Minimum cost to make two strings identical by deleting the digits

• Difficulty Level : Medium
• Last Updated : 28 May, 2021

Given two strings X and Y consisting of only digits ‘0’ to ‘9’. Find minimum cost required to make the given two strings identical. Only operation allowed is to delete characters from any of the string. The cost of operation of deleting the digit ‘d’ is d units.

Input:  X = 3759, Y = 9350
Output: 23
Explanation
For making both string identical, delete
characters 3, 7, 5 from first string and
delete characters 3, 5, 0 from second
string. Total cost of operation is
3 + 7 + 5 + 3 + 5 + 0 = 23

Input:  X = 3198, Y = 98
Output: 4

This problem is a variation of Longest Common Subsequence( LCS ) and this one. The idea is simple, instead of finding the length of longest common subsequence, find the maximum cost by adding identical characters from both the string.
Now to find the minimum cost, subtract the above result from total cost of both strings i.e.,

costX = Cost of removing all characters
from string 'X'
CostY = Cost of removing all characters
from string 'Y'
cost_Id = Cost of removing identical characters
from both strings

Minimum cost to make both string identical =
costX + costY - cost_Id

Below is the implementation of above approach:

C++

 /* C++ code to find minimum cost to make two strings   identical */#include using namespace std; /* Function to returns cost of removing the identical   characters in 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 cost       of removing identical characters in 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;             // If both characters are same, add both            // of them            else if (X[i - 1] == Y[j - 1])                L[i][j] = L[i - 1][j - 1] +                          2 * (X[i - 1] - '0');             // Otherwise find the maximum cost among them            else                L[i][j] = max(L[i - 1][j], L[i][j - 1]);        }    }     return L[m][n];} // Returns cost of making X[] and Y[] identicalint findMinCost(char X[], char Y[]){    // Find LCS of X[] and Y[]    int m = strlen(X), n = strlen(Y);     // Initialize the cost variable    int cost = 0;     // Find cost of all characters in    // both strings    for (int i = 0; i < m; ++i)        cost += X[i] - '0';     for (int i = 0; i < n; ++i)        cost += Y[i] - '0';     return cost - lcs(X, Y, m, n);} /* Driver program to test above function */int main(){    char X[] = "3759";    char Y[] = "9350";    cout << "Minimum Cost to make two strings "         << "identical is = " << findMinCost(X, Y);    return 0;}

Java

 // Java code to find minimum cost to// make two strings identicalimport java.util.*;import java.lang.*; public class GfG{     /* Function to returns cost of removing the identicalcharacters in LCS for X[0..m-1], Y[0..n-1] */static int lcs(char[] X, char[] 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    cost of removing identical characters in    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;             // If both characters are same,            // add both of them            else if (X[i - 1] == Y[j - 1])                L[i][j] = L[i - 1][j - 1] +                        2 * (X[i - 1] - '0');             // Otherwise find the maximum            // cost among them            else                L[i][j] = L[i - 1][j] > L[i][j - 1] ?                          L[i - 1][j] : L[i][j - 1];        }    }     return L[m][n];} // Returns cost of making X[] and Y[] identicalstatic int findMinCost(char X[], char Y[]){    // Find LCS of X[] and Y[]    int m = X.length, n = Y.length;     // Initialize the cost variable    int cost = 0;     // Find cost of all characters in    // both strings    for (int i = 0; i < m; ++i)        cost += X[i] - '0';     for (int i = 0; i < n; ++i)        cost += Y[i] - '0';     return cost - lcs(X, Y, m, n);} // driver function    public static void main(String argc[]){     char X[] = ("3759").toCharArray();    char Y[] = ("9350").toCharArray();         System.out.println("Minimum Cost to make two strings"+                 " identical is = " +findMinCost(X, Y));    }} // This code is contributed by Prerna Saini

Python3

 # Python3 code to find minimum cost to make two strings#   identical # Function to returns cost of removing the identical# characters in 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 cost    # of removing identical characters in 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               # If both characters are same, add both            # of them            elif (X[i - 1] == Y[j - 1]):                L[i][j] = L[i - 1][j - 1] + 2 * (ord(X[i - 1]) - 48)               # Otherwise find the maximum cost among them            else:                L[i][j] = max(L[i - 1][j], L[i][j - 1])    return L[m][n]   # Returns cost of making X[] and Y[] identicaldef findMinCost( X,  Y):    # Find LCS of X[] and Y[]    m = len(X)    n = len(Y)    # Initialize the cost variable    cost = 0       # Find cost of all acters in    # both strings    for i in range(m):        cost += ord(X[i]) - 48       for i in range(n):        cost += ord(Y[i]) - 48    ans=cost - lcs(X, Y, m, n)    return ans   # Driver program to test above functionX = "3759"Y = "9350"print("Minimum Cost to make two strings ",     "identical is = " ,findMinCost(X, Y)) #this code is contributed by sahilshelangia

C#

 // C# code to find minimum cost to// make two strings identicalusing System; public class GfG{         /* Function to returns cost of removing the identical    characters in 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        cost of removing identical characters in        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;                     // If both characters are same,                // add both of them                else if (X[i - 1] == Y[j - 1])                    L[i,j] = L[i - 1,j - 1] +                            2 * (X[i - 1] - '0');                     // Otherwise find the maximum                // cost among them                else                    L[i,j] = L[i - 1,j] > L[i,j - 1] ?                            L[i - 1,j] : L[i,j - 1];            }        }             return L[m,n];    }         // Returns cost of making X[] and Y[] identical    static int findMinCost( string X, string Y)    {        // Find LCS of X[] and Y[]        int m = X.Length, n = Y.Length;             // Initialize the cost variable        int cost = 0;             // Find cost of all characters in        // both strings        for (int i = 0; i < m; ++i)            cost += X[i] - '0';             for (int i = 0; i < n; ++i)            cost += Y[i] - '0';             return cost - lcs(X, Y, m, n);    }         // Driver function    public static void Main()    {        string X = "3759";        string Y= "9350";                 Console.WriteLine("Minimum Cost to make two strings"+                    " identical is = " +findMinCost(X, Y));    }} // This code is contributed by vt_m

PHP

 \$L[\$i][\$j - 1] ?                        \$L[\$i - 1][\$j] : \$L[\$i][\$j - 1];        }    }     return \$L[\$m][\$n];} // Returns cost of making X[] and Y[] identicalfunction findMinCost(\$X, \$Y){    // Find LCS of X[] and Y[]    \$m = sizeof(\$X); \$n = sizeof(\$Y);     // Initialize the cost variable    \$cost = 0;     // Find cost of all characters in    // both strings    for (\$i = 0; \$i < \$m; ++\$i)        \$cost += \$X[\$i] - '0';     for (\$i = 0; \$i < \$n; ++\$i)        \$cost += \$Y[\$i] - '0';     return \$cost - lcs(\$X, \$Y, \$m, \$n);} // Driver code     \$X = str_split("3759");    \$Y = str_split("9350");         echo("Minimum Cost to make two strings".                " identical is = " .findMinCost(\$X, \$Y));     // This code is contributed by Code_Mech.

Javascript



Output:

Minimum Cost to make two strings  identical is = 23

Time complexity: O(m*n)
Auxiliary space: O(m*n)

My Personal Notes arrow_drop_up