Print the path common to the two paths from the root to the two given nodes
Given a binary tree with distinct nodes(no two nodes have the same have data values). The problem is to print the path common to the two paths from the root to the two given nodes n1 and n2. If either of the nodes are not present then print “No Common Path”.
Examples:
Input : 1
/ \
2 3
/ \ / \
4 5 6 7
/ \
8 9
n1 = 4, n2 = 8
Output : 1->2
Path form root to n1:
1->2->4
Path form root to n2:
1->2->5->8
Common Path:
1->2
Approach:The following steps are:
- Find the LCA(Lowest Common Ancestor) of the two nodes n1 and n2. Refer this.
- If LCA exits then print the path from the root to LCA. Refer this. Else print “No Common Path”.
C++
// C++ implementation to print the path common to the // two paths from the root to the two given nodes #include <bits/stdc++.h> using namespace std; // structure of a node of binary tree struct Node { int data; Node *left, *right; }; /* Helper function that allocates a new node with the given data and NULL left and right pointers. */struct Node* getNode(int data) { struct Node *newNode = (struct Node*)malloc(sizeof(struct Node)); newNode->data = data; newNode->left = newNode->right = NULL; return newNode; } // This function returns pointer to LCA of two given values n1 and n2. // v1 is set as true by this function if n1 is found // v2 is set as true by this function if n2 is found struct Node *findLCAUtil(struct Node* root, int n1, int n2, bool &v1, bool &v2) { // Base case if (root == NULL) return NULL; // If either n1 or n2 matches with root's data, report the presence // by setting v1 or v2 as true and return root (Note that if a key // is ancestor of other, then the ancestor key becomes LCA) if (root->data == n1) { v1 = true; return root; } if (root->data == n2) { v2 = true; return root; } // Look for nodes in left and right subtrees Node *left_lca = findLCAUtil(root->left, n1, n2, v1, v2); Node *right_lca = findLCAUtil(root->right, n1, n2, v1, v2); // If both of the above calls return Non-NULL, then one node // is present in one subtree and other is present in other, // So this current node is the LCA if (left_lca && right_lca) return root; // Otherwise check if left subtree or right subtree is LCA return (left_lca != NULL)? left_lca: right_lca; } // Returns true if key k is present in tree rooted with root bool find(Node *root, int k) { // Base Case if (root == NULL) return false; // If key k is present at root, or in left subtree // or right subtree, return true if (root->data == k || find(root->left, k) || find(root->right, k)) return true; // Else return false return false; } // This function returns LCA of n1 and n2 only if both n1 and n2 // are present in tree, otherwise returns NULL Node *findLCA(Node *root, int n1, int n2) { // Initialize n1 and n2 as not visited bool v1 = false, v2 = false; // Find lca of n1 and n2 Node *lca = findLCAUtil(root, n1, n2, v1, v2); // Return LCA only if both n1 and n2 are present in tree if (v1 && v2 || v1 && find(lca, n2) || v2 && find(lca, n1)) return lca; // Else return NULL return NULL; } // function returns true if // there is a path from root to // the given node. It also populates // 'arr' with the given path bool hasPath(Node *root, vector<int>& arr, int x) { // if root is NULL // there is no path if (!root) return false; // push the node's value in 'arr' arr.push_back(root->data); // if it is the required node // return true if (root->data == x) return true; // else check whether there the required node lies in the // left subtree or right subtree of the current node if (hasPath(root->left, arr, x) || hasPath(root->right, arr, x)) return true; // required node does not lie either in the // left or right subtree of the current node // Thus, remove current node's value from 'arr' // and then return false; arr.pop_back(); return false; } // function to print the path common // to the two paths from the root // to the two given nodes if the nodes // lie in the binary tree void printCommonPath(Node *root, int n1, int n2) { // vector to store the common path vector<int> arr; // LCA of node n1 and n2 Node *lca = findLCA(root, n1, n2); // if LCA of both n1 and n2 exists if (lca) { // then print the path from root to // LCA node if (hasPath(root, arr, lca->data)) { for (int i=0; i<arr.size()-1; i++) cout << arr[i] << "->"; cout << arr[arr.size() - 1]; } } // LCA is not present in the binary tree // either n1 or n2 or both are not present else cout << "No Common Path"; } // Driver program to test above int main() { // binary tree formation struct Node *root = getNode(1); root->left = getNode(2); root->right = getNode(3); root->left->left = getNode(4); root->left->right = getNode(5); root->right->left = getNode(6); root->right->right = getNode(7); root->left->right->left = getNode(8); root->right->left->right = getNode(9); int n1 = 4, n2 = 8; printCommonPath(root, n1, n2); return 0; } |
