[i]:
l0 = i
perm[k0], perm[l0] = perm[l0], perm[k0]
perm[k0+1:] = reversed(perm[k0+1:])
return perm
perm=list("12345")
while perm:
print perm
perm = nextPermutation(perm)
You might look at "Efficiently Enumerating the Subsets of a Set", which describes an algorithm to do part of what you want - quickly generate all subsets of N characters from length x to y. It contains an implementation in C.
For each subset, you'd still have to generate all the permutations. For instance if you wanted 3 characters from "abcde", this algorithm would give you "abc","abd", "abe"...
but you'd have to permute each one to get "acb", "bac", "bca", etc.
Some working Java code based on Sarp's answer:
public class permute {
static void permute(int level, String permuted,
boolean used[], String original) {
int length = original.length();
if (level == length) {
System.out.println(permuted);
} else {
for (int i = 0; i < length; i++) {
if (!used[i]) {
used[i] = true;
permute(level + 1, permuted + original.charAt(i),
used, original);
used[i] = false;
}
}
}
}
public static void main(String[] args) {
String s = "hello";
boolean used[] = {false, false, false, false, false};
permute(0, "", used, s);
}
}
Here is a simple solution in C#.
It generates only the distinct permutations of a given string.
static public IEnumerable<string> permute(string word)
{
if (word.Length > 1)
{
char character = word[0];
foreach (string subPermute in permute(word.Substring(1)))
{
for (int index = 0; index <= subPermute.Length; index++)
{
string pre = subPermute.Substring(0, index);
string post = subPermute.Substring(index);
if (post.Contains(character))
continue;
yield return pre + character + post;
}
}
}
else
{
yield return word;
}
}
There are a lot of good answers here. I also suggest a very simple recursive solution in C++.
#include <string>
#include <iostream>
template<typename Consume>
void permutations(std::string s, Consume consume, std::size_t start = 0) {
if (start == s.length()) consume(s);
for (std::size_t i = start; i < s.length(); i++) {
std::swap(s[start], s[i]);
permutations(s, consume, start + 1);
}
}
int main(void) {
std::string s = "abcd";
permutations(s, [](std::string s) {
std::cout << s << std::endl;
});
}
Note: strings with repeated characters will not produce unique permutations.
I just whipped this up quick in Ruby:
def perms(x, y, possible_characters)
all = [""]
current_array = all.clone
1.upto(y) { |iteration|
next_array = []
current_array.each { |string|
possible_characters.each { |c|
value = string + c
next_array.insert next_array.length, value
all.insert all.length, value
}
}
current_array = next_array
}
all.delete_if { |string| string.length < x }
end
You might look into language API for built in permutation type functions, and you might be able to write more optimized code, but if the numbers are all that high, I'm not sure there is much of a way around having a lot of results.
Anyways, the idea behind the code is start with string of length 0, then keep track of all the strings of length Z where Z is the current size in the iteration. Then, go through each string and append each character onto each string. Finally at the end, remove any that were below the x threshold and return the result.
I didn't test it with potentially meaningless input (null character list, weird values of x and y, etc).
