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What is the time complexity of the bottom-up dynamic programming solution for the Ones and Zeroes problem given strs has length l, and constraints m zeros and n ones?

medium🪤 Complexity Trap Q5 of Q15

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

What is the time complexity of the bottom-up dynamic programming solution for the Ones and Zeroes problem given strs has length l, and constraints m zeros and n ones?

AO(2^l)

BO(l * (m + n))

CO(l * max(m, n))

DO(l * m * n)

Step-by-Step Solution

Solution:

Step 1: Analyze nested loops
Outer loop iterates over l strings; inner loops iterate over m and n capacities.
Step 2: Multiply iterations
Total time is O(l * m * n) due to triple nested iteration.
Final Answer:
Option D -> Option D
Quick Check:
Triple nested loops -> O(l * m * n) [OK]

Quick Trick: Triple nested loops multiply complexities [OK]

Common Mistakes:

MISTAKES

Confusing sum with product of m and n
Ignoring one dimension in complexity

Trap Explanation:

PITFALL

Candidates often mistake O(l * (m + n)) or O(l * max(m,n)) for the true complexity.

Interviewer Note:

CONTEXT

Tests understanding of DP time complexity with multiple constraints.

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