剑指Offer----面试题18：树的子结构

题目：

输入两颗二叉树A和B，判断B是不是A的子结构。如下图：树B是树A的子结构。

方法一：

分析：要判断树B是否为树A的子结构，可以分为两步，第一步在树A中找到和树B的根节点的值一样的结点R，第二步再判断树A中以R为根节点的子树是不是包含和树B一样的结构。

源代码如下：

#include"BinaryTree.h"#include<iostream>using std::cout;using std::endl;using namespace OrdinaryBinaryTreeSpace2;bool Total(BinaryTreeNode *root1, BinaryTreeNode *root2);bool HasSubTree(BinaryTreeNode *root1, BinaryTreeNode *root2);bool DoesTreeOneHaveTreeTwo(BinaryTreeNode *root1, BinaryTreeNode *root2);bool Total(BinaryTreeNode *root1, BinaryTreeNode *root2){if (root1 == NULL && root2 != NULL)return false;else if (root1 == NULL && root2 == NULL)return false;else if (root1 != NULL && root2 == NULL)return true;return HasSubTree(root1, root2);}bool HasSubTree(BinaryTreeNode *root1, BinaryTreeNode *root2){bool result = false;if (root1 != NULL && root2 != NULL){if (root1->element == root2->element)result = DoesTreeOneHaveTreeTwo(root1, root2);if (!result)result = HasSubTree(root1->left, root2);if (!result)result = HasSubTree(root1->right, root2);}return result;}bool DoesTreeOneHaveTreeTwo(BinaryTreeNode *root1, BinaryTreeNode *root2){if (root2 == NULL)return true;if (root1 == NULL)return false;if (root1->element != root2->element)return false;return DoesTreeOneHaveTreeTwo(root1->left, root2->left) && DoesTreeOneHaveTreeTwo(root1->right, root2->right);}void test11(){cout << "\t===========树A含有树B============" << endl;BinaryTreeNode *node1 = CreateBinaryTreeNode(8);BinaryTreeNode *node2 = CreateBinaryTreeNode(8);BinaryTreeNode *node3 = CreateBinaryTreeNode(7);BinaryTreeNode *node4 = CreateBinaryTreeNode(9);BinaryTreeNode *node5 = CreateBinaryTreeNode(2);BinaryTreeNode *node6 = CreateBinaryTreeNode(4);BinaryTreeNode *node7 = CreateBinaryTreeNode(7);ConnectBinaryTreeNodes(node1, node2, node3);ConnectBinaryTreeNodes(node2, node4, node5);ConnectBinaryTreeNodes(node3, NULL, NULL);ConnectBinaryTreeNodes(node4, NULL, NULL);ConnectBinaryTreeNodes(node5, node6, node7);ConnectBinaryTreeNodes(node6, NULL, NULL);ConnectBinaryTreeNodes(node7, NULL, NULL);BinaryTreeNode *node21 = CreateBinaryTreeNode(8);BinaryTreeNode *node22 = CreateBinaryTreeNode(9);BinaryTreeNode *node23 = CreateBinaryTreeNode(2);ConnectBinaryTreeNodes(node21, node22, node23);ConnectBinaryTreeNodes(node22, NULL, NULL);ConnectBinaryTreeNodes(node23, NULL, NULL);bool result = Total(node1, node21);if (result)cout << "Tree A contains tree B" << endl;elsecout << "Tree A not contains tree B" << endl;}void test12(){cout << "\t===========树A不含有树B============" << endl;BinaryTreeNode *node1 = CreateBinaryTreeNode(8);BinaryTreeNode *node2 = CreateBinaryTreeNode(8);BinaryTreeNode *node3 = CreateBinaryTreeNode(7);BinaryTreeNode *node4 = CreateBinaryTreeNode(9);BinaryTreeNode *node5 = CreateBinaryTreeNode(2);BinaryTreeNode *node6 = CreateBinaryTreeNode(4);BinaryTreeNode *node7 = CreateBinaryTreeNode(7);ConnectBinaryTreeNodes(node1, node2, node3);ConnectBinaryTreeNodes(node2, node4, node5);ConnectBinaryTreeNodes(node3, NULL, NULL);ConnectBinaryTreeNodes(node4, NULL, NULL);ConnectBinaryTreeNodes(node5, node6, node7);ConnectBinaryTreeNodes(node6, NULL, NULL);ConnectBinaryTreeNodes(node7, NULL, NULL);BinaryTreeNode *node21 = CreateBinaryTreeNode(8);BinaryTreeNode *node22 = CreateBinaryTreeNode(9);BinaryTreeNode *node23 = CreateBinaryTreeNode(3);ConnectBinaryTreeNodes(node21, node22, node23);ConnectBinaryTreeNodes(node22, NULL, NULL);ConnectBinaryTreeNodes(node23, NULL, NULL);bool result = Total(node1, node21);if (result)cout << "Tree A contains tree B" << endl;elsecout << "Tree A not contains tree B" << endl;}void test13(){cout << "\t===========树A非空，树B为空============" << endl;BinaryTreeNode *node1 = CreateBinaryTreeNode(8);BinaryTreeNode *node2 = CreateBinaryTreeNode(8);BinaryTreeNode *node3 = CreateBinaryTreeNode(7);BinaryTreeNode *node4 = CreateBinaryTreeNode(9);BinaryTreeNode *node5 = CreateBinaryTreeNode(2);BinaryTreeNode *node6 = CreateBinaryTreeNode(4);BinaryTreeNode *node7 = CreateBinaryTreeNode(7);ConnectBinaryTreeNodes(node1, node2, node3);ConnectBinaryTreeNodes(node2, node4, node5);ConnectBinaryTreeNodes(node3, NULL, NULL);ConnectBinaryTreeNodes(node4, NULL, NULL);ConnectBinaryTreeNodes(node5, node6, node7);ConnectBinaryTreeNodes(node6, NULL, NULL);ConnectBinaryTreeNodes(node7, NULL, NULL);bool result = Total(node1, NULL);if (result)cout << "Tree A contains tree B" << endl;elsecout << "Tree A not contains tree B" << endl;}void test14(){cout << "\t===========树A为空，树B非空============" << endl;BinaryTreeNode *node21 = CreateBinaryTreeNode(8);BinaryTreeNode *node22 = CreateBinaryTreeNode(9);BinaryTreeNode *node23 = CreateBinaryTreeNode(3);ConnectBinaryTreeNodes(node21, node22, node23);ConnectBinaryTreeNodes(node22, NULL, NULL);ConnectBinaryTreeNodes(node23, NULL, NULL);bool result = Total(NULL, node21);if (result)cout << "Tree A contains tree B" << endl;elsecout << "Tree A not contains tree B" << endl;}void test15(){cout << "\t===========树A树B都为空============" << endl;bool result = Total(NULL, NULL);if (result)cout << "Tree A contains tree B" << endl;elsecout << "Tree A not contains tree B" << endl;}int main(){test11();test12();test13();test14();test15();system("pause");return 0;}

