This problem is know as Clock angle problem where we need to find angle between hands of an analog clock at a given time.
Examples:
Input: h = 12:00, m = 30.00 Output: 165 degree Input: h = 3.00, m = 30.00 Output: 75 degree
The idea is to take 12:00 (h = 12, m = 0) as a reference. Following are detailed steps.
1) Calculate the angle made by hour hand with respect to 12:00 in h hours and m minutes.
2) Calculate the angle made by minute hand with respect to 12:00 in h hours and m minutes.
3) The difference between two angles is the angle between two hands.
How to calculate the two angles with respect to 12:00?
The minute hand moves 360 degree in 60 minute(or 6 degree in one minute) and hour hand moves 360 degree in 12 hours(or 0.5 degree in 1 minute). In h hours and m minutes, the minute hand would move (h*60 + m)*6 and hour hand would move (h*60 + m)*0.5.
C++
// C++ program to find angle between hour and minute hands #include <bits/stdc++.h> using namespace std; // Utility function to find minimum of two integers int min(int x, int y) { return (x < y)? x: y; } 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; } // Driver program to test above function int main() { cout << calcAngle(9, 60) << endl; cout << calcAngle(3, 30) << endl; return 0; } // This is code is contributed by rathbhupendra |
C
// C program to find angle between hour and minute hands #include <stdio.h> #include <stdlib.h> // Utility function to find minimum of two integers int min(int x, int y) { return (x < y)? x: y; } 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; } // Driver program to test above function int main() { printf("%d n", calcAngle(9, 60)); printf("%d n", calcAngle(3, 30)); return 0; } |
Java
// Java program to find angle between hour and minute hands import java.io.*; class GFG { // Function to calculate the angle static int calcAngle(double h, double m) { // validate the input if (h <0 || m < 0 || h >12 || m > 60) System.out.println("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); // smaller angle of two possible angles angle = Math.min(360-angle, angle); return angle; } // Driver program public static void main (String[] args) { System.out.println(calcAngle(9, 60)+" degree"); System.out.println(calcAngle(3, 30)+" degree"); } } // Contributed by Pramod Kumar |
Python
# Python program to find angle # between hour and minute hands # Function to Calculate angle b/w # 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 # Driver program h = 9m = 60print('Angle ', calcAngle(h,m)) # This code is contributed by Danish Raza |
C#
// C# program to find angle between // hour and minute hands using System; class GFG { // Function to calculate the angle 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); // smaller angle of two possible angles angle = Math.Min(360 - angle, angle); return angle; } // Driver code public static void Main () { Console.WriteLine(calcAngle(9, 60)); Console.Write(calcAngle(3, 30)); } } // This code is contributed by Nitin Mittal. |
PHP
<?php // PHP program to find // angle between hour // and minute hands // Utility function to // find minimum of two // integers function mintwo($x, $y) { return ($x < $y) ? $x : $y; } function calcAngle($h, $m) { // validate the input if ($h <0 || $m < 0 || $h >12 || $m > 60) echo "Wrong input"; if ($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; } // Driver Code echo calcAngle(9, 60), "
"; echo calcAngle(3, 30), "
"; // This code is contributed by ajit ?> |
Output:
90 75
Exercise: Find all times when hour and minute hands get superimposed.
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