Given a binary tree. Find if a given vertical level of the binary tree is sorted or not.
(For the case when two nodes are overlapping, check if they form a sorted sequence in the level they lie.)
Prerequisite: Vertical Order Traversal
Input : 1 / \ 2 5 / \ 7 4 / 6 Level l = -1 Output : Yes Nodes in level -1 are 2 -> 6 which forms a sorted sequence. Input: 1 / \ 2 6 \ / 3 4 Level l = 0 Output : Yes Note that nodes with value 3 and 4 are overlapping in the binary tree. So we check if this form a sorted sequence level wise. The sequence formed at level 0 is 1 -> 3 -> 4 which is sorted.
A simple solution is to first do level order traversal of the binary tree and store each vertical level in different arrays. After this check, if array corresponding to level l is sorted or not. This solution has large memory requirements that can be reduced.
A efficient solution is to do vertical level order traversal of the binary tree and keep track of node values in vertical level l of the binary tree. A sequence is sorted if the previous element is less than or equal to the current element. While doing vertical level order traversal store previous value and compare current node in vertical level l with this previous value of level l. If current node value is greater than or equal to the previous value, then repeat the same procedure until the end of level l. If at any stage current node value is less than previous value then the level l is not sorted. If we reach at the end of level l then the level is sorted.
Time Complexity: O(n)
Auxiliary Space: O(n)
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