给定时间的时分和分针的终点之间的距离

给定四个整数H ， M ， L1和L2 ，它们分别表示12小时制时钟中的小时和分钟，L1和L2分别表示时针和分针的长度。任务是找到时针和分针的端点之间的距离。
例子：

Input: H = 3, M = 30, L1 = 3, L2 = 4 
Output: 4.33499 
Explanation: 
At 3:30, distance between end point of hour hand and minute hand is 4.33499 
 

Input: H = 10, M = 30, L1 = 3, L2 = 4 
Output: 6.47898 
Explanation: 
At 10:30, distance between end point of hour hand and minute hand is 6.47898 
 

方法：想法是找到给定时间的时针和分针之间的角度，然后可以借助余弦公式来计算时针和分针的端点之间的距离–

Distance Between End Points of the Hour and minute hand = 

$\sqrt{L1^{2} + L2^{2} - 2 * L1 * L2 * cos(angle^{o})}$

下面是上述方法的实现：

C++

// C++ implementation to find the
// distance between the end points
// of the hour and minute hand
 
#include 
using namespace std;
 
// Function to find the angle between
// Hour hand and minute hand
int calcAngle(double h, double m)
{
    // Validate the input
    if (h < 0 || m < 0
        || h > 12 || m > 60)
        printf("Wrong input");
 
    if (h == 12)
        h = 0;
    if (m == 60)
        m = 0;
 
    // Calculate the angles moved
    // by hour and minute hands
    // with reference to 12:00
    int hour_angle = 0.5 * (h * 60 + m);
    int minute_angle = 6 * m;
 
    // Find the difference
    // between two angles
    int angle = abs(hour_angle - minute_angle);
 
    // Return the smaller angle
    // of two possible angles
    angle = min(360 - angle, angle);
 
    return angle;
}
 
// Function to calculate
// cos value of angle c
float cal_cos(float n)
{
    float accuracy = 0.0001, x1,
          denominator, cosx, cosval;
 
    // Converting degrees to radian
    n = n * (3.142 / 180.0);
 
    x1 = 1;
 
    // Maps the sum
    // along the series
    cosx = x1;
 
    // Holds the actual
    // value of sin(n)
    cosval = cos(n);
    int i = 1;
    do {
        denominator = 2 * i * (2 * i - 1);
        x1 = -x1 * n * n / denominator;
        cosx = cosx + x1;
        i = i + 1;
    } while (accuracy <= fabs(cosval - cosx));
 
    return cosx;
}
 
// Function to distance between the
// endpoints of the hour and minute hand
float distanceEndpoints(
    int a, int b, float c)
{
    float angle = cal_cos(c);
    return sqrt((a * a)
                + (b * b)
                - 2 * a * b * angle);
}
 
// Driver Code
int main()
{
    // Time
    int hour = 3;
    int min = 30;
 
    // Length of
    // hour hand
    int hourHand = 3;
 
    // Length of
    // minute hand
    int minHand = 4;
 
    // calling Function for
    // finding angle
    // between hour hand
    // and minute hand
    double angle = calcAngle(hour, min);
 
    // Function for finding
    // distance between
    // end points of minute
    // hand and hour hand
    float distance = distanceEndpoints(
        minHand, hourHand, angle);
    cout << distance;
    return 0;
}

Java

// Java implementation to find the
// distance between the end points
// of the hour and minute hand
class GFG{
 
// Function to find the angle between
// Hour hand and minute hand
static int calcAngle(double h, double m)
{
     
    // Validate the input
    if (h < 0 || m < 0 ||
        h > 12 || m > 60)
        System.out.printf("Wrong input");
 
    if (h == 12)
        h = 0;
    if (m == 60)
        m = 0;
 
    // Calculate the angles moved
    // by hour and minute hands
    // with reference to 12:00
    int hour_angle = (int)(0.5 * (h * 60 + m));
    int minute_angle = (int)(6 * m);
 
    // Find the difference
    // between two angles
    int angle = Math.abs(hour_angle -
                         minute_angle);
 
    // Return the smaller angle
    // of two possible angles
    angle = Math.min(360 - angle, angle);
 
    return angle;
}
 
// Function to calculate
// cos value of angle c
static float cal_cos(float n)
{
    float accuracy = (float) 0.0001, x1,
                            denominator,
                           cosx, cosval;
 
    // Converting degrees to radian
    n = (float)(n * (3.142 / 180.0));
 
    x1 = 1;
 
    // Maps the sum along
    // the series
    cosx = x1;
 
    // Holds the actual
    // value of sin(n)
    cosval = (float)Math.cos(n);
    int i = 1;
     
    do
    {
        denominator = 2 * i * (2 * i - 1);
        x1 = -x1 * n * n / denominator;
        cosx = cosx + x1;
        i = i + 1;
    } while (accuracy <= Math.abs(cosval - cosx));
 
    return cosx;
}
 
// Function to distance between the
// endpoints of the hour and minute hand
static float distanceEndpoints(int a, int b,
                                    float c)
{
    float angle = cal_cos(c);
    return (float) Math.sqrt((a * a) +
                             (b * b) -
                              2 * a * b * angle);
}
 
// Driver code
public static void main(String[] args)
{
     
    // Time
    int hour = 3;
    int min = 30;
 
