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

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 <bits/stdc++.h>
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

<?php
// PHP program to find
// time for a given angle.

// Function to find angle between
// hour hand and minute hand
function 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
function printTime( $theta)
{
    for ($hh = 0; $hh < 12; $hh++)
    {
        for ($mm = 0; $mm < 60; $mm++)
        {
            if (calcAngle($hh, $mm) == $theta)
            {
                echo $hh, ":", $mm;
                return;
            }
        }
    }
    echo "Input angle not valid.\n";
    return;
}

// Driver Code
$theta = 90.0;
printTime($theta);

// This code is contributed by anuj_67.
?>

Javascript

<script>

      // JavaScript program to find
      // time for a given angle.
      // function to find angle between
      // hour hand and minute hand
      function calcAngle(hh, mm)
      {
        // Calculate the angles moved by hour and
        // minute hands with reference to 12:00
        var hour_angle = 0.5 * (hh * 60 + mm);
        var minute_angle = 6 * mm;

        // Find the difference between two angles
        var 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
      function printTime(theta) {
        for (var hh = 0; hh < 12; hh++)
        {
          for (var mm = 0; mm < 60; mm++)
          {
            if (calcAngle(hh, mm) === theta)
            {
              document.write(hh + ":" + mm + "<br>");
              return;
            }
          }
        }
        document.write("Input angle not valid.<br>");
        return;
      }

      // driver code to test above function
      var theta = 90.0;
      printTime(theta);

</script>

Output :

3:0

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