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This approach involves calculating the angles made by the hour hand and the minute hand with respect to 12:00 and then finding the smallest angle between them. The minute hand moves 6 degrees per minute (360 degrees / 60 minutes), and the hour hand moves 30 degrees per hour (360 degrees / 12 hours) plus an additional 0.5 degrees per minute. The difference between these angles gives us the desired result.
Time Complexity: O(1) - The computation involves a fixed number of arithmetic operations.
Space Complexity: O(1) - No additional space is required beyond fixed-size variables.
1public class Solution {
2 public double angleClock(int hour, int minutes) {
3 double minute_angle = minutes * 6.0;
4 double hour_angle = (hour % 12) * 30.0 + minutes * 0.5;
5 double angle = Math.abs(minute_angle - hour_angle);
6 return angle > 180 ? 360 - angle : angle;
7 }
8
9 public static void main(String[] args) {
10 Solution sol = new Solution();
11 System.out.printf("%.5f\n", sol.angleClock(12, 30)); // Output: 165.00000
12 System.out.printf("%.5f\n", sol.angleClock(3, 30)); // Output: 75.00000
13 System.out.printf("%.5f\n", sol.angleClock(3, 15)); // Output: 7.50000
14 }
15}Java implementation calculates the angles for the hour and minute hands using similar arithmetic expressions, comparing the absolute difference to 180 degrees to return the smaller angle. The results are printed using formatted output for precision.
This alternative approach converts the movement of the clock hands into their equivalent rotations, effectively translating this into angles. The goal is to determine the position of both hands as angles relative to the 12 o'clock position and compute the minimal angular difference.
Time Complexity: O(1) - Fixed-time operations based on input.
Space Complexity: O(1) - Uses a constant number of variables.
1
Using JavaScript, the solution delves into the minute-hour expansions, employing modular arithmetic for positioning both hands on a conceptual clock face, coupling this synthesis with angular calculus to produce the minimal span.