题目19：20世纪有多少个星期日是当月的第一天？

欧拉计划

Counting Sundays

You are given the following information, but you may prefer to do some research for yourself.

• 1 Jan 1900 was a Monday.
• Thirty days has September,
  April, June and November.
  All the rest have thirty-one,
  Saving February alone,
  Which has twenty-eight, rain or shine.
  And on leap years, twenty-nine.
• A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400.
  

How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?

题目：

以下是一些已知信息，但是或许你需要自己做一些其他的调查。

• 1900 年 1 月 1 日是星期一。
• 30 天的月份有：9 月，4 月，6 月，1 1月。
• 此外的月份都是 31 天，当然 2 月除外。
• 2 月在闰年有 29 天，其他时候有 28 天。
• 年份可以被 4 整除的时候是闰年，但是不能 400 整除的世纪年（100 的整数倍年）除外。
  

20 世纪（1901 年 1 月 1 日到 2000 年 12 月 31 日）一共有多少个星期日落在了当月的第一天？

hsiamer

目前电脑只有数据库环境,先用sql写一下吧 . 其实结果不是最重要的,思路有了, 不管什么语言,就都能实现了.
set serveroutput on;
DECLARE
v_month INTEGER;
v_start date;
v_end   date;
v_3 INTEGER;
v_enddays date;
j INTEGER := 0;
begin
  v_start := date'1900-01-01';
  v_end   := date'2001-01-01';
  v_month := months_between(v_end,v_start);
  for v_3 in 0..v_month-1
  LOOP
        v_enddays := add_months(v_start,v_3);
        if TRIM(to_char(v_enddays,'day'))= 'sunday' then
                j:=j+1;
                -- dbms_output.put_line(v_enddays);
        end if;
  end loop;
    dbms_output.put_line(j);
end;
/

ps : 原来oracle检索出来的结果带空格,导致我的计算结果一直为0 --!

Plusenxue

y = 1900
m = 1
xingqi = 1
day = 1
count = 0
def run(x):
    if x%400 == 0:
        return True
    else:
        if x%100 == 0:
            return False
        if x%4 == 0:
            return True
        return False




while y < 2001:

    if m in [4,6,9,11]:
        if day == 31:
            m += 1
            day = 1
            
    if m in [1,3,5,7,8,10,12]:
        if day == 32:
            m += 1
            day = 1

    if m == 13:
        y += 1
        m = 1

    if m == 2:
        if run(y) == True:
            if day == 30:
                m += 1
                day = 1
        else:
            if day == 29:
                m += 1
                day = 1

    if xingqi == 8:
        xingqi = 1
        
    if y > 1900 and day == 1 and xingqi == 7:
        count += 1      
    day += 1
    xingqi += 1

jerryxjr1220

重新查证了一下，题目错了，1901年1月1日是星期二。
171
[Finished in 0.1s]

直接用datetime库

import datetime as dt 
c = 0
for y in range(1901,2001):
        for m in range(1,13):
                dd = dt.datetime(y,m,1)
                if dd.weekday()==6:
                        c += 1
print(c)

芒果加黄桃

# encoding:utf-8
# 20世纪每月的第一天是星期天的  有多少

'''
蔡勒（Zeller）公式W=Y+[Y/4]+[C/4]-2C+[26(M+1)/10]+d-1
公式中的符号含义如下：W为星期数；C为世纪；Y为年（两位数）； 
M为月数（M=m（当m>2）；M=m+12（m<3））；d为日。
相比于通用通用计算公式而言，蔡勒（Zeller）公式大大降低了计算的复杂度。
'''
from time import time

def euler019():
    count = 0
    for year in range(1901, 2001):
        for month in range(1, 13):
            temp = str(year) + '-' + str(month) + '-' + '1'
            # 1、2月份，看做上一年的13、14月份
            if month in [1, 2]:
                M = month + 12
                Y = year - 1
            else:
                M = month
                Y = year
            # 世纪数  年份的前两位
            C = int(year / 100)
            # 年  年份的后两位
            Y = Y % 100
            # 日  日期数 本题默认为1
            D = 1
            W = (Y + int(Y / 4) + int(C / 4) - 2 * C + int(26 * (M + 1) / 10) + D - 1) % 7
            if not W:
                count += 1
                #print(temp) 
    return count

if __name__ == '__main__':
    start = time()
    print(euler019())
    print('cost %.6f sec' % (time() - start))

