What is the formula for calculating the angle between the clock hands?

To calculate the angle, compute the absolute difference between the hour and minute hand positions. If the difference exceeds 180 degrees, subtract it from 360 to get the smaller angle.

How do I handle the minute hand affecting the hour hand's position?

The hour hand moves by 0.5 degrees per minute, so for each minute, the hour hand shifts slightly. Include this shift when calculating the angle.

Can this problem be solved using a brute force approach?

A brute force approach would be inefficient, as you would need to simulate the movement of the hands for every minute. A math-driven solution is more optimal.

What are the time and space complexities for this problem?

Both time and space complexity are O(1), as only a few basic calculations are required, with no additional memory usage.

What happens if the input time is outside the valid range?

The problem statement guarantees that inputs will be within the valid range (1 <= hour <= 12 and 0 <= minutes <= 59), so no special handling for out-of-range values is needed.

#1344

Medium

auto_awesome数学·driven

LeetCode 题解工作台

时钟指针的夹角

给你两个数 hour 和 minutes 。请你返回在时钟上，由给定时间的时针和分针组成的较小角的角度（60 单位制）。示例 1：输入： hour = 12, minutes = 30 输出： 165 示例 2：输入： hour = 3, minutes = 30 输出； 75 示例 3：输…

数学

题目描述

给你两个数 hour 和 minutes 。请你返回在时钟上，由给定时间的时针和分针组成的较小角的角度（60 单位制）。

示例 1：

输入：hour = 12, minutes = 30
输出：165

示例 2：

输入：hour = 3, minutes = 30
输出；75

示例 3：

输入：hour = 3, minutes = 15
输出：7.5

示例 4：

输入：hour = 4, minutes = 50
输出：155

示例 5：

输入：hour = 12, minutes = 0
输出：0

提示：

1 <= hour <= 12
0 <= minutes <= 59
与标准答案误差在 10^-5 以内的结果都被视为正确结果。

lightbulb

解题思路

方法一：数学

时针每小时移动 30 度，每分钟移动 0.5 度。分针每分钟移动 6 度。如果指针之间的夹角大于 180 度，则取其与 360 度的差值，以确保获得最小的夹角。

时间复杂度 $O(1)$ ，空间复杂度 $O(1)$ 。

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class Solution:
    def angleClock(self, hour: int, minutes: int) -> float:
        h = 30 * hour + 0.5 * minutes
        m = 6 * minutes
        diff = abs(h - m)
        return min(diff, 360 - diff)

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
Pay attention to how the minute hand shifts the hour hand slightly as time progresses.
question_mark
Candidates should show awareness of the fact that the angle must be adjusted for the smaller value, ensuring the correct result is found.
question_mark
Look for clarity in the explanation of the mechanics of both hands and how their positions affect the angle.

warning

常见陷阱

外企场景

error
Forgetting to account for the minute hand's effect on the hour hand.
error
Not adjusting the angle when it exceeds 180 degrees to ensure the smaller angle is returned.
error
Misunderstanding how to convert time into angles, leading to incorrect calculations.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Return the larger angle instead of the smaller one.
arrow_right_alt
Calculate the angle between the hands at a different scale, like a 24-hour format clock.
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Consider a case where the input time is provided in 24-hour format and adjust the formula accordingly.

help

常见问题

外企场景

继续练习

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