Freaks City

Tree-Based Resource Distribution When distributing a fixed quantity of resources across a tree structure where each node must eventually hold an equal amount, removing any edge partitions the graph into two independent substructures. Let the total resource sum be $S$ and the number of nodes be $N$. The target allocation per node is $k = S / N$. ...

A Given a sequence ${a_n}$, select the largest possible subset such that no two selected elements sum to a prime number. Constraints: $T \leq 4$, $n \leq 750$, $a_i \leq 10^9$. Identical values can be merged into counts. Note that at most one instance of 1 may be included. This becomes a bipartite graph problem: odd numbers connect to the sourc ...