أصغر Palindrome بعد الاستبدال

إعطاء سلسلة تحتوي على بعض الأحرف الأبجدية الصغيرة وحرف خاص واحد (.). نحتاج إلى استبدال جميع النقاط ببعض الأحرف الأبجدية بطريقة تجعل السلسلة الناتجة متناظرة في حالة وجود العديد من البدائل المحتملة، نحتاج إلى اختيار سلسلة متناظرة أصغر من الناحية المعجمية. إذا لم يكن من الممكن تحويل السلسلة إلى متناظرة بعد كل الاستبدالات الممكنة، فعندئذٍ يكون الإخراج غير ممكن. 

أمثلة:  

Input : str = ab..e.c.a Output : abcaeacba The smallest palindrome which can be made after replacement is 'abcaeacba' We replaced first dot with 'c' second dot with 'a' third dot with 'a' and fourth dot with 'b' Input : str = ab..e.c.b Output : Not Possible It is not possible to convert above string into palindrome 

يمكننا حل هذه المشكلة على النحو التالي بما أن السلسلة الناتجة يجب أن تكون متناظرة، يمكننا التحقق من زوج من الأحرف غير النقطية في البداية نفسها إذا لم تتطابق، فإن العودة المباشرة غير ممكنة لأنه يمكننا وضع حرف جديد في موضع النقاط فقط وليس في أي مكان آخر. 

بعد ذلك، نقوم بالتكرار على أحرف السلسلة إذا كان الحرف الحالي نقطة، ثم نتحقق من الحرف المقترن به (الحرف في الموضع (n - i -1)) إذا كان هذا الحرف أيضًا نقطة، فيمكننا استبدال كلا الحرفين بـ "a" لأن "a" هي أصغر أبجدية صغيرة مما يضمن أصغر سلسلة معجمية في النهاية سيؤدي استبدال كليهما بأي حرف آخر إلى سلسلة متناظرة أكبر من الناحية المعجمية. في حالة أخرى، إذا لم يكن الحرف المقترن نقطة، فيجب علينا استبدال الحرف الحالي بحرفه المقترن لإنشاء سلسلة متناظرة. 

So in short If both 'i' and 'n- i- 1' are dot replace them by ‘a’ If one of them is a dot character replace that by other non-dot character 

الإجراء أعلاه يعطينا أصغر سلسلة متناظرة من الناحية المعجمية. 

تطبيق:

C++
   // C++ program to get lexicographically smallest   // palindrome string   #include          using     namespace     std  ;   // Utility method to check str is possible palindrome   // after ignoring .   bool     isPossiblePalindrome  (  string     str  )   {      int     n     =     str  .  length  ();      for     (  int     i  =  0  ;     i   <  n  /  2  ;     i  ++  )      {      /* If both left and right character are not    dot and they are not equal also then it    is not possible to make this string a    palindrome */      if     (  str  [  i  ]     !=     '.'     &&      str  [  n  -  i  -1  ]     !=     '.'     &&      str  [  i  ]     !=     str  [  n  -  i  -1  ])      return     false  ;      }      return     true  ;   }   // Returns lexicographically smallest palindrom   // string if possible   string     smallestPalindrome  (  string     str  )   {      if     (  !  isPossiblePalindrome  (  str  ))      return     'Not Possible'  ;      int     n     =     str  .  length  ();      // loop through character of string      for     (  int     i     =     0  ;     i      <     n  ;     i  ++  )      {      if     (  str  [  i  ]     ==     '.'  )      {      // if one of character is dot replace dot      // with other character      if     (  str  [  n     -     i     -     1  ]     !=     '.'  )      str  [  i  ]     =     str  [  n     -     i     -     1  ];      // if both character are dot then replace      // them with smallest character 'a'      else      str  [  i  ]     =     str  [  n     -     i     -     1  ]     =     'a'  ;      }      }      // return the result      return     str  ;   }   // Driver code to test above methods   int     main  ()   {      string     str     =     'ab..e.c.a'  ;      cout      < <     smallestPalindrome  (  str  )      < <     endl  ;      return     0  ;   }   
Java
   // Java program to get lexicographically    // smallest palindrome string   class   GFG      {   // Utility method to check str is   // possible palindrome after ignoring   static     boolean     isPossiblePalindrome  (  char     str  []  )   {   int     n     =     str  .  length  ;   for     (  int     i     =     0  ;     i      <     n     /     2  ;     i  ++  )   {      /* If both left and right character     are not dot and they are not     equal also then it is not     possible to make this string a    palindrome */      if     (  str  [  i  ]     !=     '.'     &&      str  [  n     -     i     -     1  ]     !=     '.'     &&      str  [  i  ]     !=     str  [  n     -     i     -     1  ]  )      return     false  ;   }   return     true  ;   }   // Returns lexicographically smallest    // palindrome string if possible   static     void     smallestPalindrome  (  char     str  []  )   {   if     (  !  isPossiblePalindrome  (  str  ))      System  .  out  .  println  (  'Not Possible'  );   int     n     =     str  .  length  ;   // loop through character of string   for     (  int     i     =     0  ;     i      <     n  ;     i  ++  )   {      if     (  str  [  i  ]     ==     '.'  )      {      // if one of character is dot       // replace dot with other character      if     (  str  [  n     -     i     -     1  ]     !=     '.'  )      str  [  i  ]     =     str  [  n     -     i     -     1  ]  ;      // if both character are dot       // then replace them with       // smallest character 'a'      else      str  [  i  ]     =     str  [  n     -     i     -     1  ]     =     'a'  ;      }   }   // return the result   for  (  int     i     =     0  ;     i      <     n  ;     i  ++  )      System  .  out  .  print  (  str  [  i  ]     +     ''  );   }   // Driver code   public     static     void     main  (  String  []     args  )   {      String     str     =     'ab..e.c.a'  ;      char  []     s     =     str  .  toCharArray  ();      smallestPalindrome  (  s  );   }   }   // This code is contributed    // by ChitraNayal   
Python 3
   # Python 3 program to get lexicographically    # smallest palindrome string   # Utility method to check str is    # possible palindrome after ignoring    def   isPossiblePalindrome  (  str  ):   n   =   len  (  str  )   for   i   in   range  (  n   //   2  ):   # If both left and right character    # are not dot and they are not    # equal also then it is not possible    # to make this string a palindrome    if   (  str  [  i  ]   !=   '.'   and   str  [  n   -   i   -   1  ]   !=   '.'   and   str  [  i  ]   !=   str  [  n   -   i   -   1  ]):   return   False   return   True   # Returns lexicographically smallest   # palindrome string if possible   def   smallestPalindrome  (  str  ):   if   (  not   isPossiblePalindrome  (  str  )):   return   'Not Possible'   n   =   len  (  str  )   str   =   list  (  str  )   # loop through character of string   for   i   in   range  (  n  ):   if   (  str  [  i  ]   ==   '.'  ):   # if one of character is dot    # replace dot with other character   if   (  str  [  n   -   i   -   1  ]   !=   '.'  ):   str  [  i  ]   =   str  [  n   -   i   -   1  ]   # if both character are dot    # then replace them with    # smallest character 'a'   else  :   str  [  i  ]   =   str  [  n   -   i   -   1  ]   =   'a'   # return the result   return   str   # Driver code   if   __name__   ==   '__main__'  :   str   =   'ab..e.c.a'   print  (  ''  .  join  (  smallestPalindrome  (  str  )))   # This code is contributed by ChitraNayal   
C#