This is a translation of Mike's Ruby version, into Common Lisp:
(defun perms (x y original-string)
(loop with all = (list "")
with current-array = (list "")
for iteration from 1 to y
do (loop with next-array = nil
for string in current-array
do (loop for c across original-string
for value = (concatenate 'string string (string c))
do (push value next-array)
(push value all))
(setf current-array (reverse next-array)))
finally (return (nreverse (delete-if #'(lambda (el) (< (length el) x)) all)))))
And another version, slightly shorter and using more loop facility features:
(defun perms (x y original-string)
(loop repeat y
collect (loop for string in (or (car (last sets)) (list ""))
append (loop for c across original-string
collect (concatenate 'string string (string c)))) into sets
finally (return (loop for set in sets
append (loop for el in set when (>= (length el) x) collect el)))))
Here is a simple word C# recursive solution:
Method:
public ArrayList CalculateWordPermutations(string[] letters, ArrayList words, int index)
{
bool finished = true;
ArrayList newWords = new ArrayList();
if (words.Count == 0)
{
foreach (string letter in letters)
{
words.Add(letter);
}
}
for(int j=index; j<words.Count; j++)
{
string word = (string)words[j];
for(int i =0; i<letters.Length; i++)
{
if(!word.Contains(letters[i]))
{
finished = false;
string newWord = (string)word.Clone();
newWord += letters[i];
newWords.Add(newWord);
}
}
}
foreach (string newWord in newWords)
{
words.Add(newWord);
}
if(finished == false)
{
CalculateWordPermutations(letters, words, words.Count - newWords.Count);
}
return words;
}
Calling:
string[] letters = new string[]{"a","b","c"};
ArrayList words = CalculateWordPermutations(letters, new ArrayList(), 0);
... and here is the C version:
void permute(const char *s, char *out, int *used, int len, int lev)
{
if (len == lev) {
out[lev] = '\0';
puts(out);
return;
}
int i;
for (i = 0; i < len; ++i) {
if (! used[i])
continue;
used[i] = 1;
out[lev] = s[i];
permute(s, out, used, len, lev + 1);
used[i] = 0;
}
return;
}
permute (ABC) -> A.perm(BC) -> A.perm[B.perm(C)] -> A.perm[(*BC), (CB*)] -> [(*ABC), (BAC), (BCA*), (*ACB), (CAB), (CBA*)]
To remove duplicates when inserting each alphabet check to see if previous string ends with the same alphabet (why? -exercise)
public static void main(String[] args) {
for (String str : permStr("ABBB")){
System.out.println(str);
}
}
static Vector<String> permStr(String str){
if (str.length() == 1){
Vector<String> ret = new Vector<String>();
ret.add(str);
return ret;
}
char start = str.charAt(0);
Vector<String> endStrs = permStr(str.substring(1));
Vector<String> newEndStrs = new Vector<String>();
for (String endStr : endStrs){
for (int j = 0; j <= endStr.length(); j++){
if (endStr.substring(0, j).endsWith(String.valueOf(start)))
break;
newEndStrs.add(endStr.substring(0, j) + String.valueOf(start) + endStr.substring(j));
}
}
return newEndStrs;
}
Prints all permutations sans duplicates
Recursive solution in C++
int main (int argc, char * const argv[]) {
string s = "sarp";
bool used [4];
permute(0, "", used, s);
}
void permute(int level, string permuted, bool used [], string &original) {
int length = original.length();
if(level == length) { // permutation complete, display
cout << permuted << endl;
} else {
for(int i=0; i<length; i++) { // try to add an unused character
if(!used[i]) {
used[i] = true;
permute(level+1, original[i] + permuted, used, original); // find the permutations starting with this string
used[i] = false;
}
}
}
In Perl, if you want to restrict yourself to the lowercase alphabet, you can do this:
my #result = ("a" .. "zzzz");
This gives all possible strings between 1 and 4 characters using lowercase characters. For uppercase, change "a" to "A" and "zzzz" to "ZZZZ".
For mixed-case it gets much harder, and probably not doable with one of Perl's builtin operators like that.
