Пронађите најдужи палиндром формиран уклањањем или мешањем знакова из низа
Дати низ пронађите најдужи палиндром који се може конструисати уклањањем или мешањем знакова из стринга. Врати само један палиндром ако постоји више низова палиндрома највеће дужине.
Примери:
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
Можемо поделити било који палиндромски низ на три дела - почетак средине и крај. За палиндромски низ непарне дужине, рецимо 2н + 1 'бег' се састоји од првих н знакова низа 'мид' ће се састојати од само 1 знака, тј. (н + 1)-ог знака, а 'енд' ће се састојати од последњих н знакова палиндромског низа. За палиндромски низ парне дужине 2н 'мид' ће увек бити празан. Треба напоменути да ће 'енд' бити обрнуто од 'бег' да би низ био палиндром.
Идеја је да користимо горњу опсервацију у нашем решењу. Пошто је мешање знакова дозвољено, редослед знакова није битан у улазном низу. Прво добијамо фреквенцију сваког знака у улазном низу. Тада ће сви карактери који се појављују парно (рецимо 2н) у улазном низу бити део излазног низа јер можемо лако да поставимо н карактера у 'без' стринг и осталих н знакова у 'крајњи' низ (сачувањем палиндромског реда). За знакове који се појављују непарно (рецимо 2н + 1) попуњавамо 'средину' једним од свих таквих знакова. а преосталих 2н карактера се деле на половине и додају на почетку и на крају.
Испод је имплементација горње идеје
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>
Излаз
abcdcba
Временска сложеност горњег решења је О(н) где је н дужина низа. Пошто је број знакова у абецеди константан, они не доприносе асимптотичкој анализи.
Помоћни простор који програм користи је М где је М број АСЦИИ карактера.