171
cost 0.003001 sec

渡风

此代码使用matlab编程
Problem19所用时间为0.0055557秒
Problem19的答案为171

%题目19：20世纪有多少个星期日是当月的第一天？
function Output=Problem19(Input)
 tic
if nargin==0
    Input=7;%星期天
end
Common=[1:31,1:28,1:31,1:30,1:31,1:30,1:31,1:31,1:30,1:31,1:30,1:31];%平年序列
Leap=[1:31,1:29,1:31,1:30,1:31,1:30,1:31,1:31,1:30,1:31,1:30,1:31];%闰年序列
Century=[];%一个世纪的时间序列
Sum=0;%当月第一天为星期天的总天数
for ii=1901:2000
    if mod(ii,4)==0
        Temp=[Century,Leap];
    else
        Temp=[Century,Common];
    end
    Century=Temp;
end
L=length(Century);%世纪的长度
Week=1:7;
if mod(L,7)==0
    Weekday=repmat(Week,[1 L/7]);%星期时间序列
else
    Weekday=repmat(Week,[1 (L+7-mod(L,7))/7]);
end
Weekday=Weekday(2:end);%1901年1月1日是星期2
for jj=1:L
    if Weekday(jj)==Input&&Century(jj)==1%当天为星期天的同时，也是当月的第一天
        Sum=Sum+1;
    end
end
toc
Output=Sum;
disp('此代码使用matlab编程')
disp(['Problem19所用时间为',num2str(toc),'秒'])
disp(['Problem19的答案为',num2str(Output)])
end

永丨恒

number = 0
day = 1
days = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]

def isleap(_year):
    if (_year % 4 == 0 and _year % 100 != 0) or (_year % 400 == 0):
        return True
    else:
        return False

for year in range(1900,2001):
    if isleap(year):
        days[1] = 29
    else:
        days[1] = 28
    for i in days:
        day += i
        if day % 7 == 0 and year >= 1901:
            number += 1

print number

永丨恒

jerryxjr1220 发表于 2016-10-11 15:48
重新查证了一下，题目错了，1901年1月1日是星期二。
171
[Finished in 0.1s]

看清楚题目。。题目说的是1900年1月1日是星期一。。。
然后问题说的是从1901年1月1日开始算起。。。

NiceB

171

month=[31,28,31,30,31,30,31,31,30,31,30,31]
sunday=0
xingqi=1
xingqi=(xingqi+365%7)%7
for years in range (1901,2001):
    if years%4==0:
        month[1]=29
    month[1]=28

    for i in month:
        xingqi=(xingqi+i%7)%7
        if xingqi==0:
            sunday+=1
print(sunday)

99592938

wek = (1+365)%7 #1901-01-01是星期几
list_sun=[]
mon=[31,28,31,30,31,30,31,31,30,31,30,31]
for year in range(1901,2001):
    if year%4:mon[1]=28
    else:mon[1]=29
    for m in range(12):
        if wek==0:list_sun.append('%d-%d' %(year,m+1))
        wek=(wek+mon[m])%7
print(len(list_sun))
print(list_sun)

结果：
171
['1901-9', '1901-12', '1902-6', '1903-2', '1903-3', '1903-11', '1904-5', '1905-1', '1905-10', '1906-4', '1906-7', '1907-9', '1907-12', '1908-3', '1908-11', '1909-8', '1910-5', '1911-1', '1911-10', '1912-9', '1912-12', '1913-6', '1914-2', '1914-3', '1914-11', '1915-8', '1916-10', '1917-4', '1917-7', '1918-9', '1918-12', '1919-6', '1920-2', '1920-8', '1921-5', '1922-1', '1922-10', '1923-4', '1923-7', '1924-6', '1925-2', '1925-3', '1925-11', '1926-8', '1927-5', '1928-1', '1928-4', '1928-7', '1929-9', '1929-12', '1930-6', '1931-2', '1931-3', '1931-11', '1932-5', '1933-1', '1933-10', '1934-4', '1934-7', '1935-9', '1935-12', '1936-3', '1936-11', '1937-8', '1938-5', '1939-1', '1939-10', '1940-9', '1940-12', '1941-6', '1942-2', '1942-3', '1942-11', '1943-8', '1944-10', '1945-4', '1945-7', '1946-9', '1946-12', '1947-6', '1948-2', '1948-8', '1949-5', '1950-1', '1950-10', '1951-4', '1951-7', '1952-6', '1953-2', '1953-3', '1953-11', '1954-8', '1955-5', '1956-1', '1956-4', '1956-7', '1957-9', '1957-12', '1958-6', '1959-2', '1959-3', '1959-11', '1960-5', '1961-1', '1961-10', '1962-4', '1962-7', '1963-9', '1963-12', '1964-3', '1964-11', '1965-8', '1966-5', '1967-1', '1967-10', '1968-9', '1968-12', '1969-6', '1970-2', '1970-3', '1970-11', '1971-8', '1972-10', '1973-4', '1973-7', '1974-9', '1974-12', '1975-6', '1976-2', '1976-8', '1977-5', '1978-1', '1978-10', '1979-4', '1979-7', '1980-6', '1981-2', '1981-3', '1981-11', '1982-8', '1983-5', '1984-1', '1984-4', '1984-7', '1985-9', '1985-12', '1986-6', '1987-2', '1987-3', '1987-11', '1988-5', '1989-1', '1989-10', '1990-4', '1990-7', '1991-9', '1991-12', '1992-3', '1992-11', '1993-8', '1994-5', '1995-1', '1995-10', '1996-9', '1996-12', '1997-6', '1998-2', '1998-3', '1998-11', '1999-8', '2000-10']

