Menor Palíndromo após substituição
Dada uma string que possui alguns caracteres alfabéticos minúsculos e um caractere especial ponto (.). Precisamos substituir todos os pontos por algum caractere do alfabeto de tal forma que a string resultante se torne um palíndromo. No caso de muitas substituições possíveis, precisamos escolher a string do palíndromo que seja lexicograficamente menor. Se não for possível converter string em palíndromo após todas as substituições possíveis, a saída Não é possível.
Exemplos:
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
Podemos resolver este problema da seguinte maneira: Como a string resultante precisa ser um palíndromo, podemos verificar o par de caracteres que não são pontos no início, se eles não corresponderem, o retorno direto não é possível porque podemos colocar o novo caractere na posição dos pontos, mas não em qualquer outro lugar.
Depois disso, iteramos sobre os caracteres da string se o caractere atual for um ponto, então verificamos seu caractere emparelhado (caractere na (n - i -1)-ésima posição). Se esse caractere também for um ponto, podemos substituir ambos os caracteres por 'a' porque 'a' é o menor alfabeto minúsculo, o que garantirá a menor string lexicográfica no final, substituindo ambos por qualquer outro caractere, resultará em uma string palindrômica lexicograficamente maior. Em outro caso, se o caractere emparelhado não for um ponto, para criar uma string palíndromo, devemos substituir o caractere atual pelo seu caractere emparelhado.
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
O procedimento acima nos fornece a menor string de palíndromo lexicograficamente.
Implementação:
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>
Saída
abcaeacba
Complexidade de tempo: O(n) onde n é o comprimento da string.
Complexidade do Espaço Auxiliar: O(1)
