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One way to verify if a date is legitimate using C++ is to use built-in libraries or functions such as the "ctime" library or the "chrono" library. For example, the following code validates a date in the format of "mm/dd/yyyy" by converting it into a "time_t" format using "mktime," and then converting it back into the original format using "strftime" to check if they match:

#include <iostream>
#include <ctime>

using namespace std;

bool validateDate(const string& dateStr) {
    struct tm tm;
    if (strptime(dateStr.c_str(), "%m/%d/%Y", &tm) == nullptr) {
        return false;
    }
    time_t t = mktime(&tm);
    char buffer[80];
    strftime(buffer, 80, "%m/%d/%Y", &tm);
    return dateStr == buffer;
}

int main() {
    cout << validateDate("02/29/2020") << endl; // true
    cout << validateDate("02/29/2021") << endl; // false
    return 0;
}

In this code, the "strptime" function converts the string "dateStr" into a "struct tm" format using the format specifier "%m/%d/%Y," which represents the month, day, and year components. If the conversion fails, it returns "nullptr" and the function returns "false." Otherwise, the "mktime" function converts the "struct tm" into a "time_t" format, which is a UNIX timestamp representing the number of seconds since January 1st, 1970. The "strftime" function converts the "struct tm" back into a string using the same format specifier, and then compares it to the original "dateStr" to make sure they match. If they match, the function returns "true," indicating a valid date.