Project Euler Problem 42

Problem 42

25 April 2003

The n^th term of the sequence of triangle numbers is given by, t_n = ½n(n+1); so the first ten triangle numbers are:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is 19 + 11 + 25 = 55 = t₁₀. If the word value is a triangle number then we shall call the word a triangle word.

Using words.txt (right click and 'Save Link/Target As...'), a 16K text file containing nearly two-thousand common English words, how many are triangle words?

Answer: 162

 

 

C#

 

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Numerics;
using System.IO;

namespace Euler {
    class Program {
        static int wordValue(string s) {
            return s.Select(x => x - 'A' + 1).Sum();
        }

        static void Main(string[] args) {
            var words = File.ReadAllText("words.txt").Replace('"', ' ').Split(',').Select(x=>x.Trim());
            var maxValue = words.Select(wordValue).Max();
            var triangleNums = new HashSet<int>();
            for (var i = 1; ; i++) {
                var c = i * (i + 1) / 2;
                triangleNums.Add(c);
                if (c >= maxValue) break;
            }
            Console.WriteLine(words.Where(x => triangleNums.Contains(wordValue(x))).Count());
        }
    }
}