如果两棵树具有相似的结构,并且它们之间的唯一区别是它们的子节点可以交换,也可以不交换,那么它们就可以称为同构树。例如:
4 4
/ \ / \
2 6 and 6 2
/ \ / \ / \ / \
1 3 5 7 1 3 7 5
下面的代码应该是我在web中找到的正确实现,但由于某些原因,它不适用于上述树我做错什么了?
#include <iostream>
using namespace std;
class Node{
public:
Node * left;
Node * right;
int val;
Node(int v){
left = NULL;
right = NULL;
val = v;
}
};
bool isIsomorphic(Node* n1, Node *n2)
{
// Both roots are NULL, trees isomorphic by definition
if (n1 == NULL && n2 == NULL)
return true;
// Exactly one of the n1 and n2 is NULL, trees not isomorphic
if (n1 == NULL || n2 == NULL)
return false;
if (n1->val != n2->val)
return false;
// There are two possible cases for n1 and n2 to be isomorphic
// Case 1: The subtrees rooted at these nodes have NOT been "Flipped".
// Both of these subtrees have to be isomorphic, hence the &&
// Case 2: The subtrees rooted at these nodes have been "Flipped"
return
(isIsomorphic(n1->left,n2->left) && isIsomorphic(n1->right,n2->right))||
(isIsomorphic(n1->left,n2->right) && isIsomorphic(n1->right,n2->left));
}
int main()
{
Node * na_4 = new Node(4);
Node * na_2 = new Node(2);
Node * na_6 = new Node(6);
Node * na_1 = new Node(1);
Node * na_3 = new Node(3);
Node * na_5 = new Node(5);
Node * na_7 = new Node(7);
na_4->left = na_2;
na_4->right = na_6;
na_2->left = na_1;
na_2->right = na_3;
na_6->left = na_5;
na_6->right = na_7;
Node * nb_4 = new Node(4);
Node * nb_6 = new Node(6);
Node * nb_2 = new Node(2);
Node * nb_1 = new Node(1);
Node * nb_3 = new Node(3);
Node * nb_7 = new Node(7);
Node * nb_5 = new Node(5);
nb_4->left = nb_6;
nb_4->right = nb_2;
nb_6->left = nb_1;
nb_6->right = nb_3;
nb_2->left = nb_7;
nb_2->right = nb_5;
if(isIsomorphic(na_4, nb_4)){
cout << "Yes they are isomorphic" << endl;
}
else
{
cout << "No there are not isomorphic" << endl;
}
return 0;
}
它输出它们不是同构的。
最佳答案
根据提供的定义,这些树不是同构的:
如果两棵树中的一棵可以通过一系列翻转(即交换多个节点的左、右子节点)从另一棵树中获得,则称之为同构树。任何级别的任意数量的节点都可以交换其子节点。两棵空树是同构的。
因为,在一棵树上,2有1和3个孩子,而在另一棵树上,2有7和5个孩子。
通过交换两个子节点,实际上是交换了它们的整个子树,而不仅仅是那些节点,让所有其他节点都留在原来的位置。
例如,这两个是同构的:
4
/ \
2 6
/ \ / \
1 3 5 7
4
/ \
6 2
/ \ / \
7 5 1 3
关于c++ - 查找两棵树是否同构,我们在Stack Overflow上找到一个类似的问题:https://stackoverflow.com/questions/21475584/