338. Familystrokes -

print(internal + horizontal)

Proof. If childCnt ≥ 2 : the children occupy at least two columns on the next row, so a horizontal line is needed to connect the leftmost to the rightmost child (rule 2). 338. FamilyStrokes

Proof. The drawing rules require a vertical line from the node down to the row of its children whenever it has at least one child. The line is mandatory and unique, hence exactly one vertical stroke. ∎ An internal node requires a horizontal stroke iff childCnt ≥ 2 . print(internal + horizontal) Proof

root = 1 stack = [(root, 0)] # (node, parent) internal = 0 horizontal = 0 The drawing rules require a vertical line from

Both bounds comfortably meet the limits for N ≤ 10⁵ . Below are clean, self‑contained implementations in C++17 and Python 3 that follow the algorithm exactly. 6.1 C++17 #include <bits/stdc++.h> using namespace std;