目录
Day of the Week
题目大意
常规方法
Python代码
Golang代码
C++代码
基姆拉尔森公式
Python代码
Golang代码
C++代码
使用库函数
Python代码
Golang代码
C++代码
Day of the Week
Given a date, return the corresponding day of the week for that date.
The input is given as three integers representing the day , month and year respectively.
Return the answer as one of the following values {"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"} .
Example 1:
Input: day = 31, month = 8, year = 2019
Output: "Saturday"
Example 2:
Input: day = 18, month = 7, year = 1999
Output: "Sunday"
Example 3:
Input: day = 15, month = 8, year = 1993
Output: "Sunday"
题目大意
给你一个日期，请你设计一个算法来判断它是对应一周中的哪一天。
输入为三个整数： day、 month 和 year，分别表示日、月、年。
您返回的结果必须是这几个值中的一个 {"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday",
"Friday", "Saturday"}。
提示：
给出的日期一定是在 1971 到 2100 年之间的有效日期。
解题思路：
给出一个日期，要求算出这一天是星期几。
常规方法
从1971.1.1起，先累计整年year、整月month-1的天数，再加上最后一个月month的天数day，然后总天数减1后与7求余。最后得到的余数在星期字串数组中位置索引，显然前提要知道1971.1.1这个基准日期是星期几，再作一个索引位移就是答案。
另外常规方法还需要判断year是否闰年，规则：y%4==0 and y%100!=0 or y%400==0，据说是1582
Python代码
python代码非常简单，不需另外导入库只用内置函数就能搞定。
class Solution(object):
def DayOfWeek(self, year, month, day):
days = 0
isLeapYear = lambda y:y%4==0 and y%100!=0 or y%400==0
monthday = [31,28,31,30,31,30,31,31,30,31,30,31]
week = ["Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"]
monthday[1] = 29 if isLeapYear(year) else 28
for i in range(1971,year):
days += 366 if isLeapYear(i) else 365
days += sum(monthday[:month-1], day-1)
return week[(days+5)%7]
if __name__ == "__main__":
s = Solution()
print(s.DayOfWeek(2019,8,31))
print(s.DayOfWeek(1999,7,18))
print(s.DayOfWeek(1993,8,15))
print(s.DayOfWeek(1971,6,12))
print(s.DayOfWeek(2023,2,22))
print(s.DayOfWeek(2040,6,13))输出：
Saturday
Sunday
Sunday
Saturday
Wednesday
Wednesday
Golang代码
基本原理相同，另外自定义一个数组求和公式即可。
package main
import "fmt"
func DayOfWeek(year int, month int, day int) string {
days := 0
isLeapYear := func(y int) bool {
return y%4 == 0 && y%100 != 0 || y%400 == 0
}
Sum := func(nums []int, initNum int) int {
var sumNum int = 0
for _, num := range nums {
sumNum += num
}
return sumNum + initNum
}
monthday := []int{31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}
week := []string{"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"}
if isLeapYear(year) {
monthday[1] = 29
} else {
monthday[1] = 28
}
for i := 1971; i < year; i++ {
if isLeapYear(i) {
days += 366
} else {
days += 365
}
}
days += Sum(monthday[:month-1], day-1)
return week[(days+5)%7]
}
func main() {
fmt.Println(DayOfWeek(2019, 8, 31))
fmt.Println(DayOfWeek(1999, 7, 18))
fmt.Println(DayOfWeek(1993, 8, 15))
fmt.Println(DayOfWeek(1971, 6, 12))
fmt.Println(DayOfWeek(2023, 2, 22))
fmt.Println(DayOfWeek(2040, 6, 13))
}输出：
Saturday
Sunday
Sunday
Saturday
Wednesday
Wednesday
成功: 进程退出代码 0.
