Print path between any two nodes in a Binary Tree | Set 2
Given a Binary Tree of distinct nodes and a pair of nodes. The task is to find and print the path between the two given nodes in the binary tree.
Examples:
Input: N1 = 7, N2 = 4
Output: 7 3 1 4
Approach: An approach to solve this problem has been discussed in this article. In this article, an even optimized recursive approach will be discussed.
In this recursive approach, below are the steps:
- Find the first value recursively, once found add the value to the stack.
- Now every node that is visited whether in backtracking or forward tracking, adds the values to the stack but if the node was added in the forward tracking then remove it in the backtracking and continue this until the second value is found or all nodes are visited.
For example: Consider the path between 7 and 9 is to be found in the above tree. We traverse the tree as DFS, once we find the value 7, we add it to the stack. Traversing path 0 -> 1 -> 3 -> 7.
Now while backtracking, add 3 and 1 to the stack. So as of now, the stack has [7, 3, 1], child 1 has a right child, so we first add it to the stack. Now, the stack contains [7, 3, 1, 4]. Visit the left child of 4, add it to the stack. The stack contains [7, 3, 1, 4, 8] now. Since there is no further node we would go back to the previous node and since 8 was already added to the stack so remove it. Now the node 4 has a right child, and we add it to the stack since this is the second value we were looking for there won’t be any further recursive calls. Finally, the stack contains [7, 3, 1, 4, 9].
Below is the implementation of the above approach:
C++
// CPP implementation of the approach #include <bits/stdc++.h> using namespace std; // A binary tree node class Node { public : int value; Node *left, *right; Node( int value) { this ->value = value; left = NULL; right = NULL; } }; bool firstValueFound = false ; bool secondValueFound = false ; stack<Node *> stk; Node *root = NULL; // Function to find the path between // two nodes in binary tree void pathBetweenNode(Node *root, int v1, int v2) { // Base condition if (root == NULL) return ; // If both the values are found then return if (firstValueFound && secondValueFound) return ; // Starting the stack frame with // isAddedToStack = false flag bool isAddedToStack = false ; // If one of the value is found then add the // value to the stack and make the isAddedToStack = true if (firstValueFound ^ secondValueFound) { stk.push(root); isAddedToStack = true ; } // If none of the two values is found if (!(firstValueFound && secondValueFound)) { pathBetweenNode(root->left, v1, v2); } // Copy of current state of firstValueFound // and secondValueFound flag bool localFirstValueFound = firstValueFound; bool localSecondValueFound = secondValueFound; // If the first value is found if (root->value == v1) firstValueFound = true ; // If the second value is found if (root->value == v2) secondValueFound = true ; bool localAdded = false ; // If one of the value is found and the value // was not added to the stack yet or there was // only one value found and now both the values // are found and was not added to // the stack then add it if (((firstValueFound ^ secondValueFound) || ((localFirstValueFound ^ localSecondValueFound) && (firstValueFound && secondValueFound))) && !isAddedToStack) { localAdded = true ; stk.push(root); } // If none of the two values is found yet if (!(firstValueFound && secondValueFound)) { pathBetweenNode(root->right, v1, v2); } if ((firstValueFound ^ secondValueFound) && !isAddedToStack && !localAdded) stk.push(root); if ((firstValueFound ^ secondValueFound) && isAddedToStack) stk.pop(); } // Function to find the path between // two nodes in binary tree stack<Node *> pathBetweenNode( int v1, int v2) { // Global root pathBetweenNode(::root, v1, v2); // If both the values are found // then return the stack if (firstValueFound && secondValueFound) { // Global Stack Object return ::stk; } // If none of the two values is // found then return empty stack stack<Node *> stk; return stk; } // Recursive function to print the // contents of a stack in reverse void print(stack<Node *> stk) { // If the stack is empty if (stk.empty()) return ; // Get the top value int value = stk.top()->value; stk.pop(); // Recursive call print(stk); // Print the popped value cout << value << " " ; } // Driver code int main( int argc, char const *argv[]) { root = new Node(0); root->left = new Node(1); root->right = new Node(2); root->left->left = new Node(3); root->left->right = new Node(4); root->right->left = new Node(5); root->right->right = new Node(6); root->left->left->left = new Node(7); root->left->right->left = new Node(8); root->left->right->right = new Node(9); // Find and print the path stack<Node *> stck = pathBetweenNode(7, 4); print(stck); } // This code is contributed by sanjeev2552 |
