Add tree_height.cpp in dynamic programming

Added tree_height.cpp in dynamic_programming directory

dynamic_programming/tree_height.cpp

@@ -0,0 +1,70 @@
+// C++ Program to find height of the tree using bottom-up dynamic programming.
+
+/*
+ * Given a rooted tree with node 1.
+ * Task is to find the height of the tree.
+ * Example: -
+ * 4
+ * 1 2
+ * 1 3
+ * 2 4
+ * which can be represented as                 
+ *   1                      
+ *  / \                     
+ * 2   3                    
+ * |                        
+ * 4            
+ * 
+ * Height of the tree : - 2
+*/
+
+#include<iostream>
+#include<vector>
+
+// global declarations
+// no of nodes max limit.
+const int MAX = 1e5;
+// adjacency list
+std::vector<int> adj[MAX];
+std::vector<bool> visited;
+std::vector<int> dp;
+
+void depth_first_search(int u) {
+    visited[u] = true;
+    int child_height = 1;
+    for (int v : adj[u]) {
+        if (!visited[v]) {
+            depth_first_search(v);
+
+            // select maximum sub-tree height from all children.
+            child_height = std::max(child_height, dp[v]+1);
+        }
+    }
+    // assigned the max child height to current visited node.
+    dp[u] = child_height;
+}
+
+int main() {
+    // number of nodes
+    int number_of_nodes;
+    std::cout << "Enter number of nodes of the tree : " << std::endl;
+    std::cin >> number_of_nodes;
+
+    // u, v denotes an undirected edge of tree.
+    int u, v;
+    // Tree contains exactly n-1 edges where n denotes the number of nodes.
+    std::cout << "Enter edges of the tree : " << std::endl;
+    for (int i = 0; i < number_of_nodes - 1; i++) {
+        std::cin >> u >> v;
+        // undirected tree u -> v and v -> u.
+        adj[u].push_back(v);
+        adj[v].push_back(u);
+    }
+    // initialize all nodes as unvisited.
+    visited.assign(number_of_nodes+1, false);
+    // initialize depth of all nodes to 0.
+    dp.assign(number_of_nodes+1, 0);
+    // function call which will initialize the height of all nodes.
+    depth_first_search(1);
+    std::cout << "Height of the Tree : " << dp[1] << std::endl;
+}