Rotating an array in place is a common task that has been studied extensively and in this article, we will discuss two algorithms that can be used to rotate an array in place.
Both algorithms have their advantages and disadvantages, so you should choose the right one for your situation.
What is an array rotation?
Array rotation is a method of transforming an array rotation so that every element becomes its logical successor (its neighbour).
For example, if we have an array like [1 2 3 4], then when rotating it by 90 degrees clockwise from where it currently sits on paper or screen (depending on your platform), you will end up with [0 2 3 4 5 6 7 8 9]. This means that every element now has its own successor value—you could just pick any one at random!
Along with the array, you should also know about the maximum product subarray. For example, A subarray is an uninterrupted section of an array. array that is contained within another array. Consider the array [1, 2, 3, 4], for instance. 10 non-empty sub-arrays are present. (1), (2), (3), (4), (1,2), (2,3), (3,4), (1,2,3), (2,3,4), and (1,2,3,4). In general, there are n*(n+1)/2 non-empty subarrays/substrings for an array or string of size n.
Algorithm 1: Reversal
A reversal algorithm is a method of array rotation where an array is in place. In this case, we will use the idea of reversing each element as discussed above. This can be done by using recursion on the array itself, or by using an auxiliary array. The array should contain all elements except the last one and then swapping it with its successor which is also contained in another auxiliary array.
This clearly illustrates why reversals are not good algorithms! They are slow because they require constant memory copying operations; they require O(n) space (where n = number of elements); and finally, they do not take advantage of locality since there is no sharing between consecutive operations performed on the same data item(s).
It is also relatively easy to implement reverse with simple algorithms.
For example, if we have a list of n elements that need to be rotated left or right n positions (where n ≥ 2), then reversing the list requires us to move only one element at a time.
The best way for us here would be by using an explicit stack that holds all of our elements as we move them around; this way there won't be any issues with loops or other problems related directly from having too many variables being used at once (which could lead toward infinite recursion).
Time complexity of algorithm 1
The Reverse algorithm is used by most programmers, and it has a time complexity of O(n). This means that it takes time proportional to the size of your array. If you have an array with 100 elements, then rotating it will take 100 steps or so.
Improving algorithm 1: block reversal
The first improvement we can make to the original algorithm is block reversal. In block reversal, each array element is reversed before being rotated by one position.
For example, if you were to rotate an array by 3 positions instead of 2 (as in algorithm 1), your new array would be rotated by 5 positions instead of 4 (1 + 2 = 3).
Block reversal works well because it allows us to reduce the number of rotations performed on our arrays without increasing their size or committing any extra resources. This can be done by reversing the order of all elements in each block prior to rotating them into place.
Algorithm 2: Block swap
This algorithm is a good solution. It has the same speed as algorithm 1, but it is much simpler to implement in hardware because there are no additional operations or memory accesses involved. It also has fewer restrictions on the array size and can be used with any type of data structure (although it will require more memory than an array). Continue reading..
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