What Is Similar Trees in Data Structure?

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Scott Campbell

A tree is a widely used data structure in computer science that represents hierarchical relationships between elements. In some cases, it becomes necessary to determine if two trees are similar or not. Similar trees have the same structure, meaning they have the same arrangement of nodes and edges.

Defining Similarity

Similarity in trees can be determined by comparing their structures recursively. Two trees are considered similar if:

  • They have the same root value.
  • Their left subtrees are similar.
  • Their right subtrees are similar.

Recursive Approach

To check for similarity between two trees, we can use a recursive algorithm. Let’s define a function isSimilar(tree1, tree2):

function isSimilar(tree1, tree2):
    // If both trees are empty, they are similar
    if tree1 is null and tree2 is null:
        return true
        
    // If one of the trees is empty while the other is not,
    // they are not similar
    if tree1 is null or tree2 is null:
        return false
        
    // If the root values of both trees are different,
    // they are not similar
    if tree1.value != tree2.value:
        return false
        
    // Recursively check for similarity in left and right subtrees
    leftSimilar = isSimilar(tree1.left, tree2.left)
    rightSimilar = isSimilar(tree1.right, tree2.right)
    
    // Return true only if both left and right subtrees are similar
    return leftSimilar and rightSimilar

Example

Let’s consider two binary trees:

        A                     X
       / \                   / \
      B   C                 Y   Z
     / \   \               /     \
    D   E   F             P       Q

Using the isSimilar() function, we can determine if these trees are similar:

tree1 = Node('A')
tree1.left = Node('B')
tree1.right = Node('C')
tree1.left.left = Node('D')
tree1.right = Node('E')
tree1.right.right = Node('F')

tree2 = Node('X')
tree2.left = Node('Y')
tree2.right = Node('Z')
tree2.left = Node('P')
tree2.right = Node('Q')

isSimilar(tree1, tree2)  // Returns true

In this example, both trees have the same structure and thus are considered similar.

Conclusion

In data structures, determining whether two trees are similar is an important problem. By comparing their structures recursively, we can check if two trees have the same arrangement of nodes and edges. This knowledge can be useful in various applications where tree comparison is required.

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