USACO习题：Friday the Thirteenth

这道题难度不大，就是比较麻烦。求解所有月份13号是星期几。

 

#include <iostream>
#include <fstream>
#include <string>
#include <vector>

using namespace std;

const int MONTHS[] = {0,31,28,31,30,31,30,31,31,30,31,30,31};
vector<int> ACC_MONTHS(13,0);
vector<int> ACC_LEAP_MONTHS(13,0); 


bool is_leap_year(int year);

void accumulate_months(vector<int> &acc_months,bool is_leap){
    int count=0;
    for(int i=0;i<=12;i++){
        int  days = MONTHS[i];
        if(i==2&&is_leap)
            days+=1;
        count+=days;
        acc_months[i] = count;
    }
}


int first_day_of_year(int year){
    int d=0;
    for(int i=1901;i<=year;++i){
        int days = 365;
        if(is_leap_year(i-1))
            days=366;
        d = (d+days)%7;
    }
    return d;
}

int weekday(int year,int month,int day,int first_day){
    vector<int> *acc_months = &ACC_MONTHS;
    if(is_leap_year(year))
        acc_months = &ACC_LEAP_MONTHS;
    return ((*acc_months)[month-1]+day-1+first_day)%7;
}


bool is_leap_year(int year){
    if(year%400==0)
        return true;
    else if( (year%4==0) && (year%100!=0) )
        return true;
    else
        return false;
}

void solve(int N, vector<int> &stat){
    for(int i =1900;i<1900+N;++i){
        int first_day = first_day_of_year(i);
        //cout<<i<<":"<<first_day<<endl;
        for(int month=1;month<=12;++month){
            int name =  weekday(i,month,13,first_day);
            stat[name]+=1;
        }
    }

}

int main() {
    ofstream fout("friday.out");
    ifstream fin("friday.in");

    accumulate_months(ACC_MONTHS,false);
    accumulate_months(ACC_LEAP_MONTHS,true);


    int N=0;
    fin>>N;
    //stat:start from monday(0) to Sunday(6)
    vector<int> stat(7,0);  
    solve(N,stat);

    for(int i=0;i<7;++i){
        fout<<stat[(i+5)%7];
        if(i<6)
            fout<<" ";
    }
    fout<<endl;
    
    fin.close();
    fout.close();
    return 0;
}