Recall & Review
beginner
What is a rotated sorted array?
A rotated sorted array is an array that was originally sorted in ascending order but then rotated (shifted) at some pivot unknown to you. For example, [4,5,6,7,0,1,2] is a rotated version of [0,1,2,4,5,6,7].
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beginner
Why can't we just scan the entire rotated sorted array to find the minimum?
Scanning the entire array takes O(n) time, which is slow for large arrays. Using a smart approach like binary search can find the minimum in O(log n) time, which is much faster.
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intermediate
In the binary search approach to find the minimum in a rotated sorted array, what does it mean if the middle element is greater than the rightmost element?
It means the minimum is in the right half of the array because the rotation point is to the right of mid.
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intermediate
What is the stopping condition for the binary search when finding the minimum in a rotated sorted array?
When the search space is reduced to one element, that element is the minimum.
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intermediate
Show the dry run steps to find the minimum in the array [4,5,6,7,0,1,2] using binary search.
Start with low=0, high=6. mid=3 (value=7). Since 7 > 2 (rightmost), move low to mid+1=4. Now low=4, high=6. mid=5 (value=1). Since 1 < 2, move high to mid=5. Now low=4, high=5. mid=4 (value=0). Since 0 < 1, move high to mid=4. Now low=4, high=4. Stop. Minimum is 0 at index 4.
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What is the time complexity of finding the minimum in a rotated sorted array using binary search?
✗ Incorrect
Binary search divides the search space in half each time, leading to O(log n) time complexity.
If the middle element is less than the rightmost element in the rotated sorted array, where is the minimum located?
✗ Incorrect
If mid element is less than rightmost, the minimum lies in the left half including mid.
What does it mean if the array is not rotated?
✗ Incorrect
If the array is not rotated, it is fully sorted, so the first element is the smallest.
Which of these arrays is a rotated sorted array?
✗ Incorrect
Array [3,4,5,1,2] is a rotated version of sorted array [1,2,3,4,5].
What is the first step in the binary search approach to find the minimum in a rotated sorted array?
✗ Incorrect
We compare the middle element with the rightmost element to decide which half to search next.
Explain how binary search helps find the minimum element in a rotated sorted array.
Think about how the rotation affects the order and how to use comparisons to find the pivot.
You got /4 concepts.
Describe the difference between a rotated sorted array and a fully sorted array and how it affects finding the minimum.
Consider where the smallest number is located in each case.
You got /4 concepts.