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What is the space complexity of the top-down memoization approach for the Ones and Zeroes problem with l strings and constraints m zeros and n ones?

medium🪤 Complexity Trap Q6 of Q15

Dynamic Programming: Knapsack - Ones and Zeroes (2D Knapsack)

What is the space complexity of the top-down memoization approach for the Ones and Zeroes problem with l strings and constraints m zeros and n ones?

AO(l * m * n)

BO(l + m + n)

CO(l)

DO(m * n)

Step-by-Step Solution

Solution:

Step 1: Memo stores states for (i, zeros_left, ones_left)
Maximum states are l * m * n, so memo size is O(l * m * n).
Step 2: Recursion stack depth is O(l)
Stack space is O(l), but memo dominates space usage.
Step 3: Total space complexity
Overall space complexity is O(l * m * n) due to memoization table.
Final Answer:
Option A -> Option A
Quick Check:
Memo dominates space -> O(l * m * n) [OK]

Quick Trick: Memoization table size dominates space [OK]

Common Mistakes:

MISTAKES

Ignoring memo size
Confusing recursion stack with memo space

Trap Explanation:

PITFALL

Candidates often confuse recursion stack space with memo size.

Interviewer Note:

CONTEXT

Tests understanding of space usage in recursive DP.

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