由我们主宰

#include<stdio.h>
int leapyear(int year)
{
        if((0==year%4&&0!=year%100)||0==year%400)
        {
                return 1;
        }
        else
        {
                return 0;
        }
}

int month(int y,int m)
{
        switch(m)
        {
                case 1:
                        return 31;
                case 2:
                        if(leapyear(y))
                        {
                                return 29;
                        }
                        else
                        {
                                return 28;
                        }
                case 3:
                        return 31;
                case 4:
                        return 30;
                case 5:
                        return 31;
                case 6:
                        return 30;
                case 7:
                        return 31;
                case 8:
                        return 31;
                case 9:
                        return 30;
                case 10:
                        return 31;
                case 11:
                        return 30;
                default:
                        return 31;
        }

}

int main()
{
        int i,y,m,d,sum=0,t=1;
        for(y=1900;y<2001;y++)
        {
                for(m=1;m<=12;m++)
                {
                        d=1;
                        while(d<=month(y,m))
                        {
                                for(i=t;i<=7;i++)
                                {
                                        if(7==i&&1==d)
                                        {
                                                sum=sum+1;
                                        }
                                        d++;                               
                                        if(d>month(y,m))
                                        {
                                                if(i<7)
                                                {
                                                        t=i+1;
                                                }
                                                else
                                                {
                                                        t=1;
                                                }
                                                break;
                                        }
                                        t=1;
                                }
                        }
                }
        }
        printf("%d\n",sum-2);//减去1990年的两个
    return 0;
}

zzzgod

#include <iostream>

using namespace std;

int main()
{
        const short NYEAR[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
        const short RYEAR[13]={0,31,29,31,30,31,30,31,31,30,31,30,31};
        int day=6,month=1,sum=0;
        for(int year=1901;year<=2000;++year)
        {
                if(year%4==0&&year%100!=0||year%400==0)
                {
                        while(month<=12)
                        {
                                day+=7;
                                if(day>=RYEAR[month])
                                {
                                        day-=RYEAR[month];
                                        ++month;
                                        if(day==1)
                                        {
                                                ++sum;
                                        }
                                }
                        }
                        month=1;
                }
                else
                {
                        while(month<=12)
                        {
                                day+=7;
                                if(day>=NYEAR[month])
                                {
                                        day-=NYEAR[month];
                                        ++month;
                                        if(day==1)
                                        {
                                                ++sum;
                                        }
                                }
                        }
                        month=1;
                }
        }
        cout<<"总共有"<<sum<<"个星期日是每个月的第一天。";
}

