Ņemot vērā virkni, uzziniet, vai virkne ir k-palindroms vai nē. K-palindroma virkne pārveidojas par palindromu, noņemot no tās ne vairāk kā K rakstzīmēm.
Piemēri:
Linux komandas
Input : String - abcdecba k = 1 Output : Yes String can become palindrome by removing 1 character i.e. either d or e Input : String - abcdeca K = 2 Output : Yes Can become palindrome by removing 2 characters b and e (or b and d). Input : String - acdcb K = 1 Output : No String can not become palindrome by removing only one character.
Mēs esam apsprieduši DP risinājumu iepriekšējs Post to, kur mēs redzējām, ka problēma būtībā ir variācija Rediģēt attālumu problēma. Šajā amatā tiek apspriests vēl viens interesants DP risinājums.
Ideja ir atrast dotās virknes garāko palindromisko secību. Ja atšķirība starp garāko palindromisko secību un oriģinālo virkni ir mazāka par vienādu ar K, tad virkne ir k-palindrome, tā nav k-palindrome.
Piemēram abcdeca ir akmens (vai aceca). Rakstzīmes, kas neveicina virknes garāko palindromisko secību, ir jānoņem, lai stīgu palindroms. Tātad, noņemot B un D (vai E) no abcdeca virknes, pārveidosies par palindromu.
Virknes garāko palindromisko secību var viegli atrast, izmantojot LCS Apvidū Tālāk ir divu posmu risinājums, lai atrastu garāko palindromisko secību, kas izmanto LCS.
- Apgrieziet doto secību un uzglabājiet atpakaļgaitā citā masīvā, sakot Rev [0..N-1]
- Dotās secības un rev [] LCS būs garākā palindromiskā secība.
Zemāk ir iepriekšminētās idejas ieviešana -
// C++ program to find if given string is K-Palindrome // or not #include
// Java program to find if given // String is K-Palindrome or not import java.util.*; import java.io.*; class GFG { /* Returns length of LCS for X[0..m-1] Y[0..n-1] */ static int lcs(String X String Y int m int n) { int L[][] = new int[m + 1][n + 1]; /* Following steps build L[m+1][n+1] in bottom up fashion. Note that L[i][j] contains length of LCS of X[0..i-1] and Y[0..j-1] */ for (int i = 0; i <= m; i++) { for (int j = 0; j <= n; j++) { if (i == 0 || j == 0) { L[i][j] = 0; } else if (X.charAt(i - 1) == Y.charAt(j - 1)) { L[i][j] = L[i - 1][j - 1] + 1; } else { L[i][j] = Math.max(L[i - 1][j] L[i][j - 1]); } } } // L[m][n] contains length // of LCS for X and Y return L[m][n]; } // find if given String is // K-Palindrome or not static boolean isKPal(String str int k) { int n = str.length(); // Find reverse of String StringBuilder revStr = new StringBuilder(str); revStr = revStr.reverse(); // find longest palindromic // subsequence of given String int lps = lcs(str revStr.toString() n n); // If the difference between longest // palindromic subsequence and the // original String is less than equal // to k then the String is k-palindrome return (n - lps <= k); } // Driver code public static void main(String[] args) { String str = 'abcdeca'; int k = 2; if (isKPal(str k)) { System.out.println('Yes'); } else System.out.println('No'); } } // This code is contributed by Rajput-JI
# Python program to find # if given string is K-Palindrome # or not # Returns length of LCS # for X[0..m-1] Y[0..n-1] def lcs(X Y m n ): L = [[0]*(n+1) for _ in range(m+1)] # Following steps build # L[m+1][n+1] in bottom up # fashion. Note that L[i][j] # contains length of # LCS of X[0..i-1] and Y[0..j-1] for i in range(m+1): for j in range(n+1): if not i or not j: L[i][j] = 0 elif X[i - 1] == Y[j - 1]: L[i][j] = L[i - 1][j - 1] + 1 else: L[i][j] = max(L[i - 1][j] L[i][j - 1]) # L[m][n] contains length # of LCS for X and Y return L[m][n] # find if given string is # K-Palindrome or not def isKPal(string k): n = len(string) # Find reverse of string revStr = string[::-1] # find longest palindromic # subsequence of # given string lps = lcs(string revStr n n) # If the difference between # longest palindromic # subsequence and the original # string is less # than equal to k then # the string is k-palindrome return (n - lps <= k) # Driver program string = 'abcdeca' k = 2 print('Yes' if isKPal(string k) else 'No') # This code is contributed # by Ansu Kumari.