   // C# program to get lexicographically    // smallest palindrome string   using     System  ;   public     class     GFG         {      // Utility method to check str is      // possible palindrome after ignoring      static     bool     isPossiblePalindrome  (  char     []  str  )      {      int     n     =     str  .  Length  ;      for     (  int     i     =     0  ;     i      <     n     /     2  ;     i  ++  )      {      /* If both left and right character     are not dot and they are not     equal also then it is not     possible to make this string a    palindrome */      if     (  str  [  i  ]     !=     '.'     &&      str  [  n     -     i     -     1  ]     !=     '.'     &&      str  [  i  ]     !=     str  [  n     -     i     -     1  ])      return     false  ;      }      return     true  ;      }      // Returns lexicographically smallest       // palindrome string if possible      static     void     smallestPalindrome  (  char     []  str  )      {      if     (  !  isPossiblePalindrome  (  str  ))      Console  .  WriteLine  (  'Not Possible'  );      int     n     =     str  .  Length  ;      // loop through character of string      for     (  int     i     =     0  ;     i      <     n  ;     i  ++  )      {      if     (  str  [  i  ]     ==     '.'  )      {      // if one of character is dot       // replace dot with other character      if     (  str  [  n     -     i     -     1  ]     !=     '.'  )      str  [  i  ]     =     str  [  n     -     i     -     1  ];      // if both character are dot       // then replace them with       // smallest character 'a'      else      str  [  i  ]     =     str  [  n     -     i     -     1  ]     =     'a'  ;      }      }      // return the result      for  (  int     i     =     0  ;     i      <     n  ;     i  ++  )      Console  .  Write  (  str  [  i  ]     +     ''  );      }      // Driver code      public     static     void     Main  ()      {      String     str     =     'ab..e.c.a'  ;      char  []     s     =     str  .  ToCharArray  ();      smallestPalindrome  (  s  );      }   }   // This code is contributed by PrinciRaj1992   
PHP
      // PHP program to get lexicographically   // smallest palindrome string   // Utility method to check str is   // possible palindrome after ignoring   function   isPossiblePalindrome  (  $str  )   {   $n   =   strlen  (  $str  );   for   (  $i   =   0  ;   $i    <   $n   /   2  ;   $i  ++  )   {   /* If both left and right     character are not dot and     they are not equal also then     it is not possible to make this     string a palindrome */   if   (  $str  [  $i  ]   !=   '.'   &&   $str  [  $n   -   $i   -   1  ]   !=   '.'   &&   $str  [  $i  ]   !=   $str  [  $n   -   $i   -   1  ])   return   false  ;   }   return   true  ;   }   // Returns lexicographically smallest    // palindrome string if possible   function   smallestPalindrome  (  $str  )   {   if   (  !  isPossiblePalindrome  (  $str  ))   return   'Not Possible'  ;   $n   =   strlen  (  $str  );   // loop through character of string   for   (  $i  =   0  ;   $i    <   $n  ;   $i  ++  )   {   if   (  $str  [  $i  ]   ==   '.'  )   {   // if one of character is dot    // replace dot with other character   if   (  $str  [  $n   -   $i   -   1  ]   !=   '.'  )   $str  [  $i  ]   =   $str  [  $n   -   $i   -   1  ];   // if both character are dot    // then replace them with    // smallest character 'a'   else   $str  [  $i  ]   =   $str  [  $n   -   $i   -   1  ]   =   'a'  ;   }   }   // return the result   return   $str  ;   }   // Driver code   $str   =   'ab..e.c.a'  ;   echo   smallestPalindrome  (  $str  );   // This code is contributed    // by ChitraNayal   ?>   
JavaScript
    <  script  >   // Javascript program to get lexicographically    // smallest palindrome string          // Utility method to check str is      // possible palindrome after ignoring      function     isPossiblePalindrome  (  str  )      {      let     n     =     str  .  length  ;      for     (  let     i     =     0  ;     i      <     Math  .  floor  (  n     /     2  );     i  ++  )      {      /* If both left and right character     are not dot and they are not     equal also then it is not     possible to make this string a    palindrome */      if     (  str  [  i  ]     !=     '.'     &&      str  [  n     -     i     -     1  ]     !=     '.'     &&      str  [  i  ]     !=     str  [  n     -     i     -     1  ])      return     false  ;      }          return     true  ;      }          // Returns lexicographically smallest       // palindrome string if possible      function     smallestPalindrome  (  str  )      {      if     (  !  isPossiblePalindrome  (  str  ))      document  .  write  (  'Not Possible'  );          let     n     =     str  .  length  ;          // loop through character of string      for     (  let     i     =     0  ;     i      <     n  ;     i  ++  )      {      if     (  str  [  i  ]     ==     '.'  )      {      // if one of character is dot       // replace dot with other character      if     (  str  [  n     -     i     -     1  ]     !=     '.'  )      str  [  i  ]     =     str  [  n     -     i     -     1  ];          // if both character are dot       // then replace them with       // smallest character 'a'      else      str  [  i  ]     =     str  [  n     -     i     -     1  ]     =     'a'  ;      }      }          // return the result      for  (  let     i     =     0  ;     i      <     n  ;     i  ++  )      document  .  write  (  str  [  i  ]     +     ''  );          }          // Driver code      let     str  =  'ab..e.c.a'  ;      let     s     =     str  .  split  (  ''  );      smallestPalindrome  (  s  );          // This code is contributed by rag2127        <  /script>   

الإخراج
abcaeacba 

تعقيد الوقت: O(n) حيث n هو طول السلسلة.
تعقيد الفضاء المساعد: O(1)