DetConan

python3 时间为0.001526 s
结果是171

import time

start = time.clock()
yearn = {1: 3, 2: 0, 3: 3, 4: 2, 5: 3, 6: 2,
         7: 3, 8: 3, 9: 2, 10: 3, 11: 2, 12: 3}
yearr = {1: 3, 2: 1, 3: 3, 4: 2, 5: 3, 6: 2,
         7: 3, 8: 3, 9: 2, 10: 3, 11: 2, 12: 3}

count = 0
daysum = 2
n = 13
for y in range(1901, 2001):
    if ((y % 4 == 0 and y % 100 != 0) or y % 400 == 0):
        year = yearr
    else:
        year = yearn
    if y == 2000:
        n = 12
    for m in range(1, n):
        daysum = (daysum + year[m]) % 7
        if daysum == 0:
            if m + 1 == 13:
                print("%d-%d-1" % (y + 1, 1))
            else:
                print("%d-%d-1" % (y, m + 1))
            count += 1
print("共有%d个" % count)

end = time.clock()
print("read:%f s" % (end - start))

cwhsmile

答案是171

mport time
import math

def test1():
    mon = {1:31,2:'leap year',3:31,4:30,5:31,6:30,7:31,8:31,9:30,10:31,11:30,12:31}
    wed = 1
    
    for m in range(1900,2001):
        if (m%4==0 and m%100!=0) or (m%400==0):
            leap = 1
        else:
            leap = 0
        for n in range(1,13):
            if n == 2:
                if leap == 1:
                    mon[2] = 29
                else:
                    mon[2] = 28
            for i in range(1,mon[n]+1):
                if wed == 8:
                    wed = 1
                if i == 1 and wed == 7:
                    if m != 1900:
                        li.append([m,n,i])
                wed += 1

    
    
    return li,len(li)
li = []
start = time.perf_counter()
print(test1())
end = time.perf_counter()
print(end-start)

刘富国

jerryxjr1220 发表于 2016-10-11 15:48
重新查证了一下，题目错了，1901年1月1日是星期二。
171
[Finished in 0.1s]

题目说的是1990年1月1日是星期一

guoquanli

#include<stdio.h>
#include<stdlib.h>
#include<stdbool.h>
//是否是润年i的判断
bool IsLeapYear(int year){
    if((year%4 == 0 && year%100 != 0) || year %400 == 0){
        return true;
    }else{
        return false;
    }
}
//测试函数
void testIsLeapYear(int year){
    if(IsLeapYear(year)){
        printf("%d year is leap year!\n",year);
    }else{
        
        printf("%d year is not leap year!\n",year);
    }
}
// 判断从1900年到year年总共有多少天
int DayCal(int year){
        int sum = 0;
        for(int i = 1900; i < year; i++){
                if(IsLeapYear(i)){
                        sum += 366;
                }else{
                        sum += 365;
                }
        }
        return sum;
}        
//测试函数
void testDayCal(int year){
        printf("from 1900 to this year,toal day :%d\n",DayCal(year));
}

//统计输入的年份中，当月第一天是星期日
void FindMonth(int year){
        int sum  = DayCal(year);
        bool flag = IsLeapYear(year);
        int dayArray[12] = {0,31,28,31,30,31,30,31,31,30,31,30};
        if(flag){
                dayArray[2] = 29;
        }
        for(int i = 0; i<12;i++){
                sum += dayArray[i];
                if((sum  + 1  ) % 7 == 0){
                        printf("%d year %d month first day is Sunday!\n",year,i+1);
                }        
        }
}
void main(){
        for(int i = 1900; i<2000;i++){
                printf("*************%d year search result *********\n",i);
                FindMonth(i);        
                printf("\n");
                        
        }
}
======运行时间======
real        0m0.005s
user        0m0.000s
sys        0m0.005s

======运行结果======
*************1900 year search result *********
1900 year 4 month first day is Sunday!
1900 year 7 month first day is Sunday!

*************1901 year search result *********
1901 year 9 month first day is Sunday!
1901 year 12 month first day is Sunday!

*************1902 year search result *********
1902 year 6 month first day is Sunday!

*************1903 year search result *********
1903 year 2 month first day is Sunday!
1903 year 3 month first day is Sunday!
1903 year 11 month first day is Sunday!

*************1904 year search result *********
1904 year 5 month first day is Sunday!

*************1905 year search result *********
1905 year 1 month first day is Sunday!
1905 year 10 month first day is Sunday!

*************1906 year search result *********
1906 year 4 month first day is Sunday!
1906 year 7 month first day is Sunday!

*************1907 year search result *********
1907 year 9 month first day is Sunday!
1907 year 12 month first day is Sunday!

*************1908 year search result *********
1908 year 3 month first day is Sunday!
1908 year 11 month first day is Sunday!

*************1909 year search result *********
1909 year 8 month first day is Sunday!

*************1910 year search result *********
1910 year 5 month first day is Sunday!

*************1911 year search result *********
1911 year 1 month first day is Sunday!
1911 year 10 month first day is Sunday!

