// 面试题26：树的子结构 // 题目：输入两棵二叉树A和B，判断B是不是A的子结构。 #include <cstdio> struct BinaryTreeNode { double m_dbValue; BinaryTreeNode* m_pLeft; BinaryTreeNode* m_pRight; }; bool DoesTree1HaveTree2(BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2); bool Equal(double num1, double num2); bool HasSubtree(BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2) { if (pRoot1 == nullptr || pRoot2 == nullptr) return false; bool result = false; if (Equal(pRoot1->m_dbValue, pRoot2->m_dbValue)) //如果匹配到B树根节点,继续匹配其他节点 result = DoesTree1HaveTree2(pRoot1, pRoot2); if (!result) result = HasSubtree(pRoot1->m_pLeft, pRoot2); //在A树左节点寻找匹配 if (!result) result = HasSubtree(pRoot1->m_pRight, pRoot2); //在A树右节点寻找匹配 return result; } bool DoesTree1HaveTree2(BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2) { if (pRoot2 == nullptr) return true; if (pRoot1 == nullptr) //A树叶节点为空 return false; if (!Equal(pRoot1->m_dbValue, pRoot2->m_dbValue)) return false; return DoesTree1HaveTree2(pRoot1->m_pLeft, pRoot2->m_pLeft) && DoesTree1HaveTree2(pRoot1->m_pRight, pRoot2->m_pRight); } bool Equal(double num1, double num2) { if (num1 - num2 < 0.0000001 && num1 - num2 > -0.0000001) return true; else return false; }
// ====================辅助测试代码==================== BinaryTreeNode* CreateBinaryTreeNode(double dbValue) { BinaryTreeNode* pNode = new BinaryTreeNode(); pNode->m_dbValue = dbValue; pNode->m_pLeft = nullptr; pNode->m_pRight = nullptr; return pNode; } void ConnectTreeNodes(BinaryTreeNode* pParent, BinaryTreeNode* pLeft, BinaryTreeNode* pRight) { if (pParent != nullptr) { pParent->m_pLeft = pLeft; pParent->m_pRight = pRight; } } void DestroyTree(BinaryTreeNode* pRoot) { if (pRoot != nullptr) { BinaryTreeNode* pLeft = pRoot->m_pLeft; BinaryTreeNode* pRight = pRoot->m_pRight; delete pRoot; pRoot = nullptr; DestroyTree(pLeft); DestroyTree(pRight); } } // ====================测试代码==================== void Test(const char* testName, BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2, bool expected) { if (HasSubtree(pRoot1, pRoot2) == expected) printf("%s passed.\n", testName); else printf("%s failed.\n", testName); } // 树中结点含有分叉，树B是树A的子结构 // 8 8 // / \ / \ // 8 7 9 2 // / \ // 9 2 // / \ // 4 7 void Test1() { BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(7); BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(9); BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(2); BinaryTreeNode* pNodeA6 = CreateBinaryTreeNode(4); BinaryTreeNode* pNodeA7 = CreateBinaryTreeNode(7); ConnectTreeNodes(pNodeA1, pNodeA2, pNodeA3); ConnectTreeNodes(pNodeA2, pNodeA4, pNodeA5); ConnectTreeNodes(pNodeA5, pNodeA6, pNodeA7); BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9); BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(2); ConnectTreeNodes(pNodeB1, pNodeB2, pNodeB3); Test("Test1", pNodeA1, pNodeB1, true); DestroyTree(pNodeA1); DestroyTree(pNodeB1); } // 树中结点含有分叉，树B不是树A的子结构 // 8 8 // / \ / \ // 8 7 9 2 // / \ // 9 3 // / \ // 4 7 void Test2() { BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(7); BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(9); BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(3); BinaryTreeNode* pNodeA6 = CreateBinaryTreeNode(4); BinaryTreeNode* pNodeA7 = CreateBinaryTreeNode(7); ConnectTreeNodes(pNodeA1, pNodeA2, pNodeA3); ConnectTreeNodes(pNodeA2, pNodeA4, pNodeA5); ConnectTreeNodes(pNodeA5, pNodeA6, pNodeA7); BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9); BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(2); ConnectTreeNodes(pNodeB1, pNodeB2, pNodeB3); Test("Test2", pNodeA1, pNodeB1, false); DestroyTree(pNodeA1); DestroyTree(pNodeB1); } // 树中结点只有左子结点，树B是树A的子结构 // 8 8 // / / // 8 9 // / / // 9 2 // / // 2 // / // 5 void Test3() { BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(9); BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(2); BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(5); ConnectTreeNodes(pNodeA1, pNodeA2, nullptr); ConnectTreeNodes(pNodeA2, pNodeA3, nullptr); ConnectTreeNodes(pNodeA3, pNodeA4, nullptr); ConnectTreeNodes(pNodeA4, pNodeA5, nullptr); BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9); BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(2); ConnectTreeNodes(pNodeB1, pNodeB2, nullptr); ConnectTreeNodes(pNodeB2, pNodeB3, nullptr); Test("Test3", pNodeA1, pNodeB1, true); DestroyTree(pNodeA1); DestroyTree(pNodeB1); } // 