מצא את הפלינדרום הארוך ביותר שנוצר על ידי הסרה או ערבוב של תווים מהמחרוזת

בהינתן מחרוזת מצא את הפלינדרום הארוך ביותר שניתן לבנות על ידי הסרה או ערבוב של תווים מהמחרוזת. החזר רק פלינדרום אחד אם יש מיתרי פלינדרום מרובים באורך הארוך ביותר.

דוגמאות: 

  Input:    abc   Output:   a OR b OR c   Input:    aabbcc   Output:   abccba OR baccab OR cbaabc OR any other palindromic string of length 6.   Input:    abbaccd   Output:   abcdcba OR ...   Input:    aba   Output:   aba 

אנחנו יכולים לחלק כל מיתר פלינדרום לשלושה חלקים - התחל באמצע וסוף. עבור מחרוזת פלינדרום באורך אי זוגי נניח ש-2n + 1 'beg' מורכב מ-n תווים ראשונים של המחרוזת 'mid' תהיה מורכבת מתו אחד בלבד, כלומר (n + 1) תו ו-'end' מורכב מ-n התווים האחרונים של המחרוזת הפלינדרומית. עבור מחרוזת פלינדרום באורך זוגי 2n 'אמצע' תמיד יהיה ריק. יש לציין ש'סוף' יהיה הפוך מ'תחנן' על מנת שהמיתר יהיה פלינדרום.

הרעיון הוא להשתמש בתצפית לעיל בפתרון שלנו. מכיוון שמותר ערבוב של תווים, סדר התווים אינו משנה במחרוזת הקלט. אנו מקבלים תחילה תדירות של כל תו במחרוזת הקלט. אז כל התווים שיופיעו אפילו (נניח 2n) במחרוזת הקלט יהיו חלק ממחרוזת הפלט, מכיוון שנוכל למקם בקלות n תווים במחרוזת 'beg' ואת n התווים האחרים במחרוזת 'סוף' (על ידי שימור הסדר הפלינדרום). עבור תווים בעלי מופע מוזר (נניח 2n + 1) אנו ממלאים 'אמצע' באחד מכל התווים הללו. ו-2n התווים הנותרים מחולקים לחצאים ומתווספים בהתחלה ובסוף.

