Enhance readability of ZeroOneKnapsack.js (TheAlgorithms#1574)

Hardvan · appgurueu · web-flow · commit e5af4c24b415 · 2023-10-30T11:04:06.000+05:30
* Enhance readability of ZeroOneKnapsack.js

* Update ZeroOneKnapsack.js

---------

Co-authored-by: Lars Müller &lt;34514239+appgurueu@users.noreply.github.com&gt;
diff --git a/Dynamic-Programming/ZeroOneKnapsack.js b/Dynamic-Programming/ZeroOneKnapsack.js
@@ -1,26 +1,34 @@
 /**
  * A Dynamic Programming based solution for calculating Zero One Knapsack
  * https://en.wikipedia.org/wiki/Knapsack_problem
+ *
+ * Time and Space Complexity: O(n*cap)
  */
-
 const zeroOneKnapsack = (arr, n, cap, cache) => {
+  // Base Case: No capacity or no items
   if (cap === 0 || n === 0) {
     cache[n][cap] = 0
     return cache[n][cap]
   }
+
+  // Lookup (value already calculated)
   if (cache[n][cap] !== -1) {
     return cache[n][cap]
   }
+
+  // Profit when excluding the nth item
+  let notPick = zeroOneKnapsack(arr, n - 1, cap, cache)
+
+  // Profit when including the nth item
+  let pick = 0
   if (arr[n - 1][0] <= cap) {
-    cache[n][cap] = Math.max(
-      arr[n - 1][1] + zeroOneKnapsack(arr, n - 1, cap - arr[n - 1][0], cache),
-      zeroOneKnapsack(arr, n - 1, cap, cache)
-    )
-    return cache[n][cap]
-  } else {
-    cache[n][cap] = zeroOneKnapsack(arr, n - 1, cap, cache)
-    return cache[n][cap]
+    // If weight of the nth item is within the capacity
+    pick =
+      arr[n - 1][1] + zeroOneKnapsack(arr, n - 1, cap - arr[n - 1][0], cache)
   }
+
+  cache[n][cap] = Math.max(pick, notPick) // maximize profit
+  return cache[n][cap]
 }
 
 const example = () => {