树中结点只有左子结点，树B不是树A的子结构 // 8 8 // / / // 8 9 // / / // 9 3 // / // 2 // / // 5 void Test4() { BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(9); BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(2); BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(5); ConnectTreeNodes(pNodeA1, pNodeA2, nullptr); ConnectTreeNodes(pNodeA2, pNodeA3, nullptr); ConnectTreeNodes(pNodeA3, pNodeA4, nullptr); ConnectTreeNodes(pNodeA4, pNodeA5, nullptr); BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9); BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(3); ConnectTreeNodes(pNodeB1, pNodeB2, nullptr); ConnectTreeNodes(pNodeB2, pNodeB3, nullptr); Test("Test4", pNodeA1, pNodeB1, false); DestroyTree(pNodeA1); DestroyTree(pNodeB1); } // 树中结点只有右子结点，树B是树A的子结构 // 8 8 // \ \ // 8 9 // \ \ // 9 2 // \ // 2 // \ // 5 void Test5() { BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(9); BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(2); BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(5); ConnectTreeNodes(pNodeA1, nullptr, pNodeA2); ConnectTreeNodes(pNodeA2, nullptr, pNodeA3); ConnectTreeNodes(pNodeA3, nullptr, pNodeA4); ConnectTreeNodes(pNodeA4, nullptr, pNodeA5); BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9); BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(2); ConnectTreeNodes(pNodeB1, nullptr, pNodeB2); ConnectTreeNodes(pNodeB2, nullptr, pNodeB3); Test("Test5", pNodeA1, pNodeB1, true); DestroyTree(pNodeA1); DestroyTree(pNodeB1); } // 树A中结点只有右子结点，树B不是树A的子结构 // 8 8 // \ \ // 8 9 // \ / \ // 9 3 2 // \ // 2 // \ // 5 void Test6() { BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(9); BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(2); BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(5); ConnectTreeNodes(pNodeA1, nullptr, pNodeA2); ConnectTreeNodes(pNodeA2, nullptr, pNodeA3); ConnectTreeNodes(pNodeA3, nullptr, pNodeA4); ConnectTreeNodes(pNodeA4, nullptr, pNodeA5); BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9); BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(3); BinaryTreeNode* pNodeB4 = CreateBinaryTreeNode(2); ConnectTreeNodes(pNodeB1, nullptr, pNodeB2); ConnectTreeNodes(pNodeB2, pNodeB3, pNodeB4); Test("Test6", pNodeA1, pNodeB1, false); DestroyTree(pNodeA1); DestroyTree(pNodeB1); } // 树A为空树 void Test7() { BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9); BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(3); BinaryTreeNode* pNodeB4 = CreateBinaryTreeNode(2); ConnectTreeNodes(pNodeB1, nullptr, pNodeB2); ConnectTreeNodes(pNodeB2, pNodeB3, pNodeB4); Test("Test7", nullptr, pNodeB1, false); DestroyTree(pNodeB1); } // 树B为空树 void Test8() { BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8); BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(9); BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(3); BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(2); ConnectTreeNodes(pNodeA1, nullptr, pNodeA2); ConnectTreeNodes(pNodeA2, pNodeA3, pNodeA4); Test("Test8", pNodeA1, nullptr, false); DestroyTree(pNodeA1); } // 树A和树B都为空 void Test9() { Test("Test9", nullptr, nullptr, false); } int main(int argc, char* argv[]) { Test1(); Test2(); Test3(); Test4(); Test5(); Test6(); Test7(); Test8(); Test9(); return 0; }
分析：递归简洁。
/* struct TreeNode { int val; struct TreeNode *left; struct TreeNode *right; TreeNode(int x) : val(x), left(NULL), right(NULL) { } };*/ class Solution { public: bool HasSubtree(TreeNode* pRoot1, TreeNode* pRoot2) { if (pRoot1 == nullptr || pRoot2 == nullptr) return false; bool result = false; if (pRoot1->val == pRoot2->val) result = DoesTree1HaveTree2(pRoot1, pRoot2); if (!result) result = HasSubtree(pRoot1->left, pRoot2); if (!result) result = HasSubtree(pRoot1->right, pRoot2); return result; } bool DoesTree1HaveTree2(TreeNode* pRoot1, TreeNode* pRoot2) { if (pRoot2 == nullptr) return true; if (pRoot1 == nullptr) return false; if (pRoot1->val != pRoot2->val) return false; return DoesTree1HaveTree2(pRoot1->left, pRoot2->left) && DoesTree1HaveTree2(pRoot1->right, pRoot2->right); } };