Java
// Java implementation of the approach import java.util.Stack; public class GFG { // A binary tree node private static class Node { public Node left; public int value; public Node right; public Node( int value) { this .value = value; left = null ; right = null ; } } private boolean firstValueFound = false ; private boolean secondValueFound = false ; private Stack<Node> stack = new Stack<Node>(); private Node root = null ; public GFG(Node root) { this .root = root; } // Function to find the path between // two nodes in binary tree public Stack<Node> pathBetweenNode( int v1, int v2) { pathBetweenNode( this .root, v1, v2); // If both the values are found // then return the stack if (firstValueFound && secondValueFound) { return stack; } // If none of the two values is // found then return empty stack return new Stack<Node>(); } // Function to find the path between // two nodes in binary tree private void pathBetweenNode(Node root, int v1, int v2) { // Base condition if (root == null ) return ; // If both the values are found then return if (firstValueFound && secondValueFound) return ; // Starting the stack frame with // isAddedToStack = false flag boolean isAddedToStack = false ; // If one of the value is found then add the // value to the stack and make the isAddedToStack = true if (firstValueFound ^ secondValueFound) { stack.add(root); isAddedToStack = true ; } // If none of the two values is found if (!(firstValueFound && secondValueFound)) { pathBetweenNode(root.left, v1, v2); } // Copy of current state of firstValueFound // and secondValueFound flag boolean localFirstValueFound = firstValueFound; boolean localSecondValueFound = secondValueFound; // If the first value is found if (root.value == v1) firstValueFound = true ; // If the second value is found if (root.value == v2) secondValueFound = true ; boolean localAdded = false ; // If one of the value is found and the value // was not added to the stack yet or there was // only one value found and now both the values // are found and was not added to // the stack then add it if (((firstValueFound ^ secondValueFound) || ((localFirstValueFound ^ localSecondValueFound) && (firstValueFound && secondValueFound))) && !isAddedToStack) { localAdded = true ; stack.add(root); } // If none of the two values is found yet if (!(firstValueFound && secondValueFound)) { pathBetweenNode(root.right, v1, v2); } if ((firstValueFound ^ secondValueFound) && !isAddedToStack && !localAdded) stack.add(root); if ((firstValueFound ^ secondValueFound) && isAddedToStack) stack.pop(); } // Recursive function to print the // contents of a stack in reverse private static void print(Stack<Node> stack) { // If the stack is empty if (stack.isEmpty()) return ; // Get the top value int value = stack.pop().value; // Recursive call print(stack); // Print the popped value System.out.print(value + " " ); } // Driver code public static void main(String[] args) { Node root = new Node( 0 ); root.left = new Node( 1 ); root.right = new Node( 2 ); root.left.left = new Node( 3 ); root.left.right = new Node( 4 ); root.right.left = new Node( 5 ); root.right.right = new Node( 6 ); root.left.left.left = new Node( 7 ); root.left.right.left = new Node( 8 ); root.left.right.right = new Node( 9 ); // Find and print the path GFG pathBetweenNodes = new GFG(root); Stack<Node> stack = pathBetweenNodes.pathBetweenNode( 7 , 4 ); print(stack); } } |
Python3
