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Enhance readability of ZeroOneKnapsack.js #1574

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Oct 30, 2023
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26 changes: 17 additions & 9 deletions Dynamic-Programming/ZeroOneKnapsack.js
Original file line number Diff line number Diff line change
@@ -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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