Challenge: Distinct Powers

Posted on: August 23, 2017 10:17:27 PM

Consider all integer combinations of a^b for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

2²=4, 2³=8, 2⁴=16, 2⁵=32
3²=9, 3³=27, 3⁴=81, 3⁵=243
4²=16, 4³=64, 4⁴=256, 4⁵=1024
5²=25, 5³=125, 5⁴=625, 5⁵=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by a^b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

This was very straight forward for me. The most simple way to do this is a simple brute force option. There are ways to calculate out most of the duplicates, but those calculations end up taking longer than 2 simple loops and feed the results into a hashset to guarantee uniqueness to get the answer.

Program.cs

using System;
using System.Collections.Generic;
using System.Diagnostics;

namespace Project_Euler_29
{
    internal class Program
    {
        private static void Main(string[] args)
        {
            Stopwatch sw = Stopwatch.StartNew();
            HashSet<double> results = new HashSet<double>();

            for (int a = 2; a <= 100; a++)
            {
                for (int b = 2; b <= 100; b++)
                {
                    results.Add(Math.Pow(a, b));
                }
            }

            sw.Stop();

            Console.WriteLine($"Number of distinct powers: {results.Count}");
            Console.WriteLine($"Took {sw.ElapsedMilliseconds}ms");
        }
    }
}

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Challenge: Distinct Powers

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