بالنظر إلى سلسلة، ابحث عن أطول متناظر يمكن إنشاؤه عن طريق إزالة الأحرف أو تبديلها من السلسلة. قم بإرجاع متناظر واحد فقط إذا كان هناك عدة سلاسل متناظرة ذات أطول طول.
أمثلة:
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
يمكننا تقسيم أي سلسلة متناوبة إلى ثلاثة أجزاء - التسول في المنتصف والنهاية. بالنسبة للسلسلة المتناوبة ذات الطول الفردي، قل 2n + 1 'beg' يتكون من أول n من الأحرف من السلسلة. 'mid' سيتألف من حرف واحد فقط، أي (n + 1) الحرف الـ و'end' سيتكون من آخر n من الأحرف من السلسلة المتناوبة. بالنسبة للسلسلة المتناوبة ذات الطول الزوجي، سيكون 2n 'منتصف' فارغًا دائمًا. تجدر الإشارة إلى أن كلمة "end" ستكون عكس كلمة "beg" حتى تكون السلسلة متناظرة.
الفكرة هي استخدام الملاحظة أعلاه في حلنا. نظرًا لأن ترتيب الأحرف مسموح به، فلا يهم ترتيب الأحرف في سلسلة الإدخال. نحصل أولاً على تردد كل حرف في سلسلة الإدخال. بعد ذلك، ستكون جميع الأحرف ذات التكرار الزوجي (على سبيل المثال 2n) في سلسلة الإدخال جزءًا من سلسلة الإخراج حيث يمكننا بسهولة وضع أحرف n في سلسلة "beg" والأحرف n الأخرى في سلسلة "end" (من خلال الحفاظ على الترتيب المتناوب). بالنسبة للأحرف ذات الأحداث الفردية (على سبيل المثال 2n + 1) فإننا نملأ "منتصف" بأحد هذه الأحرف. ويتم تقسيم الأحرف 2n المتبقية إلى نصفين وإضافتها في البداية والنهاية.
وفيما يلي تنفيذ الفكرة المذكورة أعلاه
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>
الإخراج
abcdcba
تعقيد الوقت الحل أعلاه هو O(n) حيث n هو طول السلسلة. نظرًا لأن عدد الأحرف في الأبجدية ثابت، فإنها لا تساهم في التحليل المقارب.
مساحة مساعدة يستخدمه البرنامج هو M حيث M هو عدد أحرف ASCII.