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# Find a time for which angle between hour and minute hands is given theta

• Difficulty Level : Medium
• Last Updated : 16 Feb, 2023

Given angle theta, find a possible time (in hh:mm format) when angle between hour hand and clock hand is theta. If no such time exists then print -1.

Examples :

```Input : theta = 90.0
Output : 3:0 ```
```Input : theta = 60.0
Output : 2:0```

We have discussed how to find angle for given time in below post.
Calculate the angle between hour hand and minute hand

In this problem, we are asked to do reverse. Since there are 12 possibilities for hour and 60 possibilities for minute, we loop through all possible time which is 12*60 = 720, if angle for any time is equal to given theta then we print that time.

## C++

 `// C++ program to find time for a given angle.``#include ``using` `namespace` `std;`` ` `// function to find angle between``// hour hand and minute hand``float` `calcAngle(``int` `hh, ``int` `mm)``{``    ``// Calculate the angles moved by hour and``    ``// minute hands with reference to 12:00``    ``float` `hour_angle = 0.5 * (hh*60 + mm);``    ``float` `minute_angle = 6*mm;`` ` `    ``// Find the difference between two angles``    ``float` `angle = ``abs``(hour_angle - minute_angle);`` ` `    ``// Return the smaller angle of two possible``    ``// angles``    ``angle = min(360-angle, angle);`` ` `    ``return` `angle;``}`` ` `// function to print all time when angle between``// hour hand and minute hand is theta``void` `printTime(``float` `theta)``{``    ``for` `(``int` `hh=0; hh<12; hh++)``    ``{``        ``for` `(``int` `mm=0; mm<60; mm++)``        ``{``            ``if` `(calcAngle(hh, mm)==theta)``            ``{``                ``printf``(``"%d:%d\n"``, hh, mm);``                ``return``;``            ``}``        ``}``    ``}``    ``printf``(``"Input angle not valid.\n"``);``    ``return``;``}`` ` `// driver code to test above function``int` `main()``{``    ``float` `theta = 90.0;``    ``printTime(theta);``    ``return` `0;``}`

## Java

 `// Java program to find time``// for a given angle.``class` `GFG``{``// function to find angle between``// hour hand and minute hand``static` `float` `calcAngle(``int` `hh, ``int` `mm)``{``    ``// Calculate the angles moved by hour and``    ``// minute hands with reference to 12:00``    ``float` `hour_angle = ``0``.5f * (hh * ``60` `+ mm);``    ``float` `minute_angle = ``6` `* mm;`` ` `    ``// Find the difference between two angles``    ``float` `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 print all time when ``// angle between hour hand and minute``// hand is theta``static` `void` `printTime(``float` `theta)``{``    ``for` `(``int` `hh = ``0``; hh < ``12``; hh++)``    ``{``        ``for` `(``int` `mm = ``0``; mm < ``60``; mm++)``        ``{``            ``if` `(calcAngle(hh, mm) == theta)``            ``{``                ``System.out.println(hh + ``":"` `+ mm);``                ``return``;``            ``}``        ``}``    ``}``     ` `    ``System.out.println(``"Input angle not valid."``);``    ``return``;``} `` ` `// Driver code ``public` `static` `void` `main (String[] args)``{``    ``float` `theta = ``90``.0f;``    ``printTime(theta);``}``}`` ` `// This code is contributed by Anant Agarwal.`

## Python3

 `# Python 3 program to find time for a``# given angle.`` ` `# function to find angle between``# hour hand and minute hand``def` `calcAngle(hh, mm):`` ` `    ``# Calculate the angles moved by``    ``# hour and minute hands with ``    ``# reference to 12:00``    ``hour_angle ``=` `0.5` `*` `(hh ``*` `60` `+` `mm)``    ``minute_angle ``=` `6` `*` `mm`` ` `    ``# 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 print all time when``# angle between hour hand and minute``# hand is theta``def` `printTime(theta):`` ` `    ``for` `hh ``in` `range``(``0``, ``12``):``        ``for` `mm ``in` `range``(``0``, ``60``):``            ``if` `(calcAngle(hh, mm)``=``=``theta):``                ``print``(hh, ``":"``, mm, sep ``=` `"")``                ``return``             ` `    ``print``(``"Input angle not valid."``)``    ``return`` ` `# driver code to test above function``theta ``=` `90.0``printTime(theta)`` ` `# This code is contributed by Smitha`

## C#

 `// C# program to find time for a given``// angle.``using` `System;`` ` `class` `GFG {`` ` `    ``// function to find angle between``    ``// hour hand and minute hand``    ``static` `float` `calcAngle(``int` `hh, ``int` `mm)``    ``{``         ` `        ``// Calculate the angles moved by hour``        ``// and minute hands with reference ``        ``// to 12:00``        ``float` `hour_angle = 0.5f * (hh * 60 + mm);``        ``float` `minute_angle = 6 * mm;``     ` `        ``// Find the difference between two angles``        ``float` `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 print all time when ``    ``// angle between hour hand and minute``    ``// hand is theta``    ``static` `void` `printTime(``float` `theta)``    ``{``        ``for` `(``int` `hh = 0; hh < 12; hh++)``        ``{``            ``for` `(``int` `mm = 0; mm < 60; mm++)``            ``{``                ``if` `(calcAngle(hh, mm) == theta)``                ``{``                    ``Console.WriteLine(hh + ``":"` `+ mm);``                    ``return``;``                ``}``            ``}``        ``}``         ` `        ``Console.WriteLine(``"Input angle not valid."``);``        ``return``;``    ``} ``     ` `    ``// Driver code ``    ``public` `static` `void` `Main ()``    ``{``        ``float` `theta = 90.0f;``         ` `        ``printTime(theta);``    ``}``}`` ` `// This code is contributed by vt_m.`

## PHP

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## Javascript

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Output :

`3:0`

Time Complexity : O(1)
Auxiliary Space : O(1)

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