diff --git a/Dynamic-Programming/ZeroOneKnapsack.js b/Dynamic-Programming/ZeroOneKnapsack.js
index 3913d016b3..52a06aa130 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 = () => {
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