Two ordered trees T1 and T2 are called isomorphic if one of the following conditions holds...
Two ordered trees T1 and T2 are called isomorphic if one of the following conditions holds true:
- Both T1 and T2 are empty.
- Both T1 and T2 comprises a single node.
- Both T1 and T2 have the same number of k _ 1 of subtrees, and the i-th subtree of T1 is isomorphic to the i-th subtree Ti for i = 1; 2; :::; k.
Design an algorithm to test if two given ordered trees are isomorphic. What is the running time of your algorithm?
Homework Answers
Algorithm: ( To check the two trees are isomorphic or
not)
Parameter: Isomorphic(Tree T1(root1),Tree T2(root2))
Step 1: If Both T1 and T2 are empty, then T1 and T2 are isomorphic
Step 2: If any one of the tree is non-empty and other is
empty , then
T1 and T2 are not isomorphic
Step 3: If the value of root1(T1) are different from
value of root2(T2), then
T1 and T2 are not isomorphic
Step 4: If the value of root1(T1) is same as that of
value of root2(T2),then
Recursively checking the subtrees are isomorphic or
not By executing Step 5
Step 5: Either Isomorphic(root1->left,root2->left)
and Isomorphic(root1->right,root2->right)
or Isomorphic(root1->right,root2->left) and
Isomorphic(root1->left,root2->right)
If any one the above two condition is true then T1 and
T2 are isomorphic
End Algorithm.
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