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Minimumsomkostninger for at lave to strenge identiske

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Givet to strenge X og Y og to værdier costX og costY. Vi skal finde minimumsomkostninger, der kræves for at gøre de givne to strenge identiske. Vi kan slette tegn fra begge strenge. Omkostningerne ved at slette et tegn fra streng X er costX og fra Y er costY. Omkostningerne ved at fjerne alle tegn fra en streng er de samme. 

Eksempler:  



Input : X = 'abcd' Y = 'acdb' costX = 10 costY = 20. Output: 30 For Making both strings identical we have to delete character 'b' from both the string hence cost will be = 10 + 20 = 30. Input : X = 'ef' Y = 'gh' costX = 10 costY = 20. Output: 60 For making both strings identical we have to delete 2-2 characters from both the strings hence cost will be = 10 + 10 + 20 + 20 = 60.
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Dette problem er en variation af Længste almindelige efterfølger ( LCS ) . Ideen er enkel, vi finder først længden af ​​den længste fælles undersekvens af strenge X og Y. Nu fratræk len_LCS med længder af individuelle strenge giver os antallet af tegn, der skal fjernes for at gøre dem identiske.  

java metode
// Cost of making two strings identical is SUM of following two // 1) Cost of removing extra characters (other than LCS) // from X[] // 2) Cost of removing extra characters (other than LCS) // from Y[] Minimum Cost to make strings identical = costX * (m - len_LCS) + costY * (n - len_LCS). m ==> Length of string X m ==> Length of string Y len_LCS ==> Length of LCS Of X and Y. costX ==> Cost of removing a character from X[] costY ==> Cost of removing a character from Y[] Note that cost of removing all characters from a string is same. 

Nedenfor er implementeringen af ​​ovenstående idé. 

