Algorithm for 0-1 Knapsack Problem

Author: archie94

algorithm/etc/dp/desc.json

@@ -12,6 +12,7 @@
     "sliding_window": "Finding the largest sum of three contiguous number",
     "max_sum_path": "Finding the maximum sum in a path from (0, 0) to (N-1, M-1) when can only move to right or down",
     "longest_increasing_subsequence": "Find the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order",
-    "max_subarray": "Find the sum of the maximum Subarray in the given Array"
+    "max_subarray": "Find the sum of the maximum Subarray in the given Array",
+    "knapsack_problem": "Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible."
   }
 }

algorithm/etc/dp/knapsack_problem/code.js

@@ -0,0 +1,46 @@
+
+for ( var i = 0; i <= N; i++ ) {
+	for( var j = 0; j <= W; j++ ) {
+		if( i === 0 || j === 0 ) { 
+			/*
+			If we have no items or maximum weight we can take in collection is 0 
+			then the total weight in our collection is 0
+			*/
+			DP[i][0] = 0;
+			tracer._notify( i, j, DP[i][j])._wait();
+			tracer._denotify( i, j);
+		} else if ( wt[i-1] <= j ) { // take the current item in our collection
+
+			dataViewer1._select(i-1)._wait();
+			dataViewer2._select(i-1)._wait();
+			tracer._select( i-1, j)._wait();
+
+			var A = val[i - 1] + DP[i - 1][j - wt[i - 1]];
+			var B = DP[i - 1][j];
+			/*
+			find the maximum of these two values
+			and take which gives us a greater weight
+			 */
+			if (A > B) {
+				DP[i][j] = A;
+				tracer._notify( i, j, DP[i][j])._wait();
+			} else {
+				DP[i][j] = B;
+				tracer._notify( i, j, DP[i][j])._wait();
+			}
+
+			tracer._deselect( i-1, j);
+			tracer._denotify( i, j);
+			dataViewer2._deselect(i-1);
+			dataViewer1._deselect(i-1);
+
+		} else { // leave the current item from our collection 
+
+			DP[i][j] = DP[i - 1][j];
+			tracer._notify( i, j, DP[i][j])._wait();
+			tracer._denotify( i, j);
+		}
+	}
+}
+
+logger._print(' Best value we can achieve is ' + DP[N][W]);

algorithm/etc/dp/knapsack_problem/data.js

@@ -0,0 +1,17 @@
+var val = [1,4,5,7]; // The value of all available items
+var wt = [1,3,4,5];  // The weights of available items
+var W = 7;           // The maximum weight we can carry in our collection
+var N = val.length;
+var DP = new Array(N+1);
+
+for (var i = 0; i < N + 1; i++) {
+    DP[i] = new Array(W+1);
+    for (var j = 0; j < W + 1; j++) {
+        DP[i][j] = 0;
+    }
+}
+
+var tracer = new Array2DTracer()._setData(DP);
+var dataViewer1 = new Array1DTracer()._setData(val);
+var dataViewer2 = new Array1DTracer()._setData(wt);
+var logger = new LogTracer();