Print Diagonal Traversal of Binary Tree

Given a binary tree, print all nodes for each diagonal having negative slope (\). Assume that the left and right child of a node makes 45 degree angle with the parent.

 

For example, consider below binary tree having three diagonals (marked in red).
The diagonals traversal is

1 3 6
2 5 8
4 7

diagonal-traversal
 


 

This problem can be easily solved with the help of Hashing. The idea is to create an empty map where each key in the map represents a diagonal in the binary tree and its value maintains all nodes present in the diagonal. Then we do a pre-order traversal of the tree and update the map. For each node, we recurse for its left subtree by increasing diagonal by 1 and recurse for right subtree with same diagonal.

 
C++ implementation –
 

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The time complexity of above solution is O(n) and auxiliary space used by the program is O(n).
 


 
Iterative version –
 

We can also use Queue to solve this problem. The idea is similar to level order traversal but instead of storing nodes of a level, we enqueue nodes in a diagonal.

 
C++ implementation –
 

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The time complexity of above solution is O(n) and auxiliary space used by the program is O(n).
 

Exercise:
Modify the solution to print diagonal elements for diagonals having positive slope (/).
 

Thanks for reading.




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