NetworkContagion.java

import java.util.Scanner;

    class TreeNode {
        String name;
        TreeNode left;
        TreeNode right;

        TreeNode(String name) {
            this.name = name;
        }
    }

    public class NetworkContagion {

        private int maxTime;

        public int minutesToInfect(TreeNode root, String start) {

            maxTime = 0;
            dfs(root, start);

            return maxTime;
        }

        private int dfs(TreeNode node, String start) {

            if (node == null)
                return 0;

            int left = dfs(node.left, start);
            int right = dfs(node.right, start);

            if (node.name.equalsIgnoreCase(start)) {
                maxTime = Math.max(
                        maxTime, Math.max(left, right));
                return -1;
            }

            if (left < 0 || right < 0) {

                int infectedDistance = Math.min(left, right);

                maxTime = Math.max(
                        maxTime,
                        Math.abs(infectedDistance) + Math.max(left, right)

                );

                return infectedDistance - 1;
            }

            return 1 + Math.max(left, right);
        }

        public static void main(String[] args) {
            TreeNode A = new TreeNode("A");
            TreeNode B = new TreeNode("B");
            TreeNode C = new TreeNode("C");
            TreeNode D = new TreeNode("D");
            TreeNode E = new TreeNode("E");

            A.left = B;
            A.right = C;
            B.left = D;
            C.right = E;

            Scanner scanner = new Scanner(System.in);

            System.out.println("Network Nodes: A, B, C, D, E");
            System.out.print("Enter starting node: ");
            String startNode = scanner.nextLine();

            NetworkContagion simulation = new NetworkContagion();

            int minutes = simulation.minutesToInfect(A, startNode);

            System.out.println("Minutes to infect network: " + minutes);

            scanner.close();
        }
    }