Find the missing and duplicate elements in an array in linear time and constant space

Question

You’re given an array of N 64 bit integers. N may be very large. You know that every integer 1..N appears once in the array, except there is one integer mis

Answer 1

The solution proposed by BrokenGlass covers the case for two unknowns (corresponding to one duplicate number and one missing number), using two formulas:

and

The formulas yield the generalized harmonic number of orders n of -1 and -2, respectively. (Power series)

This solution is generalizable for 3 unknowns by including the value of generalized harmonic number of order n of -3.

To solve for m unknowns (duplicates and missing numbers), use m generalized harmonic numbers of orders n of -1 through -m.

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Moron notes that this approach was discussed earlier in StackOverflow at Easy interview question got harder.