// C# program to find if given // String is K-Palindrome or not using System; class GFG { /* Returns length of LCS for X[0..m-1] Y[0..n-1] */ static int lcs(String X String Y int m int n) { int []L = new int[m + 1n + 1]; /* Following steps build L[m+1n+1] in bottom up fashion. Note that L[ij] contains length of LCS of X[0..i-1] and Y[0..j-1] */ for (int i = 0; i <= m; i++) { for (int j = 0; j <= n; j++) { if (i == 0 || j == 0) { L[i j] = 0; } else if (X[i - 1] == Y[j - 1]) { L[i j] = L[i - 1 j - 1] + 1; } else { L[i j] = Math.Max(L[i - 1 j] L[i j - 1]); } } } // L[mn] contains length // of LCS for X and Y return L[m n]; } // find if given String is // K-Palindrome or not static bool isKPal(String str int k) { int n = str.Length; // Find reverse of String str = reverse(str); // find longest palindromic // subsequence of given String int lps = lcs(str str n n); // If the difference between longest // palindromic subsequence and the // original String is less than equal // to k then the String is k-palindrome return (n - lps <= k); } static String reverse(String input) { char[] temparray = input.ToCharArray(); int left right = 0; right = temparray.Length - 1; for (left = 0; left < right; left++ right--) { // Swap values of left and right char temp = temparray[left]; temparray[left] = temparray[right]; temparray[right] = temp; } return String.Join(''temparray); } // Driver code public static void Main(String[] args) { String str = 'abcdeca'; int k = 2; if (isKPal(str k)) { Console.WriteLine('Yes'); } else Console.WriteLine('No'); } } // This code is contributed by PrinciRaj1992
<script> // JavaScript program to find // if given string is K-Palindrome // or not // Returns length of LCS // for X[0..m-1] Y[0..n-1] function lcs(X Y m n ){ let L = new Array(m+1); for(let i=0;i<m+1;i++){ L[i] = new Array(n+1).fill(0); } // Following steps build // L[m+1][n+1] in bottom up // fashion. Note that L[i][j] // contains length of // LCS of X[0..i-1] and Y[0..j-1] for(let i = 0; i < m + 1; i++) { for(let j = 0; j < n + 1; j++) { if(!i || !j) L[i][j] = 0 else if(X[i - 1] == Y[j - 1]) L[i][j] = L[i - 1][j - 1] + 1 else L[i][j] = Math.max(L[i - 1][j] L[i][j - 1]) } } // L[m][n] contains length // of LCS for X and Y return L[m][n] } // find if given string is // K-Palindrome or not function isKPal(string k){ let n = string.length // Find reverse of string let revStr = string.split('').reverse().join('') // find longest palindromic // subsequence of // given string let lps = lcs(string revStr n n) // If the difference between // longest palindromic // subsequence and the original // string is less // than equal to k then // the string is k-palindrome return (n - lps <= k) } // Driver program let string = 'abcdeca' let k = 2 document.write(isKPal(string k)?'Yes' : 'No') // This code is contributed by shinjanpatra </script>
Izvade
Yes
Laika sarežģītība no iepriekš minētā šķīduma ir O (nRādītājs).
Papildu telpa programmas izmanto O (nRādītājs). To var vēl vairāk samazināt līdz O (n), izmantojot Telpa optimizēts LCS risinājums Apvidū
Paldies Grava jūs sašaurinājāt Ieteikumam par iepriekš minēto risinājumu.