Najmenší palindróm po výmene
Daný reťazec, ktorý obsahuje malé písmená abecedy a jeden špeciálny znak bodka(.). Potrebujeme nahradiť všetky bodky nejakým abecedným znakom tak, aby sa výsledný reťazec stal palindrómom, v prípade mnohých možných zámen je potrebné zvoliť reťazec palindrómu, ktorý je lexikograficky najmenší. Ak nie je možné konvertovať reťazec na palindróm po všetkých možných náhradách, potom výstup Nie je možné.
Príklady:
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
Tento problém môžeme vyriešiť nasledovne Keďže výsledný reťazec musí byť palindróm, môžeme pri samotnom štarte skontrolovať pár bezbodových znakov, ak sa nezhodujú, potom priamy návrat nie je možný, pretože nový znak môžeme umiestniť len na miesto bodiek, nie nikde inde.
Potom iterujeme znaky reťazca, ak je aktuálny znak bodka, potom skontrolujeme jeho spárovaný znak (znak na (n – i -1)-tej pozícii), ak je tento znak tiež bodkou, potom môžeme oba znaky nahradiť písmenom „a“, pretože „a“ je najmenšia malá abeceda, ktorá zaručí najmenší lexikografický reťazec na konci nahradenie oboch akýmkoľvek iným znakom bude mať za následok lexikograficky väčší palindro. V opačnom prípade, ak párový znak nie je bodka, na vytvorenie reťazcového palindrómu musíme nahradiť aktuálny znak jeho párovým znakom.
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
Vyššie uvedený postup nám dáva lexikograficky najmenší palindrómový reťazec.
Implementácia:
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>
Výstup
abcaeacba
Časová zložitosť: O(n) kde n je dĺžka reťazca.
Zložitosť pomocného priestoru: O(1)