# Python3 implementation of # the above approach # A binary tree node class Node: def __init__( self , value): self .left = None self .right = None self .value = value firstValueFound = False secondValueFound = False stack = [] root = None # Function to find the path # between two nodes in binary # tree def pathBetweennode(v1, v2): global firstValueFound, secondValueFound pathBetweenNode(root, v1, v2) # If both the values are found # then return the stack if (firstValueFound and secondValueFound): return stack # If none of the two values is # found then return empty stack return [] # Function to find the path # between two nodes in binary # tree def pathBetweenNode(root, v1, v2): global firstValueFound, secondValueFound # Base condition if (root = = None ): return # If both the values are found # then return if (firstValueFound and secondValueFound): return # Starting the stack frame with # isAddedToStack = false flag isAddedToStack = False # If one of the value is found # then add the value to the # stack and make the isAddedToStack = true if (firstValueFound ^ secondValueFound): stack.append(root) isAddedToStack = True # If none of the two values # is found if ( not (firstValueFound and secondValueFound)): pathBetweenNode(root.left, v1, v2) # Copy of current state of # firstValueFound and # secondValueFound flag localFirstValueFound = firstValueFound localSecondValueFound = secondValueFound # If the first value is found if (root.value = = v1): firstValueFound = True # If the second value is found if (root.value = = v2): secondValueFound = True localAdded = False # If one of the value is found # and the value was not added # to the stack yet or there was # only one value found and now # both the values are found and # was not added to the stack # then add it if (((firstValueFound ^ secondValueFound) or ((localFirstValueFound ^ localSecondValueFound) and (firstValueFound and secondValueFound))) and not isAddedToStack): localAdded = True stack.append(root) # If none of the two values # is found yet if ( not (firstValueFound and secondValueFound)): pathBetweenNode(root.right, v1, v2) if ((firstValueFound ^ secondValueFound) and not isAddedToStack and not localAdded): stack.append(root) if ((firstValueFound ^ secondValueFound) and isAddedToStack): stack.pop() # Recursive function to print # the contents of a stack in # reverse def pri(stack): # If the stack is empty if ( len (stack) = = 0 ): return # Get the top value value = stack.pop().value # Recursive call pri(stack) # Print the popped value print (value, end = " " ) # Driver code if __name__ = = "__main__" : root = Node( 0 ) root.left = Node( 1 ) root.right = Node( 2 ) root.left.left = Node( 3 ) root.left.right = Node( 4 ) root.right.left = Node( 5 ) root.right.right = Node( 6 ) root.left.left.left = Node( 7 ) root.left.right.left = Node( 8 ) root.left.right.right = Node( 9 ) # Find and print the path stack = pathBetweennode( 7 , 4 ) pri(stack) # This code is contributed by Rutvik_56 |
C#
// C# implementation of the approach using System; using System.Collections; using System.Collections.Generic; class GFG { // A binary tree node public class Node { public Node left; public int value; public Node right; public Node( int value) { this .value = value; left = null ; right = null ; } } private Boolean firstValueFound = false ; private Boolean secondValueFound = false ; private Stack<Node> stack = new Stack<Node>(); private Node root = null ; public GFG(Node root) { this .root = root; } // Function to find the path between // two nodes in binary tree public Stack<Node> pathBetweenNode( int v1, int v2) { pathBetweenNode( this .root, v1, v2); // If both the values are found // then return the stack if (firstValueFound && secondValueFound) { return stack; } // If none of the two values is // found then return empty stack return new Stack<Node>(); } // Function to find the path between // two nodes in binary tree private void pathBetweenNode(Node root, int v1, int v2) { // Base condition if (root == null ) return ; // If both the values are found then return if (firstValueFound && secondValueFound) return ; // Starting the stack frame with // isAddedToStack = false flag Boolean isAddedToStack = false ; // If one of the value is found then add the // value to the stack and make the isAddedToStack = true if (firstValueFound ^ secondValueFound) { stack.Push(root); isAddedToStack = true ; } // If none of the two values is found if (!(firstValueFound && secondValueFound)) { pathBetweenNode(root.left, v1, v2); } // Copy of current state of firstValueFound // and secondValueFound flag Boolean localFirstValueFound = firstValueFound; Boolean localSecondValueFound = secondValueFound; // If the first value is found if (root.value == v1) firstValueFound = true ; // If the second value is found if (root.value == v2) secondValueFound = true ; Boolean localAdded = false ; // If one of the value is found and the value // was not added to the stack yet or there was // only one value found and now both the values // are found and was not added to // the stack then add it if (((firstValueFound ^ secondValueFound) || ((localFirstValueFound ^ localSecondValueFound) && (firstValueFound && secondValueFound))) && !isAddedToStack) { localAdded = true ; stack.Push(root); } // If none of the two values is found yet if (!