Project Euler（42）
Posted on Monday, January 12th, 2009 at 7:04 pm by Universe QueenProblem 42:
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 = t_(10). 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
Implementation in Java:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 | import java.io.BufferedReader; import java.io.FileReader; public class Euler42 { public static boolean isTriangleWords( String s ) { int number = 0; for( int i=0; i<s.length(); i++ ) { number += s.charAt(i) - 'A' + 1; } int n = (int)Math.floor( Math.sqrt( number*2 ) ); if( n*(n+1) == number*2 ) { return true; } return false; } public static void main(String[] args) throws Exception { int result = 0; try { BufferedReader r = new BufferedReader( new FileReader("words.txt") ); String[] s = r.readLine().split(","); for( int i=0; i<s.length; i++ ) { s[i] = s[i].substring( 1, s[i].length()-1 ); if( isTriangleWords( s[i] ) ) { result++; } } } catch ( Exception e ) { throw e; } System.out.println( result ); } } |
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