The task requires processing an input string to remove all vowel characters (A, O, Y, E, U, I in both upper and lower case) and then format the remaining consonant characters. The formatting involves prefixing each consonant with a period ('.') and converting the character to its lowercase form. The algorithm must guarantee a non-empty output string.

The core algorithm is as follows:

1. Define a set containing all target vowel characters, accounting for case sensitivity.
2. Iterate through each character in the input string.
3. For each character, check if it exists in the vowel set.
4. If its a vowel, discard it.
5. If it is a consonant, append a '.' character followed by the lowercase version of the consonant character to the result string.
6. After processing all characters, the constructed result string is the final output.

The following C++ code implements this logic:

#include <iostream>
#include <string>
#include <cctype>
using namespace std;

int main() {
    string inputStr, outputStr;
    // Read the input string
    getline(cin, inputStr);
    // Define vowel characters (upper and lower case)
    string vowels = "AaOoYyEeUuIi";
    // Process each character in the input
    for (char ch : inputStr) {
        // Check if the character is a vowel
        if (vowels.find(ch) != string::npos) {
            // Skip vowels
            continue;
        } else {
            // For consonants, add a dot and the lowercase character
            outputStr.push_back('.');
            outputStr.push_back(tolower(ch));
        }
    }
    // Output the final processed string
    cout << outputStr << endl;
    return 0;
}

Key components of the code:

• getline(cin, inputStr): Reads a line of input, which can handle strings with spaces. cin >> inputStr would stop at whitespace.
• string vowels: A string serving as a set of characters to identify vowels.
• for (char ch : inputStr): A range-based for loop that iterates over each character ch in inputStr.
• vowels.find(ch) != string::npos: Checks if the character ch exists within the vowels string. string::npos is a constant representing 'not found'.
• outputStr.push_back('.'): Appends a period to the end of the result string.
• outputStr.push_back(tolower(ch)): Appends the lowercase version of the consonant character. The tolower function from <cctype> handles the case conversion.
• cout << outputStr << endl;: Prints the final formatted string.