Ruby answer that works:
class String
def each_char_with_index
0.upto(size - 1) do |index|
yield(self[index..index], index)
end
end
def remove_char_at(index)
return self[1..-1] if index == 0
self[0..(index-1)] + self[(index+1)..-1]
end
end
def permute(str, prefix = '')
if str.size == 0
puts prefix
return
end
str.each_char_with_index do |char, index|
permute(str.remove_char_at(index), prefix + char)
end
end
# example
# permute("abc")
The following Java recursion prints all permutations of a given string:
//call it as permut("",str);
public void permut(String str1,String str2){
if(str2.length() != 0){
char ch = str2.charAt(0);
for(int i = 0; i <= str1.length();i++)
permut(str1.substring(0,i) + ch + str1.substring(i,str1.length()),
str2.substring(1,str2.length()));
}else{
System.out.println(str1);
}
}
Following is the updated version of above "permut" method which makes n! (n factorial) less recursive calls compared to the above method
//call it as permut("",str);
public void permut(String str1,String str2){
if(str2.length() > 1){
char ch = str2.charAt(0);
for(int i = 0; i <= str1.length();i++)
permut(str1.substring(0,i) + ch + str1.substring(i,str1.length()),
str2.substring(1,str2.length()));
}else{
char ch = str2.charAt(0);
for(int i = 0; i <= str1.length();i++)
System.out.println(str1.substring(0,i) + ch + str1.substring(i,str1.length()),
str2.substring(1,str2.length()));
}
}
import java.util.*;
public class all_subsets {
public static void main(String[] args) {
String a = "abcd";
for(String s: all_perm(a)) {
System.out.println(s);
}
}
public static Set<String> concat(String c, Set<String> lst) {
HashSet<String> ret_set = new HashSet<String>();
for(String s: lst) {
ret_set.add(c+s);
}
return ret_set;
}
public static HashSet<String> all_perm(String a) {
HashSet<String> set = new HashSet<String>();
if(a.length() == 1) {
set.add(a);
} else {
for(int i=0; i<a.length(); i++) {
set.addAll(concat(a.charAt(i)+"", all_perm(a.substring(0, i)+a.substring(i+1, a.length()))));
}
}
return set;
}
}
I'm not sure why you would want to do this in the first place. The resulting set for any moderately large values of x and y will be huge, and will grow exponentially as x and/or y get bigger.
Lets say your set of possible characters is the 26 lowercase letters of the alphabet, and you ask your application to generate all permutations where length = 5. Assuming you don't run out of memory you'll get 11,881,376 (i.e. 26 to the power of 5) strings back. Bump that length up to 6, and you'll get 308,915,776 strings back. These numbers get painfully large, very quickly.
Here's a solution I put together in Java. You'll need to provide two runtime arguments (corresponding to x and y). Have fun.
public class GeneratePermutations {
public static void main(String[] args) {
int lower = Integer.parseInt(args[0]);
int upper = Integer.parseInt(args[1]);
if (upper < lower || upper == 0 || lower == 0) {
System.exit(0);
}
for (int length = lower; length <= upper; length++) {
generate(length, "");
}
}
private static void generate(int length, String partial) {
if (length <= 0) {
System.out.println(partial);
} else {
for (char c = 'a'; c <= 'z'; c++) {
generate(length - 1, partial + c);
}
}
}
}
Here's a non-recursive version I came up with, in javascript.
It's not based on Knuth's non-recursive one above, although it has some similarities in element swapping.
I've verified its correctness for input arrays of up to 8 elements.
A quick optimization would be pre-flighting the out array and avoiding push().
The basic idea is:
Given a single source array, generate a first new set of arrays which swap the first element with each subsequent element in turn, each time leaving the other elements unperturbed.
eg: given 1234, generate 1234, 2134, 3214, 4231.
Use each array from the previous pass as the seed for a new pass,
but instead of swapping the first element, swap the second element with each subsequent element. Also, this time, don't include the original array in the output.
Repeat step 2 until done.
Here is the code sample:
function oxe_perm(src, depth, index)
{
var perm = src.slice(); // duplicates src.
perm = perm.split("");
perm[depth] = src[index];
perm[index] = src[depth];
perm = perm.join("");
return perm;
}
function oxe_permutations(src)
{
out = new Array();
out.push(src);
for (depth = 0; depth < src.length; depth++) {
var numInPreviousPass = out.length;
for (var m = 0; m < numInPreviousPass; ++m) {
for (var n = depth + 1; n < src.length; ++n) {
out.push(oxe_perm(out[m], depth, n));
}
}
}
return out;
}
In ruby:
str = "a"
100_000_000.times {puts str.next!}
It is quite fast, but it is going to take some time =). Of course, you can start at "aaaaaaaa" if the short strings aren't interesting to you.
I might have misinterpreted the actual question though - in one of the posts it sounded as if you just needed a bruteforce library of strings, but in the main question it sounds like you need to permutate a particular string.
Your problem is somewhat similar to this one: http://beust.com/weblog/archives/000491.html (list all integers in which none of the digits repeat themselves, which resulted in a whole lot of languages solving it, with the ocaml guy using permutations, and some java guy using yet another solution).
I needed this today, and although the answers already given pointed me in the right direction, they weren't quite what I wanted.
