1430 - A Question of Time

#include <bits/stdc++.h>
using namespace std;
//fun()=3600*(2*h0-hx)+60*(2*m0-13*mx)+2*s0
//13*sx=fun()
//13*sx=fun()+360*120
//13*sx=fun()-360*120
const double eps=1e-10;
const double eps2=1e-3;
int h0,m0,s0;
int t1,t2;
int ans[50];
int len;
double fun(int tmp)
{
    double h,m,s;
    s=tmp%(13*60)/13.0;
    tmp/=13*60;
    m=tmp%60;
    h=tmp/60;
    double ang0=(30*h0)+(m0/2.0)+(s0/120.0);
    double ang1=(30*h)+(m/2.0)+(s/120.0);
    double ang2=(6*m)+(s/10.0);
    return ang1+ang2-2*ang0;
}
int bs(int l,int r,double x)
{
    int mid;
    while(r-l>1)
    {
        mid=(l+r)/2;
        double cmp=fun(mid)-x;
        if(cmp>=eps)
            r=mid;
        else
            l=mid;
    }
    if(t1<=l&&l<=t2&&fabs(fun(l)-x)<eps2)
        return l;
    else if(t1<=r&&r<=t2&&fabs(fun(r)-x)<eps2)
        return r;
    return -1;
}
void solve(int i)
{
    int l=i*46800,r=l+46800-1;
    int tmp=bs(l,r,0.0);
    if(tmp!=-1)
    {
        ans[len++]=tmp;
    }
    tmp=bs(l,r,360.0);
    if(tmp!=-1)
    {
        ans[len++]=tmp;
    }
    tmp=bs(l,r,-360.0);
    if(tmp!=-1)
    {
        ans[len++]=tmp;
    }
}
int main()
{
    //freopen("in","r",stdin);
    //freopen("out","w",stdout);
    int t,Case=0;
    int h,m,s;
    scanf("%d",&t);
    while(t--)
    {
        len=0;
        scanf("%d:%d:%d",&h0,&m0,&s0);
        scanf("%d:%d:%d",&h,&m,&s);
        t1=((h*60+m)*60+s)*13;
        scanf("%d:%d:%d",&h,&m,&s);
        t2=((h*60+m)*60+s)*13;

        for(int i=0; i<12; i++)
        {
            solve(i);
        }

        sort(ans,ans+len);
        len=unique(ans,ans+len)-ans;
        printf("Case %d: %d\n",++Case,len);
        int mod;
        for(int i=0; i<len; i++)
        {
            mod=ans[i]%13;
            ans[i]/=13;
            s=ans[i]%60;
            ans[i]/=60;
            m=ans[i]%60;
            h=ans[i]/60;
            printf("%02d:%02d:%02d",h,m,s);
            if(mod)
                printf(" %d/13",mod);
            puts("");
        }
    }
}