From e5af4c24b4156279827f6a6cc4349f70247a53f2 Mon Sep 17 00:00:00 2001
From: Hardik Pawar <97388607+Hardvan@users.noreply.github.com>
Date: Mon, 30 Oct 2023 11:04:06 +0530
Subject: [PATCH] Enhance readability of ZeroOneKnapsack.js (#1574)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* Enhance readability of ZeroOneKnapsack.js

* Update ZeroOneKnapsack.js

---------

Co-authored-by: Lars Müller <34514239+appgurueu@users.noreply.github.com>
---
 Dynamic-Programming/ZeroOneKnapsack.js | 26 +++++++++++++++++---------
 1 file changed, 17 insertions(+), 9 deletions(-)

diff --git a/Dynamic-Programming/ZeroOneKnapsack.js b/Dynamic-Programming/ZeroOneKnapsack.js
index 3913d016b..52a06aa13 100644
--- 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 = () => {