题目19：20世纪有多少个星期日是当月的第一天？,欧拉计划（Project Euler）,数据结构与算法,鱼C论坛

欧拉计划 发表于 2015-4-21 17:01:13

题目19：20世纪有多少个星期日是当月的第一天？

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 发表于 2016-7-1 13:34:23

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 发表于 2016-8-27 15:59:11

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 :
   if day == 31:
         m += 1
         day = 1

if m in :
   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 发表于 2016-10-11 15:48:23

本帖最后由 jerryxjr1220 于 2017-10-4 14:20 编辑

重新查证了一下，题目错了，1901年1月1日是星期二。
171

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 发表于 2017-1-10 22:08:37

# 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++-2C++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 :
            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

渡风发表于 2017-1-18 16:44:49

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=;%平年序列
Leap=;%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=;
else
   Temp=;
end
Century=Temp;
end
L=length(Century);%世纪的长度
Week=1:7;
if mod(L,7)==0
Weekday=repmat(Week,);%星期时间序列
else
Weekday=repmat(Week,);
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 发表于 2017-2-22 08:26:37

number = 0
day = 1
days =

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 = 29
else:
   days = 28
for i in days:
   day += i
   if day % 7 == 0 and year >= 1901:
         number += 1

print number

永丨恒 发表于 2017-2-22 10:03:09

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

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 发表于 2017-3-7 13:42:07

171

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

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

99592938 发表于 2017-3-15 11:00:28

本帖最后由 99592938 于 2017-3-15 11:05 编辑

wek = (1+365)%7 #1901-01-01是星期几
list_sun=[]
mon=
for year in range(1901,2001):
if year%4:mon=28
else:mon=29
for m in range(12):
if wek==0:list_sun.append('%d-%d' %(year,m+1))
wek=(wek+mon)%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 发表于 2018-3-15 22:29:50

#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 发表于 2018-6-28 20:49:33

#include <iostream>

using namespace std;

int main()
{
const short NYEAR={0,31,28,31,30,31,30,31,31,30,31,30,31};
const short RYEAR={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)
{
day-=RYEAR;
++month;
if(day==1)
{
++sum;
}
}
}
month=1;
}
else
{
while(month<=12)
{
day+=7;
if(day>=NYEAR)
{
day-=NYEAR;
++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 发表于 2018-9-15 20:38:41

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) % 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 发表于 2019-4-26 14:55:13

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 = 29
            else:
               mon = 28
         for i in range(1,mon+1):
            if wed == 8:
               wed = 1
            if i == 1 and wed == 7:
               if m != 1900:
                     li.append()
            wed += 1

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

刘富国 发表于 2019-12-6 09:28:01

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

题目说的是1990年1月1日是星期一

guoquanli 发表于 2020-1-10 13:06:35

本帖最后由 guoquanli 于 2020-1-10 13:13 编辑

#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 = {0,31,28,31,30,31,30,31,31,30,31,30};
if(flag){
dayArray = 29;
}
for(int i = 0; i<12;i++){
sum += dayArray;
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 发表于 2020-8-2 08:36:16

本帖最后由永恒的蓝色梦想于 2021-1-8 19:57 编辑

#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 发表于 2020-9-20 19:53:40

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
   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 发表于 2021-3-8 18:07:03

#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！

番杰发表于 2021-10-29 13:57:22

本帖最后由番杰于 2021-10-29 14:06 编辑

#include<stdio.h>
// 123456789 10 11 12
const int Y[] = {0,31,28,31,30,31,30,31,31,30,31,30,31};
typedef struct{
year;
month;
} 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 + 1;
}
else
{
sum += Y ;
}

if(sum % 7 = 6)
{
Year.year = i;
Year.month = j;
num++;
}
}
}

printf("%d",num);

return 0;
}

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题目19：20世纪有多少个星期日是当月的第一天？