X-Git-Url: http://svarog.pmf.uns.ac.rs/gitweb/?a=blobdiff_plain;f=kodovi%2Fefikasnost-algoritama%2FPitagora.java;fp=kodovi%2Fefikasnost-algoritama%2FPitagora.java;h=f4e890e468059239f2979d50c642ce6fb50db91f;hb=8b9bc1b025e43687b00777fe9f2dae1bd626e985;hp=0000000000000000000000000000000000000000;hpb=5cecf742a63598e1107ae576b584d0064786ebbc;p=spa1-materijali.git

diff --git a/kodovi/efikasnost-algoritama/Pitagora.java b/kodovi/efikasnost-algoritama/Pitagora.java
new file mode 100644
index 0000000..f4e890e
--- /dev/null
+++ b/kodovi/efikasnost-algoritama/Pitagora.java
@@ -0,0 +1,131 @@
+public class Pitagora {
+
+	/**
+	 * Generisanje svih trojki brojeva do neke granice uz proveru da li je to
+	 * upravo Pitagorina trojka.
+	 */
+	static void trojke1() {
+		int br = 0;
+		int gr = 100;
+
+		System.out.println("\nPitagorine trojke\n");
+
+		for (int x = 1; x <= gr; x++) {
+			for (int y = 1; y <= gr; y++) {
+				for (int z = 1; z <= gr; z++) {
+					if (x * x + y * y == z * z) {
+						br++;
+						stampajTrojku(br, x, y, z);
+					}
+				}
+			}
+		}
+	}
+
+	/**
+	 * Generisanje parova brojeva a,b i provera da li postoji celo c koje bi
+	 * formiralo Pitagorinu trojku.
+	 */
+	static void trojke2() {
+		int br = 0;
+		int gr = 100;
+
+		System.out.println("\nPitagorine trojke 2\n");
+
+		for (int x = 1; x <= gr; x++) {
+			for (int y = 1; y <= gr; y++) {
+				double zreal = x * x + y * y;
+				zreal = Math.sqrt(zreal);
+				// Provera da li je ceo broj
+				int z = (int) zreal;
+				if (zreal == z) {
+					br++;
+					stampajTrojku(br, x, y, z);
+				}
+			}
+		}
+	}
+
+	/**
+	 * Euklidova teorema daje Pitagorinu trojku za bilo koja dva prirodna broja
+	 * n i m.
+	 */
+	static void trojke3() {
+		int br = 0;
+		int gr3 = 10;
+
+		System.out.println("\nPitagorine trojke 3\n");
+
+		for (int m = 1; m <= gr3; m++) {
+			for (int n = 1; n <= m - 1; n++) {
+				int x = m * m - n * n;
+				int y = 2 * m * n;
+				int z = m * m + n * n;
+				br++;
+				stampajTrojku(br, x, y, z);
+			}
+		}
+	}
+
+	/**
+	 * Generisanje trojki kod kojih je razlika izmedju a i c 1. Postupak je
+	 * izveden preko Euklidove teoreme.
+	 */
+	static void trojke4() {
+		int br = 0;
+		int gr4 = 10;
+
+		System.out.println("\nPitagorine trojke 4\n");
+
+		for (int m = 2; m <= gr4; m++) {
+			int n = m - 1;
+			int a = 2 * m * n;
+			int b = m * m - n * n;
+			int c = m * m + n * n;
+			br++;
+			stampajTrojku(br, a, b, c);
+		}
+	}
+
+	/**
+	 * Generisanje trojki kod kojih je razlika izmedju a i b 1. Postupak je
+	 * izveden preko Euklidove teoreme i koriste se inkrementalna resenja
+	 * dobijene Pell-ove jednacine.
+	 */
+	static void trojke5() {
+		int gr5 = 6;
+		int br = 0;
+
+		System.out.println("\nPitagorine trojke 5\n");
+
+		int w = 3;
+		int n = 2;
+		for (int i = 1; i <= gr5; i++) {
+			int m = n + w;
+			int a = 2 * m * n;
+			int b = m * m - n * n;
+			int c = m * m + n * n;
+			br++;
+			stampajTrojku(br, a, b, c);
+			int temp = w;
+			w = 3 * w + 4 * n;
+			n = 2 * temp + 3 * n;
+		}
+	}
+
+	public static void stampajTrojku(int br, int x, int y, int z) {
+		System.out.print(br + " ");
+		System.out.print("a = " + x);
+		System.out.print(", b = " + y);
+		System.out.print(", c = " + z);
+		System.out.println();
+	}
+
+	public static void main(String[] args) {
+		trojke1();
+		trojke2();
+		trojke3();
+		trojke4();
+		trojke5();
+	}
+}