Try to consider all possible trees, like complete binary tree or right skew tree etc.
when you try with all possible trees you'll find out that array size somewhat equal to number of nodes in complete binary tree.
For right skew tree with 4 nodes, we need maximum size of an array that is 15([2^n] -1)
But, here they asked about minimum size, so they are talking about complete binary tree.
Size of array required= $2^{\left \lceil log(n+1) \right \rceil}-1$