Question

Consider the set of strings A = {c,cc,ccc}.
What is the shortest string the set of strings A⁵.

Answer 1

Here, we have A = {c,cc,ccc}
We want to find the shortest string in the set of A^5.

• There are many ways to do it. Let's understand it using a program.
• I have used C++ for the program.
• You can use any other language too according to your requirement as the basic logic will be the same.

Algorithm/Steps to follow:

1. First of all, find the string with minimum length from A.
2. For finding the string with minimum length, we take a variable(minimumLength), initialize with the minimumLength with INT_MAX and then compare.
3. If A[i] is less than the minimumLength then we update the minimumLength.
4. Now by traversing the entire array, we will find the string having minimum length.
5. After this concatenate the string power-times(Here, power = 5).
6. The final string after the concatenation will be the required string.

Please refer to the comments of the program for more clarity.

#include<bits/stdc++.h>
using namespace std;


int main()
{
    int len = 3;  // Length of the given string array
    string A[len] = {"c", "cc", "ccc"};  // The string array
    int power = 5;   // Given power
    int minimumLength = INT_MAX;  // Initialized the minimum length
    string minimumLengthString = A[0];  // Initialized the minimum length string

    // Finding the shortest string and its length for a A
    for(int i=0;i <len; i++)
    {
        if(A[i].length()<minimumLength)
        {
            minimumLength = A[i].length();
            minimumLengthString = A[i];
        }
    }

    // Finding the shortest length string for A^power
    string shortestStringWithTheGivenPower = "";
    for(int i=1; i<=power; i++)
    {
        shortestStringWithTheGivenPower = shortestStringWithTheGivenPower + minimumLengthString; // Concatenation of string
    }

    // Finally printing the values

    // Printing the shortest string for A^5
    cout << "The shortest string the set of strings A^5: " << shortestStringWithTheGivenPower << endl;

    // Printing the length of the above string
    cout << "Length of final string: " << minimumLength*power << endl;

    return 0;
}

Code-run/Output:

Please let me know in the comments in case of any confusion. Also, please upvote if you like.