Find 2 missing numbers in an array of integers with two missing values

Question

How do you do this? The values are unsorted but are of [1..n] Example array [3,1,2,5,7,8]. Answer: 4, 6

I saw this solution in

Answer 1

Let x and y be the roots of a quadratic equation.

• Sum of the roots, SUM = x + y
• Product of the roots, PRODUCT = x * y

If we know the sum and the product, we can reconstruct the quadratic equation as:

z^2 - (SUM)z + (PRODUCT) = 0

In the algorithm you mentioned, we find the sum and the product, and from that, we reconstruct the quadratic equation using the above formula.

If you are interested in a detailed derivation, here is a reference. Read "Reconstruction of the quadratic equation from the sum and product of roots".