We have two unsorted arrays and each array has a length of n. These arrays contain random integers in the range of 0-n100. How to find if these two arrays have any common elements in O(n)/linear time? Sorting is not allowed.
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We have two unsorted arrays and each array has a length of n. These arrays contain random integers in the range of 0-n100. How to find if these two arrays have any common elements in O(n)/linear time? Sorting is not allowed.
You have not defined the model of computation. Assuming you can only read O(1) bits in O(1) time (anything else would be a rather exotic model of computation), there can be no algorithm solving the problem in O(n) worst case time complexity.
Proof Sketch:
Each number in the input takes O(log(n ^ 100)) = O(100 log n) = O(log n) bits. The entire input therefore O(n log n) bits, which can not be read in O(n) time. Any O(n) algorithm can therefore not read the entire input, and hence not react if these bits matter.