What is the time complexity of Minimum Number of Operations to Reinitialize a Permutation?

The optimal solution for Minimum Number of Operations to Reinitialize a Permutation runs in O(n) time and uses O(1) space. The time complexity is O(n) because we iterate through each index once and track its position, leading to a linear time complexity overall.

What is the brute force solution for Minimum Number of Operations to Reinitialize a Permutation?

The brute force approach for Minimum Number of Operations to Reinitialize a Permutation is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach simulates the operation repeatedly until the permutation returns to its original state. It checks how many times we need to perform the operation to revert back to the initial permutation. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Minimum Number of Operations to Reinitialize a Permutation?

Minimum Number of Operations to Reinitialize a Permutation uses the following concepts: Array, Math, Simulation. The recommended patterns to study are: Array, Simulation.

What are the interview tips for Minimum Number of Operations to Reinitialize a Permutation?

Always think about the properties of the problem — in this case, the cyclic nature of the operations. Start with a brute force solution to understand the problem better before optimizing. Explain your thought process clearly during the interview, as it shows your problem-solving skills.

What are common mistakes when solving Minimum Number of Operations to Reinitialize a Permutation?

Failing to recognize the cycle nature of the operations, leading to unnecessary simulations. Not considering edge cases, such as when n is the smallest even number.

#1806

Minimum Number of Operations to Reinitialize a Permutation

Medium

ArrayMathSimulationArraySimulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal solution recognizes that the operations form a cycle. By tracking the position of each index, we can determine how many operations it takes to return to the original state without simulating each operation.

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Algorithm

3 steps

1Step 1: Initialize a variable to track the number of operations.
2Step 2: Use a loop to track the position of each index until it returns to the original index.
3Step 3: Count the number of operations needed for each index and return the maximum.

solution.py19 lines

1# Full working Python code
2
3def min_operations(n):
4    operations = 0
5    for start in range(n):
6        current = start
7        count = 0
8        while True:
9            count += 1
10            if current % 2 == 0:
11                current //= 2
12            else:
13                current = n // 2 + (current - 1) // 2
14            if current == start:
15                break
16        operations = max(operations, count)
17    return operations
18
19print(min_operations(4))  # Example usage

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Complexity note: The time complexity is O(n) because we iterate through each index once and track its position, leading to a linear time complexity overall.

1The operations form a cycle, and tracking the position of each index helps determine the number of operations needed.
2The maximum number of operations across all indices gives the total operations required to return to the original permutation.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.