Given a tree with N vertices numbered 1 through N with vertex 1 as root vertex and N – 1 edges. We have to color exactly k number of vertices and count the number of uncolored vertices between root vertex and every colored vertex. We have to include the root vertex in the count if it is not colored. The task to maximize the number of uncolored vertices occurring between the path from root vertex and the colored vertices.
Input : 1 / | \ / | \ 2 3 4 / \ \ / \ \ 5 6 7 k = 4 Output : 7 Explanation: If we color vertex 2, 5, 6 and 7, the number of uncolored vertices between the path from root to colored vertices is maximum which is 7. Input : 1 / \ / \ 2 3 / / 4 k = 1 Output : 2
To solve the above-mentioned problem we observe that if a vertex is chosen to be uncolored then its parent must be chosen to be uncolored. Then we can calculate how many uncolored vertices we will get if we choose a certain path to the colored vertex. Simply calculate the difference between the number of vertices between root to each vertex and the number of vertices that occur below the current vertex. Take the largest k of all the difference and calculate the sum. Use nth_element stl to get an O(n) solution.
Below is the implementation of the above approach:
Time Complexity: O(N)
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Maximum difference of count of black and white vertices in a path containing vertex V
- Find K vertices in the graph which are connected to at least one of remaining vertices
- Longest path between any pair of vertices
- Find if there is a path between two vertices in an undirected graph
- Find if there is a path between two vertices in a directed graph | Set 2
- Find if there is a path between two vertices in a directed graph
- Number of pairs such that path between pairs has the two vertices A and B
- Number of trees whose sum of degrees of all the vertices is L
- Minimum number of edges between two vertices of a graph using DFS
- Number of Simple Graph with N Vertices and M Edges
- Minimum number of edges between two vertices of a Graph
- Find maximum number of edge disjoint paths between two vertices
- Calculate number of nodes between two vertices in an acyclic Graph by Disjoint Union method
- Count all possible paths between two vertices
- Finding in and out degrees of all vertices in a graph
- Construct a graph from given degrees of all vertices
- Shortest paths from all vertices to a destination
- Articulation Points (or Cut Vertices) in a Graph
- Maximum and minimum isolated vertices in a graph
- Minimum Operations to make value of all vertices of the tree Zero
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.