*************1912 year search result *********
1912 year 9 month first day is Sunday!
1912 year 12 month first day is Sunday!

*************1913 year search result *********
1913 year 6 month first day is Sunday!

*************1914 year search result *********
1914 year 2 month first day is Sunday!
1914 year 3 month first day is Sunday!
1914 year 11 month first day is Sunday!

*************1915 year search result *********
1915 year 8 month first day is Sunday!

*************1916 year search result *********
1916 year 10 month first day is Sunday!

*************1917 year search result *********
1917 year 4 month first day is Sunday!
1917 year 7 month first day is Sunday!

*************1918 year search result *********
1918 year 9 month first day is Sunday!
1918 year 12 month first day is Sunday!

*************1919 year search result *********
1919 year 6 month first day is Sunday!

*************1920 year search result *********
1920 year 2 month first day is Sunday!
1920 year 8 month first day is Sunday!

*************1921 year search result *********
1921 year 5 month first day is Sunday!

*************1922 year search result *********
1922 year 1 month first day is Sunday!
1922 year 10 month first day is Sunday!

*************1923 year search result *********
1923 year 4 month first day is Sunday!
1923 year 7 month first day is Sunday!

*************1924 year search result *********
1924 year 6 month first day is Sunday!

*************1925 year search result *********
1925 year 2 month first day is Sunday!
1925 year 3 month first day is Sunday!
1925 year 11 month first day is Sunday!

*************1926 year search result *********
1926 year 8 month first day is Sunday!

*************1927 year search result *********
1927 year 5 month first day is Sunday!

*************1928 year search result *********
1928 year 1 month first day is Sunday!
1928 year 4 month first day is Sunday!
1928 year 7 month first day is Sunday!

*************1929 year search result *********
1929 year 9 month first day is Sunday!
1929 year 12 month first day is Sunday!

*************1930 year search result *********
1930 year 6 month first day is Sunday!

*************1931 year search result *********
1931 year 2 month first day is Sunday!
1931 year 3 month first day is Sunday!
1931 year 11 month first day is Sunday!

*************1932 year search result *********
1932 year 5 month first day is Sunday!

*************1933 year search result *********
1933 year 1 month first day is Sunday!
1933 year 10 month first day is Sunday!

*************1934 year search result *********
1934 year 4 month first day is Sunday!
1934 year 7 month first day is Sunday!

*************1935 year search result *********
1935 year 9 month first day is Sunday!
1935 year 12 month first day is Sunday!

*************1936 year search result *********
1936 year 3 month first day is Sunday!
1936 year 11 month first day is Sunday!

*************1937 year search result *********
1937 year 8 month first day is Sunday!

*************1938 year search result *********
1938 year 5 month first day is Sunday!

*************1939 year search result *********
1939 year 1 month first day is Sunday!
1939 year 10 month first day is Sunday!

*************1940 year search result *********
1940 year 9 month first day is Sunday!
1940 year 12 month first day is Sunday!

*************1941 year search result *********
1941 year 6 month first day is Sunday!

*************1942 year search result *********
1942 year 2 month first day is Sunday!
1942 year 3 month first day is Sunday!
1942 year 11 month first day is Sunday!

*************1943 year search result *********
1943 year 8 month first day is Sunday!

*************1944 year search result *********
1944 year 10 month first day is Sunday!

*************1945 year search result *********
1945 year 4 month first day is Sunday!
1945 year 7 month first day is Sunday!

*************1946 year search result *********
1946 year 9 month first day is Sunday!
1946 year 12 month first day is Sunday!

*************1947 year search result *********
1947 year 6 month first day is Sunday!

*************1948 year search result *********
1948 year 2 month first day is Sunday!
1948 year 8 month first day is Sunday!

*************1949 year search result *********
1949 year 5 month first day is Sunday!

*************1950 year search result *********
1950 year 1 month first day is Sunday!
1950 year 10 month first day is Sunday!

*************1951 year search result *********
1951 year 4 month first day is Sunday!
1951 year 7 month first day is Sunday!

*************1952 year search result *********
1952 year 6 month first day is Sunday!

*************1953 year search result *********
1953 year 2 month first day is Sunday!
1953 year 3 month first day is Sunday!
1953 year 11 month first day is Sunday!

