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//Title of this code
//g++  4.9.2

#include <iostream>

#include <sstream>
#include <iomanip>
#include <string>

#include <algorithm>

bool is_valid_date ( int (&date)[3] )
{
    static const int days_count_from_month[12] = { 31 , 28 , 31 , 30 , 31 , 30 , 31 , 31 , 30 , 31 , 30 , 31 } ;
    int count_days = 0 ;
    bool result = false ;
    if ( date[2] < 13 )
    {
        count_days = days_count_from_month [ date[2] - 1 ] + ( (date[2] == 2) && (date[0] % 4 == 0 ) ) ;
        result = ( date [1] <= count_days ) ;
    }
    //std::cout << "Result for [" << date[0] << "." << date[1] << "." << date[2] << "] " << result << " | count days = " << count_days << std::endl ;
    return result ;
}

std::string answer(int x, int y, int z)
{
    int dateBuffer [ 3 ] = { x , y , z } ;
    int count_valid = 0 ;
    std::sort ( dateBuffer , dateBuffer + 3 ) ;
    std::string resultMessage = "Incorrect" ;
    do
    {
        if ( is_valid_date ( dateBuffer )  )
        {
            if ( ++count_valid > 1 )
            {
                resultMessage = "Ambiguous" ;
                break ;
            }
            std::stringstream ss ;
            ss << std::setw(2) << std::setfill('0') << dateBuffer[1]
                << "." << std::setw(2) << dateBuffer[2]
                << "." << std::setw(2) << dateBuffer[0] ;
            resultMessage = ss.str() ;
        }
    } while ( std::next_permutation( dateBuffer , dateBuffer + 3 ) ) ;
    return resultMessage ;
}

int main()
{
    srand ( time(0) ) ;
    for ( size_t i = 0 ; i < 100 ; ++i )
    {
        int a = rand() % 50 + 1 ; //TODO 100
        int b = rand() % 50 + 1 ; //TODO 100
        int c = rand() % 50 + 1 ; //TODO 100
        std::cout << "Result for [" << a << "." << b << "." << c << "]: " << answer ( a , b , c ) << std::endl ;
    }
}

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Compilation time: 1.83 sec, absolute running time: 0.15 sec, cpu time: 0 sec, memory peak: 4 Mb, absolute service time: 1.99 sec

Result for [13.40.50]: Incorrect Result for [14.49.41]: Incorrect Result for [10.31.29]: Ambiguous Result for [13.39.16]: Incorrect Result for [44.18.4]: 18.04.44 Result for [19.21.12]: Ambiguous Result for [43.7.2]: Ambiguous Result for [7.36.33]: Incorrect Result for [10.2.35]: Ambiguous Result for [24.24.44]: Incorrect Result for [20.38.35]: Incorrect Result for [19.4.33]: 19.04.33 Result for [11.13.16]: Ambiguous Result for [41.27.4]: 27.04.41 Result for [7.20.21]: Ambiguous Result for [10.41.44]: Incorrect Result for [24.33.50]: Incorrect Result for [25.41.37]: Incorrect Result for [8.2.40]: Ambiguous Result for [42.25.15]: Incorrect Result for [37.45.3]: Incorrect Result for [21.13.8]: Ambiguous Result for [5.26.22]: Ambiguous Result for [20.16.49]: Incorrect Result for [25.22.20]: Incorrect Result for [46.32.10]: Incorrect Result for [41.7.44]: Incorrect Result for [42.31.37]: Incorrect Result for [29.38.38]: Incorrect Result for [18.31.15]: Incorrect Result for [33.19.9]: 19.09.33 Result for [37.39.23]: Incorrect Result for [46.44.48]: Incorrect Result for [17.15.14]: Incorrect Result for [17.40.37]: Incorrect Result for [37.37.20]: Incorrect Result for [46.27.26]: Incorrect Result for [40.20.7]: 20.07.40 Result for [26.48.46]: Incorrect Result for [15.18.29]: Incorrect Result for [29.2.47]: Incorrect Result for [39.40.38]: Incorrect Result for [14.35.31]: Incorrect Result for [11.3.45]: Ambiguous Result for [26.20.36]: Incorrect Result for [13.6.22]: Ambiguous Result for [32.1.48]: Incorrect Result for [8.42.18]: 18.08.42 Result for [16.19.17]: Incorrect Result for [13.36.36]: Incorrect Result for [41.14.37]: Incorrect Result for [40.3.26]: 26.03.40 Result for [27.16.12]: Ambiguous Result for [9.28.15]: Ambiguous Result for [5.6.34]: Ambiguous Result for [41.20.41]: Incorrect Result for [12.3.43]: Ambiguous Result for [12.12.35]: 12.12.35 Result for [31.27.5]: Ambiguous Result for [47.42.40]: Incorrect Result for [33.34.4]: Incorrect Result for [19.23.8]: Ambiguous Result for [47.1.25]: 25.01.47 Result for [8.11.4]: Ambiguous Result for [24.18.11]: Ambiguous Result for [9.8.30]: Ambiguous Result for [49.21.33]: Incorrect Result for [42.34.44]: Incorrect Result for [28.14.23]: Incorrect Result for [32.11.14]: 14.11.32 Result for [24.45.47]: Incorrect Result for [29.15.22]: Incorrect Result for [38.11.22]: 22.11.38 Result for [12.21.35]: 21.12.35 Result for [17.46.2]: 17.02.46 Result for [28.5.11]: Ambiguous Result for [9.3.31]: Ambiguous Result for [41.46.15]: Incorrect Result for [37.23.30]: Incorrect Result for [9.7.40]: Ambiguous Result for [24.30.34]: Incorrect Result for [20.8.49]: 20.08.49 Result for [43.47.11]: Incorrect Result for [17.8.33]: 17.08.33 Result for [1.26.29]: Ambiguous Result for [2.5.33]: Ambiguous Result for [12.14.37]: 14.12.37 Result for [44.6.33]: Incorrect Result for [10.44.7]: Ambiguous Result for [40.4.15]: 15.04.40 Result for [31.27.46]: Incorrect Result for [15.49.5]: 15.05.49 Result for [15.41.1]: 15.01.41 Result for [27.7.10]: Ambiguous Result for [10.7.36]: Ambiguous Result for [38.10.42]: Incorrect Result for [22.23.5]: Ambiguous Result for [8.17.13]: Ambiguous Result for [42.28.6]: 28.06.42 Result for [1.17.10]: Ambiguous