knapSack dp

Author: loiane

chapter11/05-KnapsackProblemDP.js

@@ -0,0 +1,53 @@
+function knapSack(capacity, weights, values, n) {
+
+    var i, w, a, b, kS = [];
+
+    for (i = 0; i <= n; i++) {
+        kS[i] = [];
+    }
+
+    for (i = 0; i <= n; i++){
+        for (w = 0; w <= capacity; w++){
+            if (i == 0 || w == 0){
+                kS[i][w] = 0;
+
+            } else if (weights[i-1] <= w){
+                a = values[i-1] + kS[i-1][w-weights[i-1]];
+                b = kS[i-1][w];
+                kS[i][w] = (a > b) ? a : b; //max(a,b)
+                console.log(a + ' can be part of the solution');
+            } else{
+                kS[i][w] = kS[i-1][w];
+            }
+        }
+        console.log(kS[i].join());
+    }
+
+    //extra algorithm to find the items that are part of the solution
+    findValues(n, capacity, kS, values, weights);
+
+    return kS[n][capacity];
+}
+
+function findValues(n, capacity, kS, weights, values){
+    var i=n, k=capacity;
+
+    console.log('Items that are part of the solution:');
+
+    while (i>0 && k>0){
+        if (kS[i][k] !== kS[i-1][k]){
+            console.log('item '+i+' can be part of solution w,v: ' + weights[i-1] + ',' + values[i-1]);
+            i--;
+            k = k - kS[i][k];
+        } else {
+            i--;
+        }
+    }
+}
+
+var values = [3,4,5],
+    weights = [2,3,4],
+    capacity = 5,
+    n = values.length;
+
+console.log('Total value that can be carried: ' + knapSack(capacity, weights, values, n));