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Java
// Java implementation to print the path common to the // two paths from the root to the two given nodes import java.util.ArrayList; public class PrintCommonPath { // Initialize n1 and n2 as not visited static boolean v1 = false, v2 = false; // This function returns pointer to LCA of two given // values n1 and n2. This function assumes that n1 and // n2 are present in Binary Tree static Node findLCAUtil(Node node, int n1, int n2) { // Base case if (node == null) return null; //Store result in temp, in case of key match so that we can search for other key also. Node temp=null; // If either n1 or n2 matches with root's key, report the presence // by setting v1 or v2 as true and return root (Note that if a key // is ancestor of other, then the ancestor key becomes LCA) if (node.data == n1) { v1 = true; temp = node; } if (node.data == n2) { v2 = true; temp = node; } // Look for keys in left and right subtrees Node left_lca = findLCAUtil(node.left, n1, n2); Node right_lca = findLCAUtil(node.right, n1, n2); if (temp != null) return temp; // If both of the above calls return Non-NULL, then one key // is present in once subtree and other is present in other, // So this node is the LCA if (left_lca != null && right_lca != null) return node; // Otherwise check if left subtree or right subtree is LCA return (left_lca != null) ? left_lca : right_lca; } // Returns true if key k is present in tree rooted with root static boolean find(Node root, int k) { // Base Case if (root == null) return false; // If key k is present at root, or in left subtree // or right subtree, return true if (root.data == k || find(root.left, k) || find(root.right, k)) return true; // Else return false return false; } // This function returns LCA of n1 and n2 only if both n1 and n2 // are present in tree, otherwise returns null static Node findLCA(Node root, int n1, int n2) { // Find lca of n1 and n2 Node lca = findLCAUtil(root, n1, n2); // Return LCA only if both n1 and n2 are present in tree if (v1 && v2 || v1 && find(lca, n2) || v2 && find(lca, n1)) return lca; // Else return null return null; } // function returns true if // there is a path from root to // the given node. It also populates // 'arr' with the given path static boolean hasPath(Node root, ArrayList<Integer> arr, int x) { // if root is null // there is no path if (root==null) return false; // push the node's value in 'arr' arr.add(root.data); // if it is the required node // return true if (root.data == x) return true; // else check whether there the required node lies in the // left subtree or right subtree of the current node if (hasPath(root.left, arr, x) || hasPath(root.right, arr, x)) return true; // required node does not lie either in the // left or right subtree of the current node // Thus, remove current node's value from 'arr' // and then return false; arr.remove(arr.size()-1); return false; } // function to print the path common // to the two paths from the root // to the two given nodes if the nodes // lie in the binary tree static void printCommonPath(Node root, int n1, int n2) { // ArrayList to store the common path ArrayList<Integer> arr=new ArrayList<>(); // LCA of node n1 and n2 Node lca = findLCA(root, n1, n2); // if LCA of both n1 and n2 exists if (lca!=null) { // then print the path from root to // LCA node if (hasPath(root, arr, lca.data)) { for (int i=0; i<arr.size()-1; i++) System.out.print(arr.get(i)+"->"); System.out.print(arr.get(arr.size() - 1)); } } // LCA is not present in the binary tree // either n1 or n2 or both are not present else System.out.print("No Common Path"); } public static void main(String args[]) { Node root = new Node(1); root.left = new Node(2); root.right = new Node(3); root.left.left = new Node(4); root.left.right = new Node(5); root.right.left = new Node(6); root.right.right = new Node(7); root.left.right.left = new Node(8); root.right.left.right = new Node(9); int n1 = 4, n2 = 8; printCommonPath(root, n1, n2); } } /* Class containing left and right child of current node and key value*/class Node { int data; Node left, right; public Node(int item) { data = item; left = right = null; } } //This code is contributed by Gaurav Tiwari |