(firstValueFound && secondValueFound)) { pathBetweenNode(root.right, v1, v2); } if ((firstValueFound ^ secondValueFound) && !isAddedToStack && !localAdded) stack.Push(root); if ((firstValueFound ^ secondValueFound) && isAddedToStack) stack.Pop(); } // Recursive function to print the // contents of a stack in reverse private static void print(Stack<Node> stack) { // If the stack is empty if (stack.Count==0) return ; // Get the top value int value = stack.Pop().value; // Recursive call print(stack); // Print the Popped value Console.Write(value + " " ); } // Driver code public static void Main(String []args) { Node root = new Node(0); root.left = new Node(1); root.right = new Node(2); root.left.left = new Node(3); root.left.right = new Node(4); root.right.left = new Node(5); root.right.right = new Node(6); root.left.left.left = new Node(7); root.left.right.left = new Node(8); root.left.right.right = new Node(9); // Find and print the path GFG pathBetweenNodes = new GFG(root); Stack<Node> stack = pathBetweenNodes.pathBetweenNode(7, 4); print(stack); } } // This code is contributed by Arnab Kundu |
Javascript
<script> // JavaScript implementation of the approach // A binary tree node class Node { constructor(value) { this .left = null ; this .right = null ; this .value = value; } } let firstValueFound = false ; let secondValueFound = false ; let stack = []; let root = null ; // Function to find the path between // two nodes in binary tree function path_BetweenNode(root, v1, v2) { // Base condition if (root == null ) return ; // If both the values are found then return if (firstValueFound && secondValueFound) return ; // Starting the stack frame with // isAddedToStack = false flag let isAddedToStack = false ; // If one of the value is found then add the // value to the stack and make the isAddedToStack = true if (firstValueFound ^ secondValueFound) { stack.push(root); isAddedToStack = true ; } // If none of the two values is found if (!(firstValueFound && secondValueFound)) { path_BetweenNode(root.left, v1, v2); } // Copy of current state of firstValueFound // and secondValueFound flag let localFirstValueFound = firstValueFound; let localSecondValueFound = secondValueFound; // If the first value is found if (root.value == v1) firstValueFound = true ; // If the second value is found if (root.value == v2) secondValueFound = true ; let localAdded = false ; // If one of the value is found and the value // was not added to the stack yet or there was // only one value found and now both the values // are found and was not added to // the stack then add it if (((firstValueFound ^ secondValueFound) || ((localFirstValueFound ^ localSecondValueFound) && (firstValueFound && secondValueFound))) && !isAddedToStack) { localAdded = true ; stack.push(root); } // If none of the two values is found yet if (!(firstValueFound && secondValueFound)) { path_BetweenNode(root.right, v1, v2); } if ((firstValueFound ^ secondValueFound) && !isAddedToStack && !localAdded) stack.push(root); if ((firstValueFound ^ secondValueFound) && isAddedToStack) stack.pop(); } // Function to find the path between // two nodes in binary tree function pathBetweenNode(v1, v2) { path_BetweenNode(root, v1, v2); // If both the values are found // then return the stack if (firstValueFound && secondValueFound) { return stack; } // If none of the two values is // found then return empty stack return []; } // Recursive function to print the // contents of a stack in reverse function print(stack) { // If the stack is empty if (stack.length == 0) return ; // Get the top value let value = stack[stack.length - 1].value; stack.pop(); // Recursive call print(stack); // Print the popped value document.write(value + " " ); } root = new Node(0); root.left = new Node(1); root.right = new Node(2); root.left.left = new Node(3); root.left.right = new Node(4); root.right.left = new Node(5); root.right.right = new Node(6); root.left.left.left = new Node(7); root.left.right.left = new Node(8); root.left.right.right = new Node(9); // Find and print the path stack = pathBetweenNode(7, 4); print(stack); </script> |
7 3 1 4
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