运行结果：

        ===========树A含有树B============Tree A contains tree B        ===========树A不含有树B============Tree A not contains tree B        ===========树A非空，树B为空============Tree A contains tree B        ===========树A为空，树B非空============Tree A not contains tree B        ===========树A树B都为空============Tree A not contains tree B请按任意键继续. . .

官方源代码：

#include"BinaryTree.h"#include<cstdio>#include<cstdlib>using namespace OrdinaryBinaryTreeSpace2;bool HasSubtreeCore(BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2);bool DoesTree1HaveTree2(BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2);bool HasSubtree(BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2){bool result = false;if (pRoot1 != NULL && pRoot2 != NULL){if (pRoot1->element == pRoot2->element)result = DoesTree1HaveTree2(pRoot1, pRoot2);if (!result)result = HasSubtree(pRoot1->left, pRoot2);if (!result)result = HasSubtree(pRoot1->right, pRoot2);}return result;}bool DoesTree1HaveTree2(BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2){if (pRoot2 == NULL)return true;if (pRoot1 == NULL)return false;if (pRoot1->element != pRoot2->element)return false;return DoesTree1HaveTree2(pRoot1->left, pRoot2->left) &&DoesTree1HaveTree2(pRoot1->right, pRoot2->right);}// ====================测试代码====================void Test(char* testName, BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2, bool expected){if (HasSubtree(pRoot1, pRoot2) == expected)printf("%s passed.\n", testName);elseprintf("%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   7void 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);ConnectBinaryTreeNodes(pNodeA1, pNodeA2, pNodeA3);ConnectBinaryTreeNodes(pNodeA2, pNodeA4, pNodeA5);ConnectBinaryTreeNodes(pNodeA5, pNodeA6, pNodeA7);BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9);BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(2);ConnectBinaryTreeNodes(pNodeB1, pNodeB2, pNodeB3);Test("Test1", pNodeA1, pNodeB1, true);DestoryTree(pNodeA1);DestoryTree(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   7void 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);ConnectBinaryTreeNodes(pNodeA1, pNodeA2, pNodeA3);ConnectBinaryTreeNodes(pNodeA2, pNodeA4, pNodeA5);ConnectBinaryTreeNodes(pNodeA5, pNodeA6, pNodeA7);BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9);BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(2);ConnectBinaryTreeNodes(pNodeB1, pNodeB2, pNodeB3);Test("Test2", pNodeA1, pNodeB1, false);DestoryTree(pNodeA1);DestoryTree(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        //       ///      5void Test3(){BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(9);BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(2);BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(5);ConnectBinaryTreeNodes(pNodeA1, pNodeA2, NULL);ConnectBinaryTreeNodes(pNodeA2, pNodeA3, NULL);ConnectBinaryTreeNodes(pNodeA3, pNodeA4, NULL);ConnectBinaryTreeNodes(pNodeA4, pNodeA5, NULL);BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9);BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(2);ConnectBinaryTreeNodes(pNodeB1, pNodeB2, NULL);ConnectBinaryTreeNodes(pNodeB2, pNodeB3, NULL);Test("Test3", pNodeA1, pNodeB1, true);DestoryTree(pNodeA1);DestoryTree(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        //       ///      5void Test4(){BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(9);BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(2);BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(5);ConnectBinaryTreeNodes(pNodeA1, pNodeA2, NULL);ConnectBinaryTreeNodes(pNodeA2, pNodeA3, NULL);ConnectBinaryTreeNodes(pNodeA3, pNodeA4, NULL);ConnectBinaryTreeNodes(pNodeA4, pNodeA5, NULL);BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9);BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(3);ConnectBinaryTreeNodes(pNodeB1, pNodeB2, NULL);ConnectBinaryTreeNodes(pNodeB2, pNodeB3, NULL);Test("Test4", pNodeA1, pNodeB1, false);DestoryTree(pNodeA1);DestoryTree(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        //              \//               5void Test5(){BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(9);BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(2);BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(5);ConnectBinaryTreeNodes(pNodeA1, NULL, pNodeA2);ConnectBinaryTreeNodes(pNodeA2, NULL, pNodeA3);ConnectBinaryTreeNodes(pNodeA3, NULL, pNodeA4);ConnectBinaryTreeNodes(pