The solution is really hard enough - you must know the
serious number theory :-) :-) :-)

#include "stdio.h"
#include "algorithm"
#include "string.h"

struct time
{
    double s, os; //os - original time
    // s - finish time (+id*30)
    char name[21];
    int I;
    time(const double S = 0, const int id = 0)
        :s(S), I(id) {}
    void inc(const int id)
    {
        os = s;
        s += 30*id;
    }
};

int cmp(const void* a, const void* b)
{
    return ( ((time*)a)->s > ((time*)b)->s );
}

int cmp2(const void* a, const void* b)
{
    return strcmp(((time*)a)->name, ((time*)b)->name);
}

int cmp3(const void* a, const void* b)
{
    return ( ((time*)a)->os < ((time*)b)->os );
}

int main()
{
    int n;
    scanf("%d\n", &n);

    time* ts = new time[n+1];
    time* ans = new time[n+1];
    int m;
    float t;
    for(int i=0; i<n; i++)
    {
        scanf("%s %d:%f\n", ts[i].name, &m, &t );
        ts[i].s = t + m * 60;
        ts[i].inc(i);
    }

    std::qsort(&ts[1], n-1, sizeof(time), cmp);
    int j=0;
    ans[j++] = ts[0];
    for(int i=1; i<n; i++)
    {
        if( cmp3( &ts[i], &ans[j-1])  ) ans[j++] = ts[i];
    }
    std::qsort(ans,j,sizeof(time),cmp2);
    printf("%d\n",j);
    for(int i=0;i<j;i++) printf("%s\n", ans[i].name);

    delete[] ans;
    delete[] ts;
    return 0;
}