Question

given 2 trees t1 and t2, where t1 has more nodes than t2, and where each of the nodes in both trees holds an integer value. further, the values in any of the trees are assumed to be unique (no duplicate values within the same tree). i) give an algorithm that determines whether or not t2 represents a subtree of t1. ii) what is the time and space complexity of your algorithm in i)? iii) will your algorithm still work if duplicate values are permitted in these trees? a. if your algorithm still works when duplicate values are allowed, explain clearly why this change could not have affected your solution. b. if your algorithm will fail if duplicate values are allowed, provide an example of the failure and propose some modification to fix this failure.

Answer 1

To determine whether t2 represents a subtree of t1, a recursive algorithm can be used to compare the nodes of the trees. The time complexity is O(m * n) and the space complexity is O(max(m, n)). The algorithm will still work even if duplicate values are permitted in the trees.

Step-by-step explanation:

i) To determine whether t2 represents a subtree of t1, we can use a recursive algorithm. The algorithm checks if the current nodes of t1 and t2 are equal. If they are, it recursively checks if the left and right subtrees of t1 and t2 are also equal. This process continues until either t2 is exhausted or a mismatch is found. If t2 is exhausted, it means t2 is a subtree of t1.

ii) The time complexity of the algorithm is O(m * n), where m is the number of nodes in t1 and n is the number of nodes in t2. The space complexity is O(max(m, n)), as the recursive call stack can go as deep as the maximum height of the trees.

iii) The algorithm will still work if duplicate values are permitted in the trees. This is because the comparison is done based on the equality of nodes, and duplicate values do not affect the structure of the trees. The same algorithm can be used without any modifications.