Greedy Algorithms - Jump Game II (Minimum Jumps)
What is the worst-case time complexity of the BFS-based solution for Jump Game II on an input array of length n?
What is the worst-case time complexity of the BFS-based solution for Jump Game II on an input array of length n?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Step 1: Identify outer and inner loops
The BFS processes each index once, but for each index, it may enqueue up to nums[pos] next positions, which can be up to n.Step 2: Analyze nested iteration
In worst case (e.g., nums[i] = n for all i), inner loop runs O(n) times for each of O(n) indices -> O(n^2) total.Final Answer:
Option A -> Option AQuick Check:
Nested loops over n indices and jumps -> O(n^2) [OK]
Quick Trick: Nested loops over n indices and jumps -> O(n^2) [OK]
Common Mistakes:
MISTAKES- Assuming BFS is always O(n)
- Confusing with greedy linear time
- Ignoring inner loop over jump range
Trap Explanation:
PITFALL- Many think BFS is linear, but here inner loop over jump range can be large, causing quadratic time.
Interviewer Note:
CONTEXT- Tests understanding of nested loops and worst-case input impact on complexity.
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