*************1954 year search result *********
1954 year 8 month first day is Sunday!

*************1955 year search result *********
1955 year 5 month first day is Sunday!

*************1956 year search result *********
1956 year 1 month first day is Sunday!
1956 year 4 month first day is Sunday!
1956 year 7 month first day is Sunday!

*************1957 year search result *********
1957 year 9 month first day is Sunday!
1957 year 12 month first day is Sunday!

*************1958 year search result *********
1958 year 6 month first day is Sunday!

*************1959 year search result *********
1959 year 2 month first day is Sunday!
1959 year 3 month first day is Sunday!
1959 year 11 month first day is Sunday!

*************1960 year search result *********
1960 year 5 month first day is Sunday!

*************1961 year search result *********
1961 year 1 month first day is Sunday!
1961 year 10 month first day is Sunday!

*************1962 year search result *********
1962 year 4 month first day is Sunday!
1962 year 7 month first day is Sunday!

*************1963 year search result *********
1963 year 9 month first day is Sunday!
1963 year 12 month first day is Sunday!

*************1964 year search result *********
1964 year 3 month first day is Sunday!
1964 year 11 month first day is Sunday!

*************1965 year search result *********
1965 year 8 month first day is Sunday!

*************1966 year search result *********
1966 year 5 month first day is Sunday!

*************1967 year search result *********
1967 year 1 month first day is Sunday!
1967 year 10 month first day is Sunday!

*************1968 year search result *********
1968 year 9 month first day is Sunday!
1968 year 12 month first day is Sunday!

*************1969 year search result *********
1969 year 6 month first day is Sunday!

*************1970 year search result *********
1970 year 2 month first day is Sunday!
1970 year 3 month first day is Sunday!
1970 year 11 month first day is Sunday!

*************1971 year search result *********
1971 year 8 month first day is Sunday!

*************1972 year search result *********
1972 year 10 month first day is Sunday!

*************1973 year search result *********
1973 year 4 month first day is Sunday!
1973 year 7 month first day is Sunday!

*************1974 year search result *********
1974 year 9 month first day is Sunday!
1974 year 12 month first day is Sunday!

*************1975 year search result *********
1975 year 6 month first day is Sunday!

*************1976 year search result *********
1976 year 2 month first day is Sunday!
1976 year 8 month first day is Sunday!

*************1977 year search result *********
1977 year 5 month first day is Sunday!

*************1978 year search result *********
1978 year 1 month first day is Sunday!
1978 year 10 month first day is Sunday!

*************1979 year search result *********
1979 year 4 month first day is Sunday!
1979 year 7 month first day is Sunday!

*************1980 year search result *********
1980 year 6 month first day is Sunday!

*************1981 year search result *********
1981 year 2 month first day is Sunday!
1981 year 3 month first day is Sunday!
1981 year 11 month first day is Sunday!

*************1982 year search result *********
1982 year 8 month first day is Sunday!

*************1983 year search result *********
1983 year 5 month first day is Sunday!

*************1984 year search result *********
1984 year 1 month first day is Sunday!
1984 year 4 month first day is Sunday!
1984 year 7 month first day is Sunday!

*************1985 year search result *********
1985 year 9 month first day is Sunday!
1985 year 12 month first day is Sunday!

*************1986 year search result *********
1986 year 6 month first day is Sunday!

*************1987 year search result *********
1987 year 2 month first day is Sunday!
1987 year 3 month first day is Sunday!
1987 year 11 month first day is Sunday!

*************1988 year search result *********
1988 year 5 month first day is Sunday!

*************1989 year search result *********
1989 year 1 month first day is Sunday!
1989 year 10 month first day is Sunday!

*************1990 year search result *********
1990 year 4 month first day is Sunday!
1990 year 7 month first day is Sunday!

*************1991 year search result *********
1991 year 9 month first day is Sunday!
1991 year 12 month first day is Sunday!

*************1992 year search result *********
1992 year 3 month first day is Sunday!
1992 year 11 month first day is Sunday!

*************1993 year search result *********
1993 year 8 month first day is Sunday!

*************1994 year search result *********
1994 year 5 month first day is Sunday!

*************1995 year search result *********
1995 year 1 month first day is Sunday!
1995 year 10 month first day is Sunday!

*************1996 year search result *********
1996 year 9 month first day is Sunday!
1996 year 12 month first day is Sunday!

*************1997 year search result *********
1997 year 6 month first day is Sunday!

*************1998 year search result *********
1998 year 2 month first day is Sunday!
1998 year 3 month first day is Sunday!
1998 year 11 month first day is Sunday!