C++代码
引入C++11的容器vector，可以省掉最后一个非整年的各月份日数循环累加，只要用<numeric>库中的函数accumulate，方便累加非整年的各月份日数，并且把day作为基准数一并累加掉。
#include<iostream>
#include<vector>
#include<numeric>
using namespace std;
class Solution
{
public:
string DayOfWeek(int year, int month, int day)
{
int days = 0;
auto isLeapYear = [](int y) { return y%4==0 && y%100!=0 || y%400==0; };
vector<int> monthday = {31,28,31,30,31,30,31,31,30,31,30,31};
vector<string> week = {"Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"};
monthday[1] = isLeapYear(year) ? 29 : 28;
for (int i=1971;i<year;i++)
days += isLeapYear(i) ? 366 : 365;
days += accumulate(monthday.begin(), monthday.begin()+month-1, day-1);
return week[(days+5)%7];
}
};
int main()
{
Solution s;
cout << s.DayOfWeek(2019,8,31) << endl;
cout << s.DayOfWeek(1999,7,18) << endl;
cout << s.DayOfWeek(1993,8,15) << endl;
cout << s.DayOfWeek(1971,6,12) << endl;
cout << s.DayOfWeek(2023,2,22) << endl;
cout << s.DayOfWeek(2040,6,13) << endl;
return 0;
}Dev C++ 6.3 编译通过：
Saturday
Sunday
Sunday
Saturday
Wednesday
Wednesday--------------------------------
Process exited after 0.02175 seconds with return value 0
请按任意键继续. . .
基姆拉尔森公式
万能的日期计算公式，不用知道基准日是哪一天，也不需要判断year是否为闰年。
公式：weekday = (day+2month+3(month+1)/5+year+year/4-year/100+year/400+1)%7
注意：1月和2月需看做上一年的13月与14月，即 month<3时， year-=1; month+=12
Python代码
class Solution(object):
def DayOfWeek(self, year, month, day):
week = ["Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"]
if month<3: year, month = year-1, month+12
weekday = (day+2*month+3*(month+1)//5+year+year//4-year//100+year//400+1)%7
return dict(zip(range(7),week)).get(weekday)
if __name__ == "__main__":
s = Solution()
print(s.DayOfWeek(2019,8,31))
print(s.DayOfWeek(1999,7,18))
print(s.DayOfWeek(1993,8,15))
print(s.DayOfWeek(1971,6,12))
print(s.DayOfWeek(2023,2,22))
print(s.DayOfWeek(2040,6,13))Golang代码
package main
import "fmt"
func DayOfWeek(year int, month int, day int) string {
week := []string{"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"}
if month < 3 {
year -= 1
month += 12
}
weekday := (day + 2*month + 3*(month+1)/5 + year + year/4 - year/100 + year/400 + 1) % 7
return week[weekday]
}
func main() {
fmt.Println(DayOfWeek(2019, 8, 31))
fmt.Println(DayOfWeek(1999, 7, 18))
fmt.Println(DayOfWeek(1993, 8, 15))
fmt.Println(DayOfWeek(1971, 6, 12))
fmt.Println(DayOfWeek(2023, 2, 22))
fmt.Println(DayOfWeek(2040, 6, 13))
}C++代码
#include<iostream>
using namespace std;
class Solution
{
public:
string DayOfWeek(int year, int month, int day)
{
const char *week[7] = {"Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"};
if (month < 3) {
year -= 1;
month += 12;
}
int weekday = (day+2*month+3*(month+1)/5+year+year/4-year/100+year/400+1)%7;
return week[weekday];
}
};
int main()
{
Solution s;
cout << s.DayOfWeek(2019,8,31) << endl;
cout << s.DayOfWeek(1999,7,18) << endl;
cout << s.DayOfWeek(1993,8,15) << endl;
cout << s.DayOfWeek(1971,6,12) << endl;
cout << s.DayOfWeek(2023,2,22) << endl;
cout << s.DayOfWeek(2040,6,13) << endl;
return 0;
}
使用库函数
Python代码
datetime库
import datetime
class Solution(object):
def DayOfWeek(self, year, month, day):
