JAVA Solution
Intuition\nFirst of all the question wants us to calculate how many nodes satisfy target condition, which essentially means number of nodes which can be reached
# Intuition\nFirst of all the question wants us to calculate how many nodes satisfy target condition, which essentially means number of nodes which can be reached with atmost k edges. We need to calculate maximum of this if you are allowed to take any node from tree1 and connect it to tree2.\n\n# Approach\nThe solution is pretty simple. You just need to calculate target nodes for each node from tree1 with k as the maximum edge count.\nIf you connect one node randomly with a node from tree2, you are creating one edge to make that connection. You need to calculate target nodes for each node in tree2 with (k - 1) as the maximum edge count. This is done to ensure the edge made from tree1, when accounted for, will result in target nodes from tree2 with k as edge count.\nA simple BFS on the entire tree is done for both of them with k and (k - 1) respectively, as the deciding parameter to satisfy target count. Once that is done, you just need to find the maximum value of target nodes amongst all the nodes from tree2. Add the maximum value to the target nodes of tree1 for each node and that is your answer.\n\n# Code\n```java []\nclass Solution {\n\n    // add null after each layer of nodes is complete to be able to count number layers we are deep\n    private void computeTargetNodes(Map<Integer, List<Integer>> graph, Map<Integer, Integer> target, int i, int n, int k) {\n        Queue<Integer> q = new LinkedList<>();\n        int[] visited = new int[n];\n        q.add(i);\n        q.add(null);\n        visited[i] = 1;\n        int layers = 0;\n        int targetNodesCount = 0;\n        while (!q.isEmpty()) {\n            if (layers > k) break;\n            Integer el = q.poll();\n            if (el == null && !q.isEmpty()) {\n                q.add(null);\n                layers++;\n            } else if (el != null) {\n                targetNodesCount++;\n                for (int node: graph.getOrDefault(el, new ArrayList<>())) {\n                    if (visited[node] == 0) {\n                        q.add(node);\n                        visited[node] = 1;\n                    }\n                }\n            }\n        }\n        target.put(i, targetNodesCount);\n        return;\n    }\n\n    public int[] maxTargetNodes(int[][] edges1, int[][] edges2, int k) {\n        int n = edges1.length + 1;\n        int m = edges2.length + 1;\n\n        // create graphs\n        Map<Integer, List<Integer>> g1 = new HashMap<>();\n        for (int[] e: edges1) {\n            List<Integer> arr = g1.getOrDefault(e[0], new ArrayList<>());\n            arr.add(e[1]);\n            g1.put(e[0], arr);\n\n            arr = g1.getOrDefault(e[1], new ArrayList<>());\n            arr.add(e[0]);\n            g1.put(e[1], arr);\n        }\n\n        Map<Integer, List<Integer>> g2 = new HashMap<>();\n        for (int[] e: edges2) {\n            List<Integer> arr = g2.getOrDefault(e[0], new ArrayList<>());\n            arr.add(e[1]);\n            g2.put(e[0], arr);\n\n            arr = g2.getOrDefault(e[1], new ArrayList<>());\n            arr.add(e[0]);\n            g2.put(e[1], arr);\n        }\n\n        // calculate target nodes for each node\n        Map<Integer, Integer> target1 = new HashMap<>();\n        for (int i = 0; i < n; i++) {\n            computeTargetNodes(g1, target1, i, n, k);\n        }\n\n        Map<Integer, Integer> target2 = new HashMap<>();\n        for (int i = 0; i < m; i++) {\n            computeTargetNodes(g2, target2, i, m, k - 1);\n        }\n\n        // compute max count of target nodes amongst all nodes from tree2\n        int mx = Integer.MIN_VALUE;\n        for (Map.Entry<Integer, Integer> el: target2.entrySet()) {\n            mx = Math.max(mx, el.getValue());\n        }\n\n        // add that to each node of tree1 to get the answer\n        int[] ans = new int[n];\n        for (Map.Entry<Integer, Integer> el: target1.entrySet()) {\n            ans[el.getKey()] = el.getValue() + mx;\n        }\n\n        return ans;\n    }\n}\n```
['Java']