This algorithm finds the minimum time difference between any two times in an array.

MinimiumTimeDifference.cs

class Program
    {
        private static List<string> MinutesArray { get; set; } = new List<string>();

        static void Main(string[] args)
        {
            string[] timeArray = { "16:15", "16:00", "12:20" };

            GetMinutesFromTimeArrayIntoMinutesArray(timeArray);
            var result = MinimiumTimeDifference(MinutesArray);

            Console.WriteLine("Result:" + " " + result);
        }

        public static void GetMinutesFromTimeArrayIntoMinutesArray(string[] timeArray)
        {
            if (timeArray == null) { }
            else
            {
                string timeArrayElement;

                for (int i = 0; i < timeArray.Length; i++)
                {
                    timeArrayElement = timeArray[i];
                    MinutesArray.Add(timeArrayElement.Substring(3));

                }
            }    

        }

        public static string MinimiumTimeDifference(List<string> minutesArray)
        {
            if (minutesArray == null) { return null; }
            else
            {
                var minutesArrayMinimum = minutesArray.Min();

                MinutesArray.Remove(minutesArrayMinimum);

                MinutesArray.Sort();

                return MinutesArray[0] + " " + "minutes";
            }

        }
    }