    // Length of
    // hour hand
    int hourHand = 3;
 
    // Length of
    // minute hand
    int minHand = 4;
 
    // Calling Function
    // for finding angle
    // between hour hand
    // and minute hand
    double angle = calcAngle(hour, min);
 
    // Function for finding
    // distance between
    // end points of minute
    // hand and hour hand
    float distance = distanceEndpoints(minHand,
                                       hourHand,
                                       (long)angle);
    System.out.printf("%.5f", distance);
}
}
 
// This code is contributed by 29AjayKumar

Python3

# Python3 implementation to find the
# distance between the end points
# of the hour and minute hand
import math
 
# Function to find the angle
# between Hour hand and minute
# hand
def calcAngle(h, m):
 
    # Validate the input
    if (h < 0 or m < 0 or
        h > 12 or m > 60):
        print("Wrong input")
 
    if (h == 12):
        h = 0
    if (m == 60):
        m = 0
 
    # Calculate the angles moved
    # by hour and minute hands
    # with reference to 12:00
    hour_angle = 0.5 * (h * 60 + m)
    minute_angle = 6 * m
 
    # Find the difference
    # between two angles
    angle = abs(hour_angle -
                minute_angle)
 
    # Return the smaller angle
    # of two possible angles
    angle = min(360 -
                angle, angle)
     
    return angle
 
# Function to calculate
# cos value of angle c
def cal_cos(n):
 
    accuracy = 0.0001
 
    # Converting degrees to
    # radian
    n = n * (3.142 / 180.0)
 
    x1 = 1
 
    # Maps the sum
    # along the series
    cosx = x1
 
    # Holds the actual
    # value of sin(n)
    cosval = math.cos(n)
    i = 1
     
    while True:
        denominator = 2 * i * (2 * i - 1)
        x1 = -x1 * n * n / denominator
        cosx = cosx + x1
        i = i + 1
         
        if accuracy > math.fabs(cosval -
                                cosx):
            break
     
    return cosx
 
# Function to distance between
# the endpoints of the hour
# and minute hand
def distanceEndpoints(a, b, c):
     
    angle = cal_cos(c)
    return math.sqrt((a * a) +
                     (b * b) -
                     2 * a * b * angle)
 
# Driver code
 
# Time
hour = 3
Min = 30
 
# Length of
# hour hand
hourHand = 3
 
# Length of
# minute hand
minHand = 4
 
# calling Function for
# finding angle
# between hour hand
# and minute hand
angle = calcAngle(hour,
                  Min)
 
# Function for finding
# distance between
# end points of minute
# hand and hour hand
distance = distanceEndpoints(minHand,
                             hourHand,
                             angle)
print ('%.5f' % distance)
 
# This code is contributed by divyeshrabadiya07

C#

// C# implementation to find the
// distance between the end points
// of the hour and minute hand
using System;
class GFG{
 
// Function to find the angle between
// Hour hand and minute hand
static int calcAngle(double h, double m)
{
     
    // Validate the input
    if (h < 0 || m < 0 ||
        h > 12 || m > 60)
        Console.Write("Wrong input");
 
    if (h == 12)
        h = 0;
    if (m == 60)
        m = 0;
 
    // Calculate the angles moved
    // by hour and minute hands
    // with reference to 12:00
    int hour_angle = (int)(0.5 * (h * 60 + m));
    int minute_angle = (int)(6 * m);
 
    // Find the difference
    // between two angles
    int angle = Math.Abs(hour_angle -
                       minute_angle);
 
    // Return the smaller angle
    // of two possible angles
    angle = Math.Min(360 - angle, angle);
 
    return angle;
}
 
// Function to calculate
// cos value of angle c
static float cal_cos(float n)
{
    float accuracy = (float) 0.0001, x1,
                            denominator,
                           cosx, cosval;
 
    // Converting degrees to radian
    n = (float)(n * (3.142 / 180.0));
 
    x1 = 1;
 
    // Maps the sum along
    // the series
    cosx = x1;
 
    // Holds the actual
    // value of sin(n)
    cosval = (float)Math.Cos(n);
    int i = 1;
     
    do
    {
        denominator = 2 * i * (2 * i - 1);
        x1 = -x1 * n * n / denominator;
        cosx = cosx + x1;
        i = i + 1;
    } while (accuracy <= Math.Abs(cosval - cosx));
 
    return cosx;
}
 
// Function to distance between the
// endpoints of the hour and minute hand
static float distanceEndpoints(int a, int b,
                                    float c)
{
    float angle = cal_cos(c);
    return (float) Math.Sqrt((a * a) +
                             (b * b) -
                          2 * a * b * angle);
}
 
// Driver code
public static void Main()
{
     
    // Time
    int hour = 3;
    int min = 30;
 
    // Length of
    // hour hand
    int hourHand = 3;
 
    // Length of
    // minute hand
    int minHand = 4;
 
    // Calling Function
    // for finding angle
    // between hour hand
    // and minute hand
    double angle = calcAngle(hour, min);
 
    // Function for finding
    // distance between
    // end points of minute
    // hand and hour hand
    float distance = distanceEndpoints(minHand,
                                      hourHand,
                                  (long)angle);
    Console.Write(distance);
}
}
 
// This code is contributed by Code_Mech

输出：

4.33499