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Python3
# Python implementation to print the path common to the # two paths from the root to the two given nodes # structure of a node of binary tree class Node: def __init__(self, data): self.data = data self.left = None self.right = None # This function returns pointer to LCA of two given values n1 and n2. # v1 is set as True by this function if n1 is found # v2 is set as True by this function if n2 is found def findLCAUtil(root: Node, n1: int, n2: int) -> Node: global v1, v2 # Base case if (root is None): return None # If either n1 or n2 matches with root's data, report the presence # by setting v1 or v2 as True and return root (Note that if a key # is ancestor of other, then the ancestor key becomes LCA) if (root.data == n1): v1 = True return root if (root.data == n2): v2 = True return root # Look for nodes in left and right subtrees left_lca = findLCAUtil(root.left, n1, n2) right_lca = findLCAUtil(root.right, n1, n2) # If both of the above calls return Non-None, then one node # is present in one subtree and other is present in other, # So this current node is the LCA if (left_lca and right_lca): return root # Otherwise check if left subtree or right subtree is LCA return left_lca if (left_lca != None) else right_lca # Returns True if key k is present in tree rooted with root def find(root: Node, k: int) -> bool: # Base Case if (root == None): return False # If key k is present at root, or in left subtree # or right subtree, return True if (root.data == k or find(root.left, k) or find(root.right, k)): return True # Else return False return False # This function returns LCA of n1 and n2 only if both n1 and n2 # are present in tree, otherwise returns None def findLCA(root: Node, n1: int, n2: int) -> Node: global v1, v2 # Initialize n1 and n2 as not visited v1 = False v2 = False # Find lca of n1 and n2 lca = findLCAUtil(root, n1, n2) # Return LCA only if both n1 and n2 are present in tree if (v1 and v2 or v1 and find(lca, n2) or v2 and find(lca, n1)): return lca # Else return None return None # function returns True if # there is a path from root to # the given node. It also populates # 'arr' with the given path def hasPath(root: Node, arr: list, x: int) -> Node: # if root is None # there is no path if (root is None): return False # push the node's value in 'arr' arr.append(root.data) # if it is the required node # return True if (root.data == x): return True # else check whether there the required node lies in the # left subtree or right subtree of the current node if (hasPath(root.left, arr, x) or hasPath(root.right, arr, x)): return True # required node does not lie either in the # left or right subtree of the current node # Thus, remove current node's value from 'arr' # and then return False; arr.pop() return False # function to print the path common # to the two paths from the root # to the two given nodes if the nodes # lie in the binary tree def printCommonPath(root: Node, n1: int, n2: int): # vector to store the common path arr = [] # LCA of node n1 and n2 lca = findLCA(root, n1, n2) # if LCA of both n1 and n2 exists if (lca): # then print the path from root to # LCA node if (hasPath(root, arr, lca.data)): for i in range(len(arr) - 1): print(arr[i], end="->") print(arr[-1]) # LCA is not present in the binary tree # either n1 or n2 or both are not present else: print("No Common Path") # Driver Code if __name__ == "__main__": v1 = 0 v2 = 0 root = Node(1) root.left = Node(2) root.right = Node(3) root.left.left = Node(4) root.left.right = Node(5) root.right.left = Node(6) root.right.right = Node(7) root.left.right.left = Node(8) root.right.left.right = Node(9) n1 = 4 n2 = 8 printCommonPath(root, n1, n2) # This code is contributed by # sanjeev2552 |
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C#
