Merge pull request algorithm-visualizer#109 from RudraNilBasu/gh-pages

Seive of Erathrones

Author: nem035

algorithm/category.json

@@ -12,6 +12,12 @@
       "page_rank": "PageRank Algorithm"
     }
   },
+  "number_theory": {
+    "name": "Number Theory",
+    "list": {
+      "seive_of_erathrones": "Seive of Erathrones"
+    }
+  },
   "cryptography": {
     "name": "Cryptography",
     "list": {

algorithm/number_theory/seive_of_erathrones/basic/code.js

@@ -0,0 +1,16 @@
+logger._print("1 is not prime");
+tracer._select(0)._wait();
+for(var i=2;i<=length;i++) {
+	if(b[i]===0) {
+		logger._print(i+" is not marked, so it is prime");
+		// a[i-1] is prime mark by red indicators
+		tracer._notify(i-1)._wait();
+		for(var j=i+i;j<=length;j+=i) {
+			b[j]=1; // a[j-1] is not prime, mark by blue indicators
+			logger._print(j+" is a multiple of "+i+" so it is marked as composite" );
+			tracer._select(j-1)._wait();
+		}
+		tracer._denotify(i-1);
+	}
+}
+logger._print("The unmarked numbers are the prime numbers from 1 to "+length);

algorithm/number_theory/seive_of_erathrones/basic/data.js

@@ -0,0 +1,10 @@
+var tracer = new Array1DTracer('Seive');
+length = 30;
+var a = [];
+var b = [];
+for (var i=1;i<=length;i++) {
+	a.push(i);
+	b.push(0);
+}
+tracer._setData(a);
+var logger = new LogTracer();

algorithm/number_theory/seive_of_erathrones/desc.json

@@ -0,0 +1,13 @@
+{
+  "Seive of Erathrones": "Finding all prime numbers upto a given range.",
+  "Complexity": {
+    "time": "O(n(log n)(log log n))",
+    "space": "O(n<sup>1/2</sup>)"
+  },
+  "References": [
+    "<a href='https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes'>Wikipedia</a>"
+  ],
+  "files": {
+    "basic": "Seive of Erathrones"
+  }
+}