How do I calculate the day of the week for a given date?

You can calculate the day of the week by using modular arithmetic or algorithms like Zeller's Congruence to count the number of days and adjust for leap years.

What is Zeller's Congruence and how does it help?

Zeller's Congruence is a formula used to calculate the day of the week for any given date. It uses the year, month, and day, with a specific adjustment for January and February.

Why do I need to account for leap years in this problem?

Leap years affect the number of days in a year, particularly in February. Failing to account for them could result in incorrect day-of-week calculations for certain dates.

How do I handle months in January and February in Zeller's Congruence?

In Zeller's Congruence, January and February are treated as the 13th and 14th months of the previous year, requiring adjustment to the year and month values.

Can this problem be solved in constant time?

Yes, using mathematical formulas like Zeller's Congruence, this problem can be solved in constant time O(1), as the algorithm only requires a few arithmetic operations.

#1185

Easy

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LeetCode 题解工作台

一周中的第几天

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", "Fri…

数学

题目描述

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"}。

注意：1971 年 1 月 1 日是星期五。

示例 1：

输入：day = 31, month = 8, year = 2019
输出："Saturday"

示例 2：

输入：day = 18, month = 7, year = 1999
输出："Sunday"

示例 3：

输入：day = 15, month = 8, year = 1993
输出："Sunday"

提示：

给出的日期一定是在 1971 到 2100 年之间的有效日期。

lightbulb

解题思路

方法一：蔡勒公式

我们可以使用蔡勒公式来计算星期几，蔡勒公式如下：

w = (\left \lfloor \frac{c}{4} \right \rfloor - 2c + y + \left \lfloor \frac{y}{4} \right \rfloor + \left \lfloor \frac{13(m+1)}{5} \right \rfloor + d - 1) \bmod 7

其中：

w: 星期（从 Sunday 开始）
c: 年份前两位
y: 年份后两位
m: 月（m 的取值范围是 3 至 14，即在蔡勒公式中，某年的 1、2 月要看作上一年的 13、14 月来计算，比如 2003 年 1 月 1 日要看作 2002 年的 13 月 1 日来计算）
d: 日
⌊⌋: 向下取整
mod: 取余

时间复杂度 $O(1)$ ，空间复杂度 $O(1)$ 。

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class Solution:
    def dayOfTheWeek(self, day: int, month: int, year: int) -> str:
        return datetime.date(year, month, day).strftime('%A')

speed

复杂度分析

指标	值
时间	Depends on the final approach
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
The candidate demonstrates a clear understanding of modular arithmetic and its application in date calculations.
question_mark
The candidate correctly handles edge cases such as leap years and month boundaries.
question_mark
The candidate exhibits a solid grasp of mathematical patterns involved in calculating days of the week.

warning

常见陷阱

外企场景

error
Forgetting to account for leap years, which may lead to incorrect weekday results for dates in February.
error
Incorrectly handling months for January and February when applying Zeller's Congruence, which adjusts the month by subtracting 1.
error
Overcomplicating the solution by introducing unnecessary loops or data structures when a constant time solution is possible.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Given a different date format, such as a string, adapt the solution to parse the input correctly before applying the same approach.
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Solve the problem without using Zeller's Congruence by calculating the days in a more manual way.
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Change the range of valid dates, for example from 1900 to 2050, and adjust the solution to handle that new range.

help

常见问题

外企场景

继续练习

#1175 质数排列 #1201 丑数 III #1154 一年中的第几天