להלן יישום הרעיון לעיל 

C++
   // C++ program to find the longest palindrome by removing   // or shuffling characters from the given string   #include          using     namespace     std  ;   // Function to find the longest palindrome by removing   // or shuffling characters from the given string   string     findLongestPalindrome  (  string     str  )   {      // to stores freq of characters in a string      int     count  [  256  ]     =     {     0     };      // find freq of characters in the input string      for     (  int     i     =     0  ;     i      <     str  .  size  ();     i  ++  )      count  [  str  [  i  ]]  ++  ;      // Any palindromic string consists of three parts      // beg + mid + end      string     beg     =     ''       mid     =     ''       end     =     ''  ;      // solution assumes only lowercase characters are      // present in string. We can easily extend this      // to consider any set of characters      for     (  char     ch     =     'a'  ;     ch      <=     'z'  ;     ch  ++  )      {      // if the current character freq is odd      if     (  count  [  ch  ]     &     1  )      {      // mid will contain only 1 character. It      // will be overridden with next character      // with odd freq      mid     =     ch  ;      // decrement the character freq to make      // it even and consider current character      // again      count  [  ch  --  ]  --  ;      }      // if the current character freq is even      else      {      // If count is n(an even number) push      // n/2 characters to beg string and rest      // n/2 characters will form part of end      // string      for     (  int     i     =     0  ;     i      <     count  [  ch  ]  /  2     ;     i  ++  )      beg  .  push_back  (  ch  );      }      }      // end will be reverse of beg      end     =     beg  ;      reverse  (  end  .  begin  ()     end  .  end  ());      // return palindrome string      return     beg     +     mid     +     end  ;   }   // Driver code   int     main  ()   {      string     str     =     'abbaccd'  ;      cout      < <     findLongestPalindrome  (  str  );      return     0  ;   }   
Java
   // Java program to find the longest palindrome by removing   // or shuffling characters from the given string   class   GFG     {   // Function to find the longest palindrome by removing   // or shuffling characters from the given string      static     String     findLongestPalindrome  (  String     str  )     {      // to stores freq of characters in a string      int     count  []     =     new     int  [  256  ]  ;      // find freq of characters in the input string      for     (  int     i     =     0  ;     i      <     str  .  length  ();     i  ++  )     {      count  [  str  .  charAt  (  i  )  ]++  ;      }      // Any palindromic string consists of three parts      // beg + mid + end      String     beg     =     ''       mid     =     ''       end     =     ''  ;      // solution assumes only lowercase characters are      // present in string. We can easily extend this      // to consider any set of characters      for     (  char     ch     =     'a'  ;     ch      <=     'z'  ;     ch  ++  )     {      // if the current character freq is odd      if     (  count  [  ch  ]     %     2     ==     1  )     {      // mid will contain only 1 character. It      // will be overridden with next character      // with odd freq      mid     =     String  .  valueOf  (  ch  );      // decrement the character freq to make      // it even and consider current character      // again      count  [  ch  --]--  ;      }     // if the current character freq is even      else     {      // If count is n(an even number) push      // n/2 characters to beg string and rest      // n/2 characters will form part of end      // string      for     (  int     i     =     0  ;     i      <     count  [  ch  ]     /     2  ;     i  ++  )     {      beg     +=     ch  ;      }      }      }      // end will be reverse of beg      end     =     beg  ;      end     =     reverse  (  end  );      // return palindrome string      return     beg     +     mid     +     end  ;      }      static     String     reverse  (  String     str  )     {      // convert String to character array       // by using toCharArray       String     ans     =     ''  ;      char  []     try1     =     str  .  toCharArray  ();      for     (  int     i     =     try1  .  length     -     1  ;     i     >=     0  ;     i  --  )     {      ans     +=     try1  [  i  ]  ;      }      return     ans  ;      }      // Driver code      public     static     void     main  (  String  []     args  )     {      String     str     =     'abbaccd'  ;      System  .  out  .  println  (  findLongestPalindrome  (  str  ));      }   }   // This code is contributed by PrinciRaj1992   
Python3
   # Python3 program to find the longest palindrome by removing   # or shuffling characters from the given string   # Function to find the longest palindrome by removing   # or shuffling characters from the given string   def   findLongestPalindrome  (  strr  ):   # to stores freq of characters in a string   count   =   [  0  ]  *  256   # find freq of characters in the input string   for   i   in   range  (  len  (  strr  )):   count  [  ord  (  strr  [  i  ])]   +=   1   # Any palindromic consists of three parts   # beg + mid + end   beg   =   ''   mid   =   ''   end   =   ''   # solution assumes only lowercase characters are   # present in string. We can easily extend this   # to consider any set of characters   ch   =   ord  (  'a'  )   while   ch    <=   ord  (  'z'  ):   # if the current character freq is odd   if   (  count  [  ch  ]   &   1  ):   # mid will contain only 1 character. It   # will be overridden with next character   # with odd freq   mid   =   ch   # decrement the character freq to make   # it even and consider current character   # again   count  [  ch  ]   -=   1   ch   -=   1   # if the current character freq is even   else  :   # If count is n(an even number) push   # n/2 characters to beg and rest   # n/2 characters will form part of end   # string   for   i   in   range  (  count  [  ch  ]  //  2  ):   beg   +=   chr  (  ch  )   ch   +=   1   # end will be reverse of beg   end   =   beg   end   =   end  [::  -  1  ]   # return palindrome string   return   beg   +   chr  (  mid  )   +   end   # Driver code   strr   =   'abbaccd'   print  (  findLongestPalindrome  (  strr  ))   # This code is contributed by mohit kumar 29   
C#
