久々のオンライン参加。
最初、時間の範囲をクラスで表現しようとしたのですが、その演算を用意するだけで１時間が経過してしまい、一旦あきらめました。
30分ほど風呂に入って頭を冷やし（？）、もう一つのアイディアであるビットフィールドで表現する方法を使って書き直してみました。
書き直しで45分ぐらいでした。
# include <iostream>
# include <sstream>
# include <iomanip>
# include <iterator>
# include <algorithm>
# include <utility>
# include <vector>
# include <bitset>

typedef std::bitset<24 * 60>              TimeSlot;
typedef std::vector<std::pair<int, int> > TimeSlots;

void reset(TimeSlot& slot, int head, int tail)
{
    head = (head / 100) * 60 + (head % 100);
    tail = (tail / 100) * 60 + (tail % 100);
    for(int i = head; i < tail; ++i)
    {
        slot.reset(i);
    }
}

void set(TimeSlot& slot, int head, int tail)
{
    head = (head / 100) * 60 + (head % 100);
    tail = (tail / 100) * 60 + (tail % 100);
    for(int i = head; i < tail; ++i)
    {
        slot.set(i);
    }
}

TimeSlots find(const TimeSlot& slot, int min)
{
    TimeSlots result;
    int pos = -1;
    for(int i = 0; i < slot.size(); ++i)
    {
        if(slot[i])
        {
            if(pos < 0)
            {
                pos = i;
            }
        }
        else
        {
            if((0 <= pos) && (min <= (i - pos)))
            {
                result.push_back(std::make_pair(pos, i - pos));
            }
            pos = -1;
        }
    }

    if(0 <= pos)
    {
        result.push_back(std::make_pair(pos, slot.size() - pos));
    }

    return result;
}

void test(const std::string& source, const std::string& expected)
{
    TimeSlot room;
    TimeSlot a;
    TimeSlot b;
    TimeSlot i;
    TimeSlot j;
    TimeSlot z;

    set(room, 1000, 1800);
    a.flip();
    b.flip();
    i.flip();
    j.flip();

    std::istringstream iss(source);
    while(iss.good())
    {
        char c;
        char sep;
        int  head;
        int  tail;
        iss >> c >> head >> sep >> tail;
        switch(c)
        {
        case 'A': reset(a, head, tail); break;
        case 'B': reset(b, head, tail); break;
        case 'I': reset(i, head, tail); break;
        case 'J': reset(j, head, tail); break;
        case 'Z': set(z, head, tail); break;
        }
        iss >> sep;
    }

    room &= z;
    room &= a;
    room &= b;

    TimeSlots slots_i = find(room & i, 60);
    TimeSlots slots_j = find(room & j, 60);

    std::ostringstream oss;
    oss.fill('0');
    int time = 0;

    if((slots_i.size() > 0) && (slots_j.size() > 0))
    {
        time = std::min(slots_i[0].first, slots_j[0].first);
    }
    else if(slots_i.size() > 0)
    {
        time = slots_i[0].first;
    }
    else if(slots_j.size() > 0)
    {
        time = slots_j[0].first;
    }

    if(time != 0)
    {
        int hour = time / 60;
        int min  = time % 60;
        oss << std::setw(2) << hour
            << std::setw(2) << min
            << '-'
            << std::setw(2) << (hour + 1)
            << std::setw(2) << min;
    }
    else
    {
        oss << "-";
    }
    std::string actual = oss.str();
    std::string result = (expected == actual) ? "o" : "x";

    std::cout
        << "expected: " << expected
        << ", actual: " << actual
        << ", result: " << result
        << std::endl;
}

int main(int argc, char* argv[])
{
    /*0*/ test( "A1050-1130,B1400-1415,I1000-1400,I1600-1800,J1100-1745,Z1400-1421,Z1425-1800", "1425-1525" );
    /*1*/ test( "A1000-1200,B1300-1800,Z1000-1215,Z1230-1800", "-" );
    /*2*/ test( "Z0800-2200", "1000-1100" );
    /*3*/ test( "A1000-1700,Z0800-2200", "1700-1800" );
    /*4*/ test( "A1000-1701,Z0800-2200", "-" );
    /*5*/ test( "A1000-1130,B1230-1800,Z0800-2200", "1130-1230" );
    /*6*/ test( "A1000-1129,B1230-1800,Z0800-2200", "1129-1229" );
    /*7*/ test( "A1000-1131,B1230-1800,Z0800-2200", "-" );
    /*8*/ test( "A1000-1130,B1229-1800,Z0800-2200", "-" );
    /*9*/ test( "A1000-1130,B1231-1800,Z0800-2200", "1130-1230" );
    /*10*/ test( "A1000-1130,B1230-1800,Z0800-1130,Z1131-2200", "-" );
    /*11*/ test( "A1000-1130,B1231-1800,Z0800-1130,Z1131-2200", "1131-1231" );
    /*12*/ test( "Z0800-0801", "-" );
    /*13*/ test( "Z0800-1031,Z1129-1220,Z1315-1400,Z1459-1600", "1459-1559" );
    /*14*/ test( "Z0800-2200,I1000-1600,J1030-1730", "1600-1700" );
    /*15*/ test( "Z0800-2200,I1000-1600,J1130-1730", "1000-1100" );
    /*16*/ test( "Z0800-2200,I1000-1600,J1130-1730,A0800-1025", "1025-1125" );
    /*17*/ test( "Z0800-2200,I1000-1600,J1130-1730,A0800-1645", "1645-1745" );
    /*18*/ test( "Z0800-2200,I1000-1600,J1130-1730,A0800-1645,I1735-2200", "-" );
    /*19*/ test( "Z0800-2200,I1000-1600,J1130-1730,A0800-1645,J1735-2200", "1645-1745" );
    /*20*/ test( "Z1030-2200,I1000-1600,J1130-1730", "1030-1130" );
    /*21*/ test( "Z1035-1500,I1000-1600,J1130-1730,Z1644-2200", "1644-1744" );
    /*22*/ test( "I2344-2350,A2016-2253,Z1246-1952", "1246-1346" );
    /*23*/ test( "Z2155-2157,B1822-2032,Z1404-2000,Z2042-2147,Z2149-2154", "1404-1504" );
    /*24*/ test( "Z2231-2250,Z2128-2219,B2219-2227,B2229-2230,Z0713-2121,A0825-1035,B1834-2001", "1035-1135" );
    /*25*/ test( "J0807-1247,I0911-1414,B1004-1553,Z0626-1732,Z1830-1905,A1946-1954,A0623-1921", "-" );
    /*26*/ test( "J1539-1733,J0633-1514,Z1831-1939,J1956-1959,I0817-1007,I1052-1524,Z1235-1756,Z0656-1144", "1524-1624" );
    /*27*/ test( "Z2319-2350,B0833-2028,I2044-2222,A1410-2201,Z2044-2228,Z0830-2023,Z2242-2306,I2355-2359", "-" );
    /*28*/ test( "B2001-2118,Z0712-1634,I1941-2102,B1436-1917", "1000-1100" );
    /*29*/ test( "A0755-1417,B2303-2335,Z0854-2150,Z2348-2356,Z2156-2340,I1024-1307,Z2357-2359", "1417-1517" );
    /*30*/ test( "A1958-1959,B0822-1155,I1518-1622,Z1406-1947,A1800-1822,A0904-1422,J1730-1924,Z1954-1958,A1946-1956", "1422-1522" );
    /*31*/ test( "B1610-1910,I2121-2139,A0619-1412,I2147-2153,Z0602-2111,I0841-2031,A1657-1905,A1956-2047,J0959-1032,Z2131-2147", "1412-1512" );
    /*32*/ test( "Z0623-1900,A0703-1129,I1815-1910,J1956-1957,I0844-1518,Z1902-1935,B1312-1342,J1817-1955", "1129-1229" );
    /*33*/ test( "J1246-1328,B1323-1449,I1039-1746,Z1218-2111", "1449-1549" );
    /*34*/ test( "A1958-1959,I1943-1944,I0731-1722,Z0845-1846,J1044-1513,Z1910-1923,B1216-1249", "1513-1613" );
    /*35*/ test( "A1855-2047,Z0946-1849,Z2056-2059,I1855-1910,B1946-2058,I1956-2025,Z1905-2054,J0644-1800,I0720-1618", "1618-1718" );
    /*36*/ test( "J1525-1950,Z0905-1933,A1648-1716,I2051-2054,I2015-2044,I0804-1958,B0934-1100,Z1953-2037", "1100-1200" );
    /*37*/ test( "Z1914-1956,J0823-1610,Z0641-1841,J1800-1835,A0831-1346,I1926-1941,I1030-1558,I1738-1803", "1558-1658" );
    /*38*/ test( "Z0625-1758,J1033-1351,B1816-2236,I0838-1615,J2247-2255", "1351-1451" );
    /*39*/ test( "J0603-1233,A1059-1213,I1326-2103,Z0710-1459", "1213-1313" );
    /*40*/ test( "B1302-1351,J1410-2038,A0755-1342,J0637-0658,Z2148-2159,Z1050-2131,A1543-1844,I1615-1810", "1351-1451" );
    /*41*/ test( "Z0746-2100,A2122-2156,I1022-1144,J0947-1441,A1333-1949", "1144-1244" );
    /*42*/ test( "J0718-1243,Z1443-1818,B2055-2057,A0714-1238,Z1045-1344,A1643-1717,B1832-2039,J1623-1931", "1238-1338" );
    /*43*/ test( "Z1921-1933,A1208-1418,I0827-1940,Z0757-1917,J0653-1554,B1859-1909", "1554-1654" );

    return 0;
}