Intuitively if you see, while building a binary tree,
At first, the root can contribute to 2 leaves.
After that, converting each leaf to a non-leaf, the effective contribution to increasing leaf node is (degree – 1). Because while it is adding “degree” number of leaves, it itself is converting to an inner node.
Therefore, subsequently, after the root, each node of degree 2 contributes only 1 leaf node to the tree.
Therefore, taking
L= no. of leaves, and
I = no of inner nodes with degree 2,
L = I + 1 (since root contributes 2 leaves).
I = L – 1 = 200 – 1 = 199.
You can check out by drawing in a paper how adding one child to a leaf node keeps the overall number of leaf nodes constant. Adding two children, however, increases the number of leaves by 1.