对于两个节点的最低父节点的定义可以分为两种情况(1)像5和8最低公共父节点是3,两节点之间不存在父子关系(2)两节点存在父子关系,如5和4,最低公共父节点是5。
引用维基百科的话:The lowest common ancestor (LCA) is a concept in graph theory and computer science. Let T be a rooted tree with n nodes. The lowest common ancestor between two nodes v and w is defined as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself).
_______3______ / \ ___5__ ___1__ / \ / \ 6 _2 0 8 / \ 7 4
可以采用从顶往下的计算及先序遍历。也可以采用树的后续遍历来实现。相比较来说后续遍历更为简洁,时间复杂度最低为O(n)
Node *LCA(Node *root,Node *p,Node *q)
{
if(!root)
return NULL;
if(root==p||root==q)
return root;
Node *L=LCA(root->left,p,q);
Node *R=LCA(root->right,p,q);
if(L&&R)
return root;
return L?L:R;
}