Knapsack

Question 1

What is the 0/1 Knapsack pattern and when is it used?

Answer 1

Solves optimization using dynamic programming for item selection.
Use Case: Maximize value within capacity.

Example: [No LeetCode match, course example: Knapsack].

Action: Verbalize use case aloud.

Question 2

What are the key steps for the 0/1 Knapsack?

Answer 2

1. Create DP table for items and capacity.
2. Fill table: max value including/excluding item.
3. Return max value.

Action: Explain steps for Knapsack aloud.

Question 3

How does the 0/1 Knapsack apply to Knapsack?

Answer 3

Maximize value of items within weight limit.
Approach: Use DP to compute max value for each capacity.

Example: Knapsack. Action: Verbalize solution logic aloud.

Question 4

What are the complexity and gotchas of the 0/1 Knapsack?

Answer 4

Time: O(nW), Space: O(nW).

Gotchas: Zero capacity, no items.

Action: List edge cases for Knapsack aloud.

Question 5

Code example for the 0/1 Knapsack.

Answer 5

```python
from typing import List
def knapsack(values: List[int], weights: List[int], capacity: int) -> int:
n = len(values)
dp = [[0] * (capacity + 1) for _ in range(n + 1)]
for i in range(1, n + 1):
for w in range(capacity + 1):
if weights[i-1] <= w:
dp[i][w] = max(dp[i-1][w], dp[i-1][w-weights[i-1]] + values[i-1])
else:
dp[i][w] = dp[i-1][w]
return dp[n][capacity]
~~~