Question

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Check if array B is a permutation of A

Is there a way to tell if two arrays of numbers (which can contain positives, negatives or repeats) are permutations of each other in O(n) time complexity and O(1) space complexity? I could not solve it because of tight space constraints.

Answer 1

If the numbers are integers – in-place radix sort can give you O(nlogk) time, where k is the range of the numbers, and n is the number of elements.

Note that the algorithm requires O(logk) space, for the stack trace of recursive calls.

If you can bound k to a constant (2^64 for example) – you get O(n) time with O(1) space.

After sorting – you can simply iterate on both arrays and check if they are identical.