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What is the time complexity of the partitioning step in Quick Sort?
What is the time complexity of the partitioning step in Quick Sort?
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Practice Questions
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Q1
What is the time complexity of the partitioning step in Quick Sort?
O(n)
O(n log n)
O(log n)
O(n^2)
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The partitioning step in Quick Sort has a time complexity of O(n) as it involves a single pass through the array.
Questions & Step-by-step Solutions
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Q
Q: What is the time complexity of the partitioning step in Quick Sort?
Solution:
The partitioning step in Quick Sort has a time complexity of O(n) as it involves a single pass through the array.
Steps: 7
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Step 1: Understand that Quick Sort is a sorting algorithm that works by dividing an array into smaller parts.
Step 2: Identify the partitioning step, which is where the array is divided based on a 'pivot' element.
Step 3: Realize that during partitioning, each element in the array is compared to the pivot.
Step 4: Count how many elements are in the array. Let's say there are 'n' elements.
Step 5: Note that each element is checked once during the partitioning process.
Step 6: Since we check each of the 'n' elements exactly once, the time taken is proportional to 'n'.
Step 7: Conclude that the time complexity of the partitioning step is O(n).
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