Merge pull request algorithm-visualizer#110 from archie94/pascalTriangle

Algorithm for Pascal Triangle

Author: Raghav Dua

algorithm/category.json

@@ -83,7 +83,8 @@
   "etc": {
     "name": "Uncategorized",
     "list": {
-      "flood_fill": "Flood Fill"
+      "flood_fill": "Flood Fill",
+      "pascal_triangle": "Pascal's Trangle"
     }
   }
 }

algorithm/etc/pascal_triangle/desc.json

@@ -0,0 +1,17 @@
+{
+  "Pascal's Triangle": " Pascal's triangle is a triangular array of the binomial coefficients.",
+  "Applications": [
+    "Binomial Expansion",
+    "Probability"
+  ],
+  "Complexity": {
+    "time": " O(N<sup>2</sup>)",
+    "space": "O(N<sup>2</sup>)"
+  },
+  "References": [
+    "<a href='https://en.wikipedia.org/wiki/Pascal%27s_triangle'>Wikipedia</a>"
+  ],
+  "files": {
+    "pascal_triangle": "Pascal's Triangle"
+  }
+}

algorithm/etc/pascal_triangle/pascal_triangle/code.js

@@ -0,0 +1,20 @@
+for ( var i = 0; i < N; i++ ) {
+	for ( var j = 0; j <= i; j++ ) {
+		if( j === i || j === 0 ) { // First and last values in every row are 1
+			A[i][j] = 1;
+
+			tracer._notify( i, j, A[i][j])._wait();
+			tracer._denotify( i, j);
+		} else { // Other values are sum of values just above and left of above
+			tracer._select( i-1, j-1)._wait();
+			tracer._select( i-1, j)._wait();
+
+			A[i][j] = A[i-1][j-1] + A[i-1][j];
+			
+			tracer._notify( i, j, A[i][j])._wait();
+			tracer._denotify( i, j);
+			tracer._deselect( i-1, j-1);
+			tracer._deselect( i-1, j);
+		}
+	}
+}

algorithm/etc/pascal_triangle/pascal_triangle/data.js

@@ -0,0 +1,13 @@
+var N = 9;
+var A = new Array (N);
+for (var i = N - 1; i >= 0; i--) {
+	A[i] = new Array (N);
+}
+
+for (var i = N - 1; i >= 0; i--) {
+	for (var j = N - 1; j >= 0; j--) {
+		A[i][j] = ' ';
+	}
+}
+
+var tracer = new Array2DTracer ('Pascal\'s Triangle')._setData(A);