What is the time complexity of the optimal max heap approach to reorganize a string of length n with k unique characters?

medium🪤 Complexity Trap Q13 of Q15

Greedy Algorithms - Reorganize String (No Two Adjacent Same)

What is the time complexity of the optimal max heap approach to reorganize a string of length n with k unique characters?

AO(n²) because each character insertion may require scanning the entire string

BO(n log k) because each of the n characters is pushed and popped from a heap of size k

CO(k log n) because the heap operations depend on the string length

DO(n) because each character is processed once without extra overhead

Step-by-Step Solution

Solution:

Step 1: Identify heap operations per character
Each character is pushed and popped at most once per occurrence, total n operations.
Step 2: Analyze heap size and operation cost
Heap size is at most k (unique chars), each push/pop is O(log k), so total O(n log k).
Final Answer:
Option B -> Option B
Quick Check:
Heap operations dominate, not scanning entire string [OK]

Quick Trick: Heap ops cost O(log k) per character [OK]

Common Mistakes:

MISTAKES

Trap Explanation:

PITFALL

Option A looks plausible as n² but heap operations limit complexity to n log k; option D ignores heap overhead.

Interviewer Note:

CONTEXT

Checks if candidate understands heap-based complexity and distinguishes n vs k parameters.

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