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 the sum of all values in the ancestral nodes of a given node in a Binary Tree.
Following figure shows a Binary Tree and the another tree with node values replaced by the ancestral sum. For e.g, for the node 1 , sum of the values of ancestral nodes is 1 + 3 + 7 = 11 and for the node 4 , sum of ancestral nodes is 4 + 5 + 3 + 7 = 19 .

ancestral node sum

Solution :-
This problem can be solved by a minor extension of any of the traversal mechanism. We can do an inorder traversal of the tree and maintain the sum of the ancestral node values. See the implementation below.

#include<iostream>
using namespace std;

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

// 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(7);
   root->left = getNewNode(3);
   root->right = getNewNode(11);
   root->left->left = getNewNode(1);
   root->left->right = getNewNode(5);
   root->left->right->left = getNewNode(4);
   root->left->right->right = getNewNode(6);
   return root;
}

// Inorder traversal of a tree
void inorderTraversal(node *ptr) {
   if(ptr == NULL)
      return;
   else {
      inorderTraversal(ptr->left);
      cout<<ptr->value<<"\t";
      inorderTraversal(ptr->right);
   }
}

// Print the sum of all values in the ancestral nodes of a given node
void ancestralSums(node *root,int sum) {
   if (!root) return;
   sum += root->value;
   ancestralSums(root->left,sum);
   cout<<sum<<"\t";
   ancestralSums(root->right,sum);
}

// main
int main() {
   node *root = createTree();
   cout<<"\nInorder traversal ...\n\n";
   inorderTraversal(root);
   cout<<"\n\nAncestral Sum :-\n\n";
   ancestralSums(root,0);
   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 )