C++
/* C++ code to find minimum cost to make two strings  identical */ #include   using namespace std; /* Returns length of LCS for X[0..m-1] Y[0..n-1] */ int lcs(char *X char *Y int m int n) {  int L[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[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[0..n-1] and  Y[0..m-1] */  return L[m][n]; } // Returns cost of making X[] and Y[] identical. costX is // cost of removing a character from X[] and costY is cost // of removing a character from Y[]/ int findMinCost(char X[] char Y[] int costX int costY) {  // Find LCS of X[] and Y[]  int m = strlen(X) n = strlen(Y);  int len_LCS = lcs(X Y m n);  // Cost of making two strings identical is SUM of  // following two  // 1) Cost of removing extra characters  // from first string  // 2) Cost of removing extra characters from  // second string  return costX * (m - len_LCS) +  costY * (n - len_LCS); } /* Driver program to test above function */ int main() {  char X[] = 'ef';  char Y[] = 'gh';  cout << 'Minimum Cost to make two strings '  << ' identical is = ' << findMinCost(X Y 10 20);  return 0; } 
Java
// Java code to find minimum cost to // make two strings identical  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[0..n-1] and Y[0..m-1]   return L[m][n];  }    // Returns cost of making X[] and Y[] identical.   // costX is cost of removing a character from X[]   // and costY is cost of removing a character from Y[]/  static int findMinCost(String X String Y int costX int costY)  {  // Find LCS of X[] and Y[]  int m = X.length();  int n = Y.length();  int len_LCS;  len_LCS = lcs(X Y m n);    // Cost of making two strings identical  // is SUM of following two  // 1) Cost of removing extra characters  // from first string  // 2) Cost of removing extra characters  // from second string  return costX * (m - len_LCS) +  costY * (n - len_LCS);  }    // Driver code  public static void main (String[] args)   {  String X = 'ef';  String Y = 'gh';  System.out.println( 'Minimum Cost to make two strings '  + ' identical is = '   + findMinCost(X Y 10 20));    } } // This code is contributed by vt_m 
Python3
# Python code to find minimum cost  # to make two strings identical # Returns length of LCS for # X[0..m-1] Y[0..n-1]  def lcs(X Y m n): L = [[0 for i in range(n + 1)] for i 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 i == 0 or 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] = max(L[i - 1][j] L[i][j - 1]) # L[m][n] contains length of  # LCS for X[0..n-1] and Y[0..m-1] return L[m][n] # Returns cost of making X[]  # and Y[] identical. costX is  # cost of removing a character # from X[] and costY is cost  # of removing a character from Y[] def findMinCost(X Y costX costY): # Find LCS of X[] and Y[] m = len(X) n = len(Y) len_LCS =lcs(X Y m n) # Cost of making two strings  # identical is SUM of following two  # 1) Cost of removing extra  # characters from first string  # 2) Cost of removing extra  # characters from second string return (costX * (m - len_LCS) + costY * (n - len_LCS)) # Driver Code X = 'ef' Y = 'gh' print('Minimum Cost to make two strings ' end = '') print('identical is = ' findMinCost(X Y 10 20)) # This code is contributed # by sahilshelangia 
C#
// C# code to find minimum cost to // make two strings identical  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 + 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[ij] = 0;    else if (X[i - 1] == Y[j - 1])  L[ij] = L[i - 1j - 1] + 1;    else  L[ij] = Math.Max(L[i - 1j] L[ij - 1]);  }  }    // L[m][n] contains length of LCS   // for X[0..n-1] and Y[0..m-1]   return L[mn];  }    // Returns cost of making X[] and Y[] identical.  // costX is cost of removing a character from X[]   // and costY is cost of removing a character from Y[]  static int findMinCost(String X String Y   int costX int costY)  {  // Find LCS of X[] and Y[]  int m = X.Length;  int n = Y.Length;  int len_LCS;  len_LCS = lcs(X Y m n);    // Cost of making two strings identical  // is SUM of following two  // 1) Cost of removing extra characters  // from first string  // 2) Cost of removing extra characters  // from second string  return costX * (m - len_LCS) +  costY * (n - len_LCS);  }    // Driver code  public static void Main ()   {  String X = 'ef';  String Y = 'gh';  Console.Write( 'Minimum Cost to make two strings ' +  ' identical is = ' +  findMinCost(X Y 10 20));  } } // This code is contributed by nitin mittal. 
PHP
 /* PHP code to find minimum cost to make two strings  identical */ /* Returns length of LCS for X[0..m-1] Y[0..n-1] */ function lcs($X $Y $m $n) { $L = array_fill(0($m+1)array_fill(0($n+1)NULL)); /* Following steps build L[m+1][n+1] in bottom  up fashion. Note that L[i][j] contains length  of LCS of X[0..i-1] and Y[0..j-1] */ for ($i=0; $i<=$m; $i++) { for ($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][$j] = max($L[$i-1][$j] $L[$i][$j-1]); } } /* L[m][n] contains length of LCS for X[0..n-1] and  Y[0..m-1] */ return $L[$m][$n]; } // Returns cost of making X[] and Y[] identical. costX is // cost of removing a character from X[] and costY is cost // of removing a character from Y[]/ function findMinCost(&$X &$Y$costX $costY) { // Find LCS of X[] and Y[] $m = strlen($X); $n = strlen($Y); $len_LCS = lcs($X $Y $m $n); // Cost of making two strings identical is SUM of // following two // 1) Cost of removing extra characters // from first string // 2) Cost of removing extra characters from // second string return $costX * ($m - $len_LCS) + $costY * ($n - $len_LCS); } /* Driver program to test above function */ $X = 'ef'; $Y = 'gh'; echo 'Minimum Cost to make two strings '. ' identical is = ' . findMinCost($X $Y 10 20); return 0; ?> 
JavaScript
<script> // Javascript code to find minimum cost to // make two strings identical     // 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);  }    for(let i = 0; i < m + 1; i++)  {  for(let j = 0; j < n + 1; j++)  {  L[i][j] = 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; i++)  {  for (let 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[m][n] contains length of LCS   // for X[0..n-1] and Y[0..m-1]   return L[m][n];  }    // Returns cost of making X[] and Y[] identical.   // costX is cost of removing a character from X[]   // and costY is cost of removing a character from Y[]/    function findMinCost(XYcostXcostY)  {  // Find LCS of X[] and Y[]  let m = X.length;  let n = Y.length;  let len_LCS;  len_LCS = lcs(X Y m n);    // Cost of making two strings identical  // is SUM of following two  // 1) Cost of removing extra characters  // from first string  // 2) Cost of removing extra characters  // from second string  return costX * (m - len_LCS) +  costY * (n - len_LCS);    }    // Driver code  let X = 'ef';  let Y = 'gh';  document.write( 'Minimum Cost to make two strings '  + ' identical is = '   + findMinCost(X Y 10 20));    // This code is contributed by avanitrachhadiya2155 </script> 

Produktion
Minimum Cost to make two strings identical is = 60

Tidskompleksitet: O(m*n)
Hjælpeplads: O(m*n)
 



Denne artikel er gennemgået af team geeksforgeeks.