/**
  蔡勒公式
  输入：year：取年份后2位，比如2021取21
  输出结果：0-星期日，1-星期一，2-星期二，3-星期三，4-星期四，5-星期五，6-星期六
**/
int getDayOfWeek(int year, int month, int day)
{
    int c, y, week;
    if (month == 1 || month == 2) //判断month是否为1或2　
    {
        year--;
        month += 12;
    }

    c = year / 100;
    y = year - c * 100;
    week = (c / 4) - 2 * c + (y + y / 4) + (13 * (month + 1) / 5) + day - 1;

    while (week < 0)
    {
        week += 7;
    }
    week %= 7;
    return week;
}

void main(void)
{
    int year = 0, month = 0, day = 0, week = 0;
    while (1)
    {
        scanf("%d%d%d", &year, &month, &day);
        printf("current input data:\r\n20%d-%d-%d\r\n", year, month, day);
        week = getDayOfWeek(year, month, day);
        printf("week: %d", week);
    }
}
 
使用如下图：
 
 

#include <stdio.h>

int getweek(int,int,int);

int getweek(int year,int month,int day)
{
    int week=0;
    int century=year/100;
    year = year%100;
    if(month==1||month==2) 
    {
        month+=12;
        year--;//在蔡勒公式中 1,2 月份特殊处理
    }     
    week= year+year/4+century/4-2*century+(26*(month+1))/10+day-1;//蔡勒公式
    week=week%7;//对结果取模
    return (week>=0)?week:(7+week);
}

int main(void)
{
	int y,m,d,week;
	printf("请输入年月日:");
	scanf("%d %d %d",&y,&m,&d);
	week = getweek(y,m,d);
	switch(week)
	{
		case 0:printf("今天是星期日!");break;
		case 1:printf("今天是星期一!");break;
		case 2:printf("今天是星期二!");break;
		case 3:printf("今天是星期三!");break;
		case 4:printf("今天是星期四!");break;
		case 5:printf("今天是星期五!");break;
		case 6:printf("今天是星期六!");break;
	}
	return 0;
 } 

# include <iostream>
# include <string.h>
using namespace std;

int CaculateWeekDay(int y, int m, int d)
{
	int week = -1;
	if(m == 1 || m == 2)
	{
	m += 12;
	y--;
	}
		

	week = (d+2*m+3*(m+1)/5+y+y/4-y/100+y/400+1)%7;

	return week;
}

int main()
{
	cout<<CaculateWeekDay(2013, 8, 4)<<endl;
	return 0;
}

 
if( M==1 || M==2 )
    {
        M+=12;
        --Y;
    }
	//1582年9月3日后：w = (d + 2*m+3*(m+1)/5+y+y/4-y/100+y/400)%7;
	//1582年9月3日前：w = (d+2*m+3*(m+1)/5+y+y/4+5） % 7;
	//0是星期一
    if( Y < 1582 || Y == 1582 && M < 9 || Y == 1582 && M == 9 && D < 3 ) return (D+2*M+3*(M+1)/5+Y+Y/4+5)%7;
    else return (D+2*M+3*(M+1)/5+Y+Y/4-Y/100+Y/400)%7;
 

 
 

int c=year/100;
int y=year-c*100;
int week=(c/4)-2*c+(y+y/4)+(13*(month+1)/5)+day-1;
while(week<0){week+=7;}
week%=7;
switch(week)
{
case 1:printf("Monday\n");break;
case 2:printf("Tuesday\n");break;
case 3:printf("Wednesday\n");break;
case 4:printf("Thursday\n");break;
case 5:printf("Friday\n");break;
case 6:printf("Saturday\n");break;
case 0:printf("Sunday\n");break;
//只有在1582 9 3后使用
}

 
 

 
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;

string weeks[7]= {"Monday","Tuesday","Wednesday","Thursday","Friday","Saturday","Sunday"};
string months[12]= {"January","February","March","April","May","June","July","August","September","October","November","December"};

int day1(int M,int D,int Y)
{
	if( M==1 || M==2 )  
    {  
        M+=12;  
        --Y;  
    }
    if( Y < 1582 || Y == 1582 && M < 9 || Y == 1582 && M == 9 && D < 3 ) return (D+2*M+3*(M+1)/5+Y+Y/4+5)%7;  
    else return (D+2*M+3*(M+1)/5+Y+Y/4-Y/100+Y/400)%7;  
}
void day2(int month,int day,int year)
{
	int c=year/100;  
	int y=year-c*100;  
	int week=(c/4)-2*c+(y+y/4)+(13*(month+1)/5)+day-1;  
	while(week<0){week+=7;}  
	week%=7;  
	switch(week)  
	{  
		case 1:printf("Monday\n");break;  
		case 2:printf("Tuesday\n");break;  
		case 3:printf("Wednesday\n");break;  
		case 4:printf("Thursday\n");break;  
		case 5:printf("Friday\n");break;  
		case 6:printf("Saturday\n");break;  
		case 0:printf("Sunday\n");break;  
		default: ;
	}  
}  

int main()
{
    int m, d, y;
    while( scanf("%d %d %d",&m, &d, &y), m+d+y )
    {
        printf("%s\n",weeks[day1(m,d,y)].c_str());
		day2(m,d,y);
    }
	return 0;
}