Given two Binary trees and two integer keys K1, K2 where both K1, K2 can be present in the same tree or in different trees. Let F1, F2 be the vectors representing the sequence of the vertices from root to K1 and K2 (K1 & K2 excluded), the task is to find the dot product of both of these vectors.
Note: There are no duplicates in the tree and both the trees are different from each other. In case if the keys are present at different depths, then only consider nodes till the same depth level.
Input: K1 = 4, K2 = 5
Clearly from the 2 trees, both the keys are present in the first tree. The sequence of the vertices from the root to the K1 or F1 vector is, F1 = (1, 2) and F2 = (1, 2).
Now the dot product i.e. F1.F2 = 1×1 + 2×2 = 5.
Input: K1 = 5, K2 = 7
F1 = (1, 2) and F2 = (6)
Since only need to consider the nodes till the same depth level, the dot product is F1.F2 = 1×6 = 6.
Approach: The idea is to find the tree in which the given key-value is present and then, calculate the dot product of the ancestors. Follow the steps below to solve the problem:
- Initialize two different auxiliary vectors.
- Store the ancestors of both the keys in the vectors.
- Traverse the vectors until the end of any one of the vectors is reached and keep on calculating the dot product of the corresponding elements of the vectors.
- Print the final dot product as the answer.
Time Complexity: O(N) where N is the number of nodes in the tree.
Auxiliary Space: O(N)
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