Algorithms‎ > ‎Trees‎ > ‎

### Nodes at distance k

http://www.geeksforgeeks.org/print-nodes-distance-k-given-node-binary-tree/

## Print all nodes at distance k from a given node

Given a binary tree, a target node in the binary tree, and an integer value k, print all the nodes that are at distance k from the given target node. No parent pointers are available. ```Consider the tree shown in diagram

Input: target = pointer to node with data 8.
root = pointer to node with data 20.
k = 2.
Output : 10 14 22

If target is 14 and k is 3, then output
should be "4 20"

```

We strongly recommend to minimize the browser and try this yourself first.

There are two types of nodes to be considered.
1) Nodes in the subtree rooted with target node. For example if the target node is 8 and k is 2, then such nodes are 10 and 14.
2) Other nodes, may be an ancestor of target, or a node in some other subtree. For target node 8 and k is 2, the node 22 comes in this category.

Finding the first type of nodes is easy to implement. Just traverse subtrees rooted with the target node and decrement k in recursive call. When the k becomes 0, print the node currently being traversed (See this for more details). Here we call the function as printkdistanceNodeDown().

How to find nodes of second type? For the output nodes not lying in the subtree with the target node as the root, we must go through all ancestors. For every ancestor, we find its distance from target node, let the distance be d, now we go to other subtree (if target was found in left subtree, then we go to right subtree and vice versa) of the ancestor and find all nodes at k-d distance from the ancestor.

Following is C++ implementation of the above approach.

 `#include ``using` `namespace` `std;` `// A binary Tree node``struct` `node``{``    ``int` `data;``    ``struct` `node *left, *right;``};` `/* Recursive function to print all the nodes at distance k in the``   ``tree (or subtree) rooted with given root. See  */``void` `printkdistanceNodeDown(node *root, ``int` `k)``{``    ``// Base Case``    ``if` `(root == NULL || k < 0)  ``return``;` `    ``// If we reach a k distant node, print it``    ``if` `(k==0)``    ``{``        ``cout << root->data << endl;``        ``return``;``    ``}` `    ``// Recur for left and right subtrees``    ``printkdistanceNodeDown(root->left, k-1);``    ``printkdistanceNodeDown(root->right, k-1);``}` `// Prints all nodes at distance k from a given target node.``// The k distant nodes may be upward or downward.  This function``// Returns distance of root from target node, it returns -1 if target``// node is not present in tree rooted with root.``int` `printkdistanceNode(node* root, node* target , ``int` `k)``{``    ``// Base Case 1: If tree is empty, return -1``    ``if` `(root == NULL) ``return` `-1;` `    ``// If target is same as root.  Use the downward function``    ``// to print all nodes at distance k in subtree rooted with``    ``// target or root``    ``if` `(root == target)``    ``{``        ``printkdistanceNodeDown(root, k);``        ``return` `0;``    ``}` `    ``// Recur for left subtree``    ``int` `dl = printkdistanceNode(root->left, target, k);` `    ``// Check if target node was found in left subtree``    ``if` `(dl != -1)``    ``{``         ``// If root is at distance k from target, print root``         ``// Note that dl is Distance of root's left child from target``         ``if` `(dl + 1 == k)``            ``cout << root->data << endl;` `         ``// Else go to right subtree and print all k-dl-2 distant nodes``         ``// Note that the right child is 2 edges away from left child``         ``else``            ``printkdistanceNodeDown(root->right, k-dl-2);` `         ``// Add 1 to the distance and return value for parent calls``         ``return` `1 + dl;``    ``}` `    ``// MIRROR OF ABOVE CODE FOR RIGHT SUBTREE``    ``// Note that we reach here only when node was not found in left subtree``    ``int` `dr = printkdistanceNode(root->right, target, k);``    ``if` `(dr != -1)``    ``{``         ``if` `(dr + 1 == k)``            ``cout << root->data << endl;``         ``else``            ``printkdistanceNodeDown(root->left, k-dr-2);``         ``return` `1 + dr;``    ``}` `    ``// If target was neither present in left nor in right subtree``    ``return` `-1;``}` `// A utility function to create a new binary tree node``node *newnode(``int` `data)``{``    ``node *temp = ``new` `node;``    ``temp->data = data;``    ``temp->left = temp->right = NULL;``    ``return` `temp;``}` `// Driver program to test above functions``int` `main()``{``    ``/* Let us construct the tree shown in above diagram */``    ``node * root = newnode(20);``    ``root->left = newnode(8);``    ``root->right = newnode(22);``    ``root->left->left = newnode(4);``    ``root->left->right = newnode(12);``    ``root->left->right->left = newnode(10);``    ``root->left->right->right = newnode(14);``    ``node * target = root->left->right;``    ``printkdistanceNode(root, target, 2);``    ``return` `0;``}`

Output:

```4
20```

Time Complexity: At first look the time complexity looks more than O(n), but if we take a closer look, we can observe that no node is traversed more than twice. Therefore the time complexity is O(n).

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