By tree it means a standard binary search tree. The question is a dynamic programming question

(a) A Colorful Tree Let G = (V, E) be an undirected graph with the vertex set V and edge set E, where each edge has a positive weight we. Let |V] = n. A K-partition of G is a coloring of the vertices with two colors (red/blue) such that K nodes are colored red, and the remaining n - K nodes are colored blue. The input is a graph and an integer K, the goal of the K-PARTITION problem is to find a K-partition of G where the total weight of split edges (edges with one endpoint red and the other blue) is minimized. In general the problem is NP-hard. However, if the graph is a tree, the K-PARTITION problem becomes easier. Design an O(n) algorithm to solve this problem on trees where each node has at most two children. (FYI: the solution can be extended to work just as efficiently with trees with no bound on the number of children.) (a) A Colorful Tree Let G = (V, E) be an undirected graph with the vertex set V and edge set E, where each edge has a positive weight we. Let |V] = n. A K-partition of G is a coloring of the vertices with two colors (red/blue) such that K nodes are colored red, and the remaining n - K nodes are colored blue. The input is a graph and an integer K, the goal of the K-PARTITION problem is to find a K-partition of G where the total weight of split edges (edges with one endpoint red and the other blue) is minimized. In general the problem is NP-hard. However, if the graph is a tree, the K-PARTITION problem becomes easier. Design an O(n) algorithm to solve this problem on trees where each node has at most two children. (FYI: the solution can be extended to work just as efficiently with trees with no bound on the number of children.)