The best programs are written so that computing machines can perform them quickly and so that human beings can understand them clearly. A programmer is ideally an essayist who works with traditional aesthetic and literary forms as
well as mathematical concepts, to communicate the way that an algorithm works and to convince a reader that the results will be correct. Donald E. Knuth

Tree

Problem :-
Print all the ancestors of a given node in a Binary Tree.
In the tree shown below, ancestors of 29 are 24 ,16 and 31 .

ancestors of a node in a binary tree

Solution :-
As we do a recursive traversal of right and left subtrees of each node, if the given node ( X ) lies in the subtree of any node ( P ), then P is the ancestor of the given node. See the implementation below.

#include<iostream>
using namespace std;

// node structure
typedef struct tree_node {
   int value;
      struct tree_node *left, *right;
}node;

// recursive function to print all the ancestors of a give node
// true denotes current node is the ancestor of target node 
bool printAncestors(node *root, int target)
{
   if (root == NULL)
      return false;
   if (root->value == target)
      return true;
   if (printAncestors(root->left,target) || printAncestors(root->right,target)) {
      // if the target lies in the left subtree or the right subtree
      // then it is the ancestor of the target
      cout<<root->value<<" ";
      return true;
   }
   return false;
}

// create a new node
node *getNewNode(int value) {
   node *new_node = new node;
   new_node->value = value;
   new_node->left = NULL;
   new_node->right = NULL;
   return new_node;
}

// create the tree
node *createTree() {
   node *root = getNewNode(31);
   root->left = getNewNode(16);
   root->right = getNewNode(52);
   root->left->left = getNewNode(7);
   root->left->right = getNewNode(24);
   root->left->right->left = getNewNode(19);
   root->left->right->right = getNewNode(29);
   return root;
}

// main 
int main() {
   node *root = NULL;
   root = createTree();
   printAncestors(root, 29);
   cout<<endl;
   return 0;
}

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All problems on Trees
* Implement the inorder , preorder and postorder traversal mechanisms of a tree
* Implement an algorithm to insert a node in a Binary Search Tree ( BST )
* Implement an algorithm to find the height of a Binary Tree
* Implement an algorithm to get the level of a node in a Binary Tree assuming root node to be at level 1
* Get the root to leaf path in a Binary Tree such that the sum of the node values in that path is minimum among all possible root to leaf paths
* Print all the ancestors of a given node in a Binary Tree
* Replace all the node values with the sum of the node values of ancestral nodes in a Binary Tree
* Check if the given tree is a sum tree i.e value at each node is equal to the value of all elements in its left subtree and right subtree
* Given a Binary Tree, create another tree which is a mirror image of the given tree
* Construct a tree, given its inorder and preorder traversals
* Find the Least Common Ancestor ( LCA ) of two nodes in a Binary Search Tree
* Find the Least Common Ancestor ( LCA ) of two nodes in a Binary Tree
* Compute the Diameter of a given Binary Tree
* Check if a given tree is a Binary Search Tree ( BST )