Here's an implementation using Heap's method. The length of the array must be at least 3 and for practical considerations not be bigger than 10 or so, depending on what you want to do, patience and clock speed.
Before you enter your loop, initialise Perm(1 To N) with the first permutation, Stack(3 To N) with zeroes*, and Level with 2**. At the end of the loop call NextPerm, which will return false when we're done.
* VB will do that for you.
** You can change NextPerm a little to make this unnecessary, but it's clearer like this.
Option Explicit
Function NextPerm(Perm() As Long, Stack() As Long, Level As Long) As Boolean
Dim N As Long
If Level = 2 Then
Swap Perm(1), Perm(2)
Level = 3
Else
While Stack(Level) = Level - 1
Stack(Level) = 0
If Level = UBound(Stack) Then Exit Function
Level = Level + 1
Wend
Stack(Level) = Stack(Level) + 1
If Level And 1 Then N = 1 Else N = Stack(Level)
Swap Perm(N), Perm(Level)
Level = 2
End If
NextPerm = True
End Function
Sub Swap(A As Long, B As Long)
A = A Xor B
B = A Xor B
A = A Xor B
End Sub
'This is just for testing.
Private Sub Form_Paint()
Const Max = 8
Dim A(1 To Max) As Long, I As Long
Dim S(3 To Max) As Long, J As Long
Dim Test As New Collection, T As String
For I = 1 To UBound(A)
A(I) = I
Next
Cls
ScaleLeft = 0
J = 2
Do
If CurrentY + TextHeight("0") > ScaleHeight Then
ScaleLeft = ScaleLeft - TextWidth(" 0 ") * (UBound(A) + 1)
CurrentY = 0
CurrentX = 0
End If
T = vbNullString
For I = 1 To UBound(A)
Print A(I);
T = T & Hex(A(I))
Next
Print
Test.Add Null, T
Loop While NextPerm(A, S, J)
J = 1
For I = 2 To UBound(A)
J = J * I
Next
If J <> Test.Count Then Stop
End Sub
Other methods are described by various authors. Knuth describes two, one gives lexical order, but is complex and slow, the other is known as the method of plain changes. Jie Gao and Dianjun Wang also wrote an interesting paper.
Here is a link that describes how to print permutations of a string.
http://nipun-linuxtips.blogspot.in/2012/11/print-all-permutations-of-characters-in.html
This code in python, when called with allowed_characters set to [0,1] and 4 character max, would generate 2^4 results:
['0000', '0001', '0010', '0011', '0100', '0101', '0110', '0111', '1000', '1001', '1010', '1011', '1100', '1101', '1110', '1111']
def generate_permutations(chars = 4) :
#modify if in need!
allowed_chars = [
'0',
'1',
]
status = []
for tmp in range(chars) :
status.append(0)
last_char = len(allowed_chars)
rows = []
for x in xrange(last_char ** chars) :
rows.append("")
for y in range(chars - 1 , -1, -1) :
key = status[y]
rows[x] = allowed_chars[key] + rows[x]
for pos in range(chars - 1, -1, -1) :
if(status[pos] == last_char - 1) :
status[pos] = 0
else :
status[pos] += 1
break;
return rows
import sys
print generate_permutations()
Hope this is of use to you. Works with any character, not only numbers
Many of the previous answers used backtracking. This is the asymptotically optimal way O(n*n!) of generating permutations after initial sorting
class Permutation {
/* runtime -O(n) for generating nextPermutaion
* and O(n*n!) for generating all n! permutations with increasing sorted array as start
* return true, if there exists next lexicographical sequence
* e.g [a,b,c],3-> true, modifies array to [a,c,b]
* e.g [c,b,a],3-> false, as it is largest lexicographic possible */
public static boolean nextPermutation(char[] seq, int len) {
// 1
if (len <= 1)
return false;// no more perm
// 2: Find last j such that seq[j] <= seq[j+1]. Terminate if no such j exists
int j = len - 2;
while (j >= 0 && seq[j] >= seq[j + 1]) {
--j;
}
if (j == -1)
return false;// no more perm
// 3: Find last l such that seq[j] <= seq[l], then exchange elements j and l
int l = len - 1;
while (seq[j] >= seq[l]) {
--l;
}
swap(seq, j, l);
// 4: Reverse elements j+1 ... count-1:
reverseSubArray(seq, j + 1, len - 1);
// return seq, add store next perm
return true;
}
private static void swap(char[] a, int i, int j) {
char temp = a[i];
a[i] = a[j];
a[j] = temp;
}
private static void reverseSubArray(char[] a, int lo, int hi) {
while (lo < hi) {
swap(a, lo, hi);
++lo;
--hi;
}
}
public static void main(String[] args) {
String str = "abcdefg";
char[] array = str.toCharArray();
Arrays.sort(array);
int cnt=0;
do {
System.out.println(new String(array));
cnt++;
}while(nextPermutation(array, array.length));
System.out.println(cnt);//5040=7!