week = ["Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"]
weekday = datetime.date(year,month,day).isoweekday()
return week[weekday%7]
if __name__ == "__main__":
s = Solution()
print(s.DayOfWeek(2019,8,31))
print(s.DayOfWeek(1999,7,18))
print(s.DayOfWeek(1993,8,15))
print(s.DayOfWeek(1971,6,12))
print(s.DayOfWeek(2023,2,22))
print(s.DayOfWeek(2040,6,13))calendar库
import calendar
class Solution(object):
def DayOfWeek(self, year, month, day):
week = ["Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"]
weekday = calendar.weekday(year,month,day)+1
return week[weekday%7]
if __name__ == "__main__":
s = Solution()
print(s.DayOfWeek(2019,8,31))
print(s.DayOfWeek(1999,7,18))
print(s.DayOfWeek(1993,8,15))
print(s.DayOfWeek(1971,6,12))
print(s.DayOfWeek(2023,2,22))
print(s.DayOfWeek(2040,6,13))Golang代码
time库，超级省事，连星期数组都不用了。
package main
import (
"fmt"
"time"
)
func DayOfWeek(year int, month int, day int) string {
return time.Date(year, time.Month(month), day, 0, 0, 0, 0, time.Local).Weekday().String()
}
func main() {
fmt.Println(DayOfWeek(2019, 8, 31))
fmt.Println(DayOfWeek(1999, 7, 18))
fmt.Println(DayOfWeek(1993, 8, 15))
fmt.Println(DayOfWeek(1971, 6, 12))
fmt.Println(DayOfWeek(2023, 2, 22))
fmt.Println(DayOfWeek(2040, 6, 13))
}C++代码
ctime库
#include<iostream>
#include<ctime>
using namespace std;
class Solution
{
public:
string DayOfWeek(int year, int month, int day)
{
const char *week[7] = {"Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"};
struct tm t = {0};
t.tm_year = year - 1900;
t.tm_mon = month - 1;
t.tm_mday = day;
mktime(&t);
return week[t.tm_wday%7];
}
};
int main()
{
Solution s;
cout << s.DayOfWeek(2019,8,31) << endl;
cout << s.DayOfWeek(1999,7,18) << endl;
cout << s.DayOfWeek(1993,8,15) << endl;
cout << s.DayOfWeek(1971,6,12) << endl;
cout << s.DayOfWeek(2023,2,22) << endl;
cout << s.DayOfWeek(2040,6,13) << endl;
return 0;
}输出：
Saturday
Sunday
Sunday
Saturday
Wednesday
Sunday--------------------------------
Process exited after 0.02402 seconds with return value 0
请按任意键继续. . .
发现没？ 2040.6.13返回的星期是错的！
网上查了资料，原来ctime库的CTime对象是有指定范围的：
static CTime WINAPI GetCurrentTime( );
获取系统当前日期和时间。返回表示当前日期和时间的CTime对象。
int GetYear( ) const；
获取CTime对象表示时间的年份。范围从1970年1月1日到2038年1月18日。
时间范围测试：
#include<iostream>
#include<ctime>
using namespace std;
class Solution
{
public:
string DayOfWeek(int year, int month, int day)
{
const char *week[7] = {"Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"};
struct tm t = {0};
t.tm_year = year - 1900;
t.tm_mon = month - 1;
t.tm_mday = day;
mktime(&t);
return week[t.tm_wday%7];
}
};
int main()
{
Solution s;
for (int i=16;i<25;i++)
cout << i << ":" << s.DayOfWeek(2038,1,i) << endl;
return 0;
}测试结果：
16:Saturday
17:Sunday
18:Monday
19:Tuesday
20:Sunday
21:Sunday
22:Sunday
23:Sunday
24:Sunday--------------------------------
Process exited after 0.05159 seconds with return value 0
请按任意键继续. . .
2038.1.19日的星期也对，之后的全部返回Sunday。
修改这个问题，技术上一点问题都没有。 目前C++都发展到C++20了，而我用的是C++11，暂不知道之后版本的库文件有没有对此问题作过更新。那么，问题来了：
之前用C语言写的的软件，用ctime或者time.h获取时间的软件在2038年1月19日之后都会发生错误。还好，还有整整15年时间来改正这个“时间Bug”。
