How to resolve the algorithm Averages/Mean time of day step by step in the Common Lisp programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Averages/Mean time of day step by step in the Common Lisp programming language
Table of Contents
Problem Statement
A particular activity of bats occurs at these times of the day: Using the idea that there are twenty-four hours in a day, which is analogous to there being 360 degrees in a circle, map times of day to and from angles; and using the ideas of Averages/Mean angle compute and show the average time of the nocturnal activity to an accuracy of one second of time.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Averages/Mean time of day step by step in the Common Lisp programming language
Source code in the common programming language
;; * Loading the split-sequence library
(eval-when (:compile-toplevel :load-toplevel :execute)
(ql:quickload '("split-sequence")))
;; * The package definition
(defpackage :mean-time-of-day
(:use :common-lisp :iterate :split-sequence))
(in-package :mean-time-of-day)
;; * The data
(defparameter *time-values*
'("23:00:17" "23:40:20" "00:12:45" "00:17:19"))
(defun time->radian (time)
"Returns the radian value for TIME given as a STRING like HH:MM:SS. Assuming a
valid input value."
(destructuring-bind (h m s)
(mapcar #'parse-integer (split-sequence #\: time))
(+ (* h (/ PI 12)) (* m (/ PI 12 60)) (* s (/ PI 12 3600)))))
(defun radian->time (radian)
"Returns the corresponding time as a string like HH:MM:SS for RADIAN."
(let* ((time (if (plusp radian)
(round (/ (* 12 3600 radian) PI))
(round (/ (* 12 3600 (+ radian (* 2 PI))) PI))))
(h (floor time 3600))
(m (floor (- time (* h 3600)) 60))
(s (- time (* h 3600) (* m 60))))
(format nil "~2,'0D:~2,'0D:~2,'0D" h m s)))
(defun make-polar (rho theta)
"Returns a complex representing the polar coordinates."
(complex (* rho (cos theta)) (* rho (sin theta))))
(defun mean-time (times)
"Returns the mean time value within 24h of the list of TIMES given as strings
HH:MM:SS."
(radian->time (phase
(reduce #'+ (mapcar (lambda (time)
(make-polar 1 (time->radian time))) times)))))
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