   // C# program to find the longest    // palindrome by removing or   // shuffling characters from    // the given string   using     System  ;   class     GFG   {      // Function to find the longest       // palindrome by removing or       // shuffling characters from       // the given string      static     String     findLongestPalindrome  (  String     str  )         {      // to stores freq of characters in a string      int     []  count     =     new     int  [  256  ];      // find freq of characters       // in the input string      for     (  int     i     =     0  ;     i      <     str  .  Length  ;     i  ++  )         {      count  [  str  [  i  ]]  ++  ;      }      // Any palindromic string consists of       // three parts beg + mid + end      String     beg     =     ''       mid     =     ''       end     =     ''  ;      // solution assumes only lowercase       // characters are present in string.      // We can easily extend this to       // consider any set of characters      for     (  char     ch     =     'a'  ;     ch      <=     'z'  ;     ch  ++  )             {      // if the current character freq is odd      if     (  count  [  ch  ]     %     2     ==     1  )         {          // mid will contain only 1 character.       // It will be overridden with next       // character with odd freq      mid     =     String  .  Join  (  ''    ch  );      // decrement the character freq to make      // it even and consider current       // character again      count  [  ch  --  ]  --  ;      }             // if the current character freq is even      else         {          // If count is n(an even number) push      // n/2 characters to beg string and rest      // n/2 characters will form part of end      // string      for     (  int     i     =     0  ;     i      <     count  [  ch  ]     /     2  ;     i  ++  )         {      beg     +=     ch  ;      }      }      }      // end will be reverse of beg      end     =     beg  ;      end     =     reverse  (  end  );      // return palindrome string      return     beg     +     mid     +     end  ;      }      static     String     reverse  (  String     str  )         {      // convert String to character array       // by using toCharArray       String     ans     =     ''  ;      char  []     try1     =     str  .  ToCharArray  ();      for     (  int     i     =     try1  .  Length     -     1  ;     i     >=     0  ;     i  --  )         {      ans     +=     try1  [  i  ];      }      return     ans  ;      }      // Driver code      public     static     void     Main  ()         {      String     str     =     'abbaccd'  ;      Console  .  WriteLine  (  findLongestPalindrome  (  str  ));      }   }   // This code is contributed by 29AjayKumar   
JavaScript
    <  script  >   // Javascript program to find the    // longest palindrome by removing   // or shuffling characters from    // the given string   // Function to find the longest    // palindrome by removing   // or shuffling characters from   // the given string      function     findLongestPalindrome  (  str  )      {      // to stores freq of characters       // in a string      let     count     =     new     Array  (  256  );      for  (  let     i  =  0  ;  i   <  256  ;  i  ++  )      {      count  [  i  ]  =  0  ;      }          // find freq of characters in       // the input string      for     (  let     i     =     0  ;     i      <     str  .  length  ;     i  ++  )     {      count  [  str  [  i  ].  charCodeAt  (  0  )]  ++  ;      }          // Any palindromic string consists      // of three parts      // beg + mid + end      let     beg     =     ''       mid     =     ''       end     =     ''  ;          // solution assumes only       // lowercase characters are      // present in string.       // We can easily extend this      // to consider any set of characters      for     (  let     ch     =     'a'  .  charCodeAt  (  0  );         ch      <=     'z'  .  charCodeAt  (  0  );     ch  ++  )     {      // if the current character freq is odd      if     (  count  [  ch  ]     %     2     ==     1  )     {      // mid will contain only 1 character. It      // will be overridden with next character      // with odd freq      mid     =     String  .  fromCharCode  (  ch  );          // decrement the character freq to make      // it even and consider current character      // again      count  [  ch  --  ]  --  ;      }     // if the current character freq is even      else     {      // If count is n(an even number) push      // n/2 characters to beg string and rest      // n/2 characters will form part of end      // string      for     (  let     i     =     0  ;     i      <     count  [  ch  ]     /     2  ;     i  ++  )         {      beg     +=     String  .  fromCharCode  (  ch  );      }      }      }          // end will be reverse of beg      end     =     beg  ;      end     =     reverse  (  end  );          // return palindrome string      return     beg     +     mid     +     end  ;      }          function     reverse  (  str  )      {      // convert String to character array       // by using toCharArray       let     ans     =     ''  ;      let     try1     =     str  .  split  (  ''  );          for     (  let     i     =     try1  .  length     -     1  ;     i     >=     0  ;     i  --  )     {      ans     +=     try1  [  i  ];      }      return     ans  ;      }          // Driver code      let     str     =     'abbaccd'  ;      document  .  write  (  findLongestPalindrome  (  str  ));          // This code is contributed by unknown2108        <  /script>   

תְפוּקָה
abcdcba 

מורכבות הזמן של הפתרון לעיל הוא O(n) כאשר n הוא אורך המיתר. מכיוון שמספר התווים באלפבית קבוע הם אינם תורמים לניתוח אסימפטוטי.
חלל עזר בשימוש התוכנית הוא M כאשר M הוא מספר תווי ASCII.