}
//if we use "bab"-> "abb", "bab", "bba", 3(#permutations)
}
Recursive Approach
func StringPermutations(inputStr string) (permutations []string) {
for i := 0; i < len(inputStr); i++ {
inputStr = inputStr[1:] + inputStr[0:1]
if len(inputStr) <= 2 {
permutations = append(permutations, inputStr)
continue
}
leftPermutations := StringPermutations(inputStr[0 : len(inputStr)-1])
for _, leftPermutation := range leftPermutations {
permutations = append(permutations, leftPermutation+inputStr[len(inputStr)-1:])
}
}
return
}
Though this doesn't answer your question exactly, here's one way to generate every permutation of the letters from a number of strings of the same length: eg, if your words were "coffee", "joomla" and "moodle", you can expect output like "coodle", "joodee", "joffle", etc.
Basically, the number of combinations is the (number of words) to the power of (number of letters per word). So, choose a random number between 0 and the number of combinations - 1, convert that number to base (number of words), then use each digit of that number as the indicator for which word to take the next letter from.
eg: in the above example. 3 words, 6 letters = 729 combinations. Choose a random number: 465. Convert to base 3: 122020. Take the first letter from word 1, 2nd from word 2, 3rd from word 2, 4th from word 0... and you get... "joofle".
If you wanted all the permutations, just loop from 0 to 728. Of course, if you're just choosing one random value, a much simpler less-confusing way would be to loop over the letters. This method lets you avoid recursion, should you want all the permutations, plus it makes you look like you know Maths(tm)!
If the number of combinations is excessive, you can break it up into a series of smaller words and concatenate them at the end.
c# iterative:
public List<string> Permutations(char[] chars)
{
List<string> words = new List<string>();
words.Add(chars[0].ToString());
for (int i = 1; i < chars.Length; ++i)
{
int currLen = words.Count;
for (int j = 0; j < currLen; ++j)
{
var w = words[j];
for (int k = 0; k <= w.Length; ++k)
{
var nstr = w.Insert(k, chars[i].ToString());
if (k == 0)
words[j] = nstr;
else
words.Add(nstr);
}
}
}
return words;
}
def gen( x,y,list): #to generate all strings inserting y at different positions
list = []
list.append( y+x )
for i in range( len(x) ):
list.append( func(x,0,i) + y + func(x,i+1,len(x)-1) )
return list
def func( x,i,j ): #returns x[i..j]
z = ''
for i in range(i,j+1):
z = z+x[i]
return z
def perm( x , length , list ): #perm function
if length == 1 : # base case
list.append( x[len(x)-1] )
return list
else:
lists = perm( x , length-1 ,list )
lists_temp = lists #temporarily storing the list
lists = []
for i in range( len(lists_temp) ) :
list_temp = gen(lists_temp[i],x[length-2],lists)
lists += list_temp
return lists
def permutation(str)
posibilities = []
str.split('').each do |char|
if posibilities.size == 0
posibilities[0] = char.downcase
posibilities[1] = char.upcase
else
posibilities_count = posibilities.length
posibilities = posibilities + posibilities
posibilities_count.times do |i|
posibilities[i] += char.downcase
posibilities[i+posibilities_count] += char.upcase
end
end
end
posibilities
end
Here is my take on a non recursive version