From e97d696f7c0e04b422727be6d3897d3900c1fbd5 Mon Sep 17 00:00:00 2001
From: chayan das <110921638+Chayandas07@users.noreply.github.com>
Date: Mon, 24 Feb 2025 22:26:45 +0530
Subject: [PATCH] Create 2467. Most Profitable Path in a Tree

---
 2467. Most Profitable Path in a Tree | 73 ++++++++++++++++++++++++++++
 1 file changed, 73 insertions(+)
 create mode 100644 2467. Most Profitable Path in a Tree

diff --git a/2467. Most Profitable Path in a Tree b/2467. Most Profitable Path in a Tree
new file mode 100644
index 0000000..a76fcf4
--- /dev/null
+++ b/2467. Most Profitable Path in a Tree	
@@ -0,0 +1,73 @@
+class Solution {
+    int midNode = -1;
+
+public:
+    void findParent(int node, int par, vector<int> adj[], unordered_map<int, int> &mp) {
+        mp[node] = par;
+        for (auto i : adj[node]) {
+            if (i != par) {
+                findParent(i, node, adj, mp);
+            }
+        }
+    }
+
+    void dfs(int node, int par, int sum, vector<int> adj[], vector<int> &amount, vector<int> &dist, vector<int> &leaf, vector<bool> &zeroNodes) {
+        bool isLeaf = true;
+        dist[node] = sum;
+        for (auto i : adj[node]) {
+            if (i != par) {
+                isLeaf = false;
+                if (i == midNode) {
+                    dfs(i, node, sum + (amount[i] / 2), adj, amount, dist, leaf, zeroNodes);
+                } else if (zeroNodes[i]) {
+                    dfs(i, node, sum, adj, amount, dist, leaf, zeroNodes);
+                } else {
+                    dfs(i, node, sum + amount[i], adj, amount, dist, leaf, zeroNodes);
+                }
+            }
+        }
+        leaf[node] = isLeaf;
+    }
+
+    int mostProfitablePath(vector<vector<int>> &edges, int bob, vector<int> &amount) {
+        int n = edges.size() + 1;
+        vector<int> adj[n];
+        for (auto e : edges) {
+            adj[e[0]].push_back(e[1]);
+            adj[e[1]].push_back(e[0]);
+        }
+
+        unordered_map<int, int> parent;
+        findParent(0, -1, adj, parent);
+
+        vector<int> bobNodes;
+
+        do {
+            bobNodes.push_back(bob);
+            bob = parent[bob];
+        } while (bob != -1);
+
+        if (bobNodes.size() % 2 == 1) {
+            midNode = bobNodes[bobNodes.size() / 2];
+        }
+
+        vector<bool> zeroNodes(n, 0);
+        for (int i = 0; i < bobNodes.size(); i++) {
+            if (i < bobNodes.size() / 2) {
+                zeroNodes[bobNodes[i]] = 1;
+            }
+        }
+
+        vector<int> dist(n, INT_MIN), leaf(n);
+        dfs(0, -1, amount[0], adj, amount, dist, leaf, zeroNodes);
+
+        int ans = INT_MIN;
+        for (int i = 0; i < n; i++) {
+            if (leaf[i]) {
+                ans = max(ans, dist[i]);
+            }
+        }
+
+        return ans;
+    }
+};