// C# implementation to print the path common to the // two paths from the root to the two given nodes using System; using System.Collections.Generic; public class PrintCommonPath { // Initialize n1 and n2 as not visited static Boolean v1 = false, v2 = false; // This function returns pointer to LCA of two given // values n1 and n2. This function assumes that n1 and // n2 are present in Binary Tree static Node findLCAUtil(Node node, int n1, int n2) { // Base case if (node == null) return null; //Store result in temp, in case of key // match so that we can search for other key also. Node temp=null; // If either n1 or n2 matches with root's key, report the presence // by setting v1 or v2 as true and return root (Note that if a key // is ancestor of other, then the ancestor key becomes LCA) if (node.data == n1) { v1 = true; temp = node; } if (node.data == n2) { v2 = true; temp = node; } // Look for keys in left and right subtrees Node left_lca = findLCAUtil(node.left, n1, n2); Node right_lca = findLCAUtil(node.right, n1, n2); if (temp != null) return temp; // If both of the above calls return Non-NULL, then one key // is present in once subtree and other is present in other, // So this node is the LCA if (left_lca != null && right_lca != null) return node; // Otherwise check if left subtree or right subtree is LCA return (left_lca != null) ? left_lca : right_lca; } // Returns true if key k is present in tree rooted with root static Boolean find(Node root, int k) { // Base Case if (root == null) return false; // If key k is present at root, or in left subtree // or right subtree, return true if (root.data == k || find(root.left, k) || find(root.right, k)) return true; // Else return false return false; } // This function returns LCA of n1 and n2 only if both n1 and n2 // are present in tree, otherwise returns null static Node findLCA(Node root, int n1, int n2) { // Find lca of n1 and n2 Node lca = findLCAUtil(root, n1, n2); // Return LCA only if both n1 and n2 are present in tree if (v1 && v2 || v1 && find(lca, n2) || v2 && find(lca, n1)) return lca; // Else return null return null; } // function returns true if // there is a path from root to // the given node. It also populates // 'arr' with the given path static Boolean hasPath(Node root, List<int> arr, int x) { // if root is null // there is no path if (root == null) return false; // push the node's value in 'arr' arr.Add(root.data); // if it is the required node // return true if (root.data == x) return true; // else check whether there the required node lies in the // left subtree or right subtree of the current node if (hasPath(root.left, arr, x) || hasPath(root.right, arr, x)) return true; // required node does not lie either in the // left or right subtree of the current node // Thus, remove current node's value from 'arr' // and then return false; arr.Remove(arr.Count-1); return false; } // function to print the path common // to the two paths from the root // to the two given nodes if the nodes // lie in the binary tree static void printCommonPath(Node root, int n1, int n2) { // ArrayList to store the common path List<int> arr = new List<int>(); // LCA of node n1 and n2 Node lca = findLCA(root, n1, n2); // if LCA of both n1 and n2 exists if (lca!=null) { // then print the path from root to // LCA node if (hasPath(root, arr, lca.data)) { for (int i=0; i<arr.Count-1; i++) Console.Write(arr[i]+"->"); Console.Write(arr[arr.Count - 1]); } } // LCA is not present in the binary tree // either n1 or n2 or both are not present else Console.Write("No Common Path"); } // Driver code public static void Main(String []args) { Node root = new Node(1); root.left = new Node(2); root.right = new Node(3); root.left.left = new Node(4); root.left.right = new Node(5); root.right.left = new Node(6); root.right.right = new Node(7); root.left.right.left = new Node(8); root.right.left.right = new Node(9); int n1 = 4, n2 = 8; printCommonPath(root, n1, n2); } } /* Class containing left and right child of current node and key value*/public class Node { public int data; public Node left, right; public Node(int item) { data = item; left = right = null; } } // This code has been contributed by 29AjayKumar |
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Output:
1->2
Time complexity: O(n), where n is the number of nodes in the binary tree.
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