P75: Added Java solution.

Answers.txt

@@ -73,6 +73,7 @@ Problem 071: 428570
 Problem 072: 303963552391
 Problem 073: 7295372
 Problem 074: 402
+Problem 075: 161667
 Problem 076: 190569291
 Problem 077: 71
 Problem 079: 73162890

p075.java

@@ -0,0 +1,80 @@
+/* 
+ * Solution to Project Euler problem 75
+ * By Nayuki Minase
+ */
+
+import java.util.HashSet;
+import java.util.Set;
+
+
+public class p075 {
+
+	public static void main(String[] args) {
+		int n = 1500000;
+
+		/*
+		 * Pythagorean triples theorem:
+		 *   Every primitive Pythagorean triple with a odd and b even can be expressed as
+		 *   a = st, b = (s^2-t^2)/2, c = (s^2+t^2)/2, where s > t >= 1 are coprime odd integers.
+		 */
+		Set<IntTriple> triples = new HashSet<IntTriple>();
+		for (int t = 1; t * t <= n; t += 2) {
+			for (int s = t + 2; s * s <= n; s += 2) {
+				if (Library.gcd(s, t) == 1) {
+					int a = s * t;
+					int b = (s * s - t * t) / 2;
+					int c = (s * s + t * t) / 2;
+					int sum = a + b + c;
+					if (sum <= n)
+						triples.add(new IntTriple(a, b, c));
+				}
+			}
+		}
+
+		byte[] ways = new byte[n + 1];
+		for (IntTriple triple : triples) {
+			int sum = triple.a + triple.b + triple.c;
+			for (int i = 1; i * sum <= n; i++)
+				ways[i * sum] = (byte)Math.min(ways[i * sum] + 1, 2);  // Increment but saturate at 2
+		}
+
+		int count = 0;
+		for (int x : ways) {
+			if (x == 1)
+				count++;
+		}
+		System.out.println(count);
+	}
+
+
+
+	private static class IntTriple {
+
+		public final int a;
+		public final int b;
+		public final int c;
+
+
+		public IntTriple(int a, int b, int c) {
+			this.a = a;
+			this.b = b;
+			this.c = c;
+		}
+
+
+		public boolean equals(Object obj) {
+			if (!(obj instanceof IntTriple))
+				return false;
+			else {
+				IntTriple other = (IntTriple)obj;
+				return a == other.a && b == other.b && c == other.c;
+			}
+		}
+
+		public int hashCode() {
+			return a + b + c;
+		}
+
+	}
+
+}