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Notes: I've thought about Radix sort, bucket sort, counting sort.
Is there anyway to achieve big O(n)?
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You can use counting sort. Counting sort (sometimes referred to as ultra sort or math sort) is a sorting algorithm which (like bucket sort) takes advantage of knowing the range of the numbers in the array to be sorted (array A).
If it's meant as speed, the radix sort is the fastest theoretical sort for this. Especially as we know that the integers are 32bit and thus can only be in a range of values.
But since it has the upper hand in the average cases for most inputs, Quicksort is generally considered the “fastest” sorting algorithm.
What is the best sorting algorithm to use for the elements in array are more than 1 million in general? Merge sort.
You can use counting sort.
Counting sort (sometimes referred to as ultra sort or math sort) is a sorting algorithm which (like bucket sort) takes advantage of knowing the range of the numbers in the array to be sorted (array A).
Counting sort is a stable sort and has a running time of Θ(n+k), where n and k are the lengths of the arrays A (the input array) and C (the counting array), respectively. In order for this algorithm to be efficient, k must not be much larger than n.
In this case k is 100 and n is 1000000.
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A counting sort would be the obvious choice under these circumstances. Yes, properly implemented it should have linear complexity.
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