*************1999 year search result *********
1999 year 8 month first day is Sunday!

永恒的蓝色梦想

#include<iostream>
#include<cmath>
using namespace std;



enum class Weekday :unsigned char {
    Sunday,
    Monday,
    Tuesday,
    Wednesday,
    Thursday,
    Friday,
    Saturday
};



long long math_mod(long long a, long long b)noexcept {
    return a - (long long)floor((long double)a / b) * b;
}



Weekday zeller(unsigned y, unsigned char m, unsigned char d)noexcept {
    if (m <= 2) {
        --y;
        m += 12;
    }

    unsigned c = y / 100;
    y -= c * 100;

    return Weekday(math_mod(y + (y >> 2) + (c >> 2) - (c << 1) + ((13 * (m + 1)) / 5) + d - 1, 7));
}



int main() {
    ios::sync_with_stdio(false);

    unsigned count = 0;
    unsigned char month;
    unsigned short year;


    for (year = 1901; year <= 2000; year++) {
        for (month = 1; month <= 12; month++) {
            if(zeller(year, month, 1) == Weekday::Sunday) {
                count++;
            }
        }
    }


    cout << count << endl;
    return 0;
}

4444567

def run(n):
    if n%100 != 0 and n%4==0:
        return 29
    elif n%100 == 0 and n%400==0:
        return 29
    else:
        return 28

n = 1901
count = 365
rz = [] #所有每个月第一天与1900 年 1 月 1 日相差余数为6的集合
while n <= 2000:
    dict1 = {1:31,2:run(n),3:31,4:30,5:31,6:30,7:31,8:31,9:30,10:31,11:30,12:31}
    yue = 1
    while yue <= 12:
        count += dict1[yue]
        if count%7 == 6:
            rz.append(count)
        yue += 1
    n += 1

print('20 世纪（1901 年 1 月 1 日到 2000 年 12 月 31 日）一共有 %s 个星期日落在了当月的第一天' % len(rz))

a1351468657

#include <stdio.h>

main()
{
        int i, j, k, count = 0;
        int day = 2;
        for (i = 1901; i <= 2000; i++)
        {
                if (day > 7)
                {
                        day %= 7;
                }
                for (j = 1; j <= 12; j++)
                {
                        k = j;
                        switch (k)
                        {
                        case 1: k = 1; break;
                        case 2: k = 32; break;
                        case 3: k = 60; break;
                        case 4: k = 91; break;
                        case 5: k = 121; break;
                        case 6: k = 152; break;
                        case 7: k = 182; break;
                        case 8: k = 213; break;
                        case 9: k = 244; break;
                        case 10: k = 274; break;
                        case 11: k = 305; break;
                        case 12: k = 335; break; 
                        }
                        if (i % 4)
                        {
                                k = k % 7;
                                k = k + day - 1;
                                if (k > 7)
                                {
                                        k %= 7;
                                }
                                if (k == 7 || k == 0)
                                {
                                        count++;
                                }
                        }
                        else
                        {
                                if (j > 2)
                                {
                                        k++;
                                }
                                k = k % 7;
                                k = k + day - 1;
                                if (k > 7)
                                {
                                        k %= 7;
                                }
                                if (k == 7 || k == 0)
                                {
                                        count++;                                
                                }
                        }                        
                }
                if (i % 4)
                {
                        day++;
                }
                else
                {
                        day += 2;
                }
        }
        printf("\n%d", count);
        
}

答案是： 171。若有改进的地方，希望大佬指出！

番杰

#include<stdio.h>
//                  1  2  3  4  5  6  7  8  9 10 11 12
const int Y[] = {0,31,28,31,30,31,30,31,31,30,31,30,31};
typedef struct  {
        year[1024];
        month[1024];
} YEAR;

int main(void)
{
        int num = 0;
        int sum = 366;
        YEAR Year;
        
        for(int i = 1901;i<2001;i++)
        {
                for(int j = 0;j <= 12;j++)
                { 
                        if((i % 4 == 0) && (j = 2))
                        {        
                                sum += Y[j] + 1;
                        }
                        else
                        {
                                sum += Y[j] ;
                        }
                        
                        if(sum % 7 = 6)
                        {                                
                                Year.year[num] = i;
                                Year.month[num] = j;
                                num++;        
                        }
                }
        }        
                
        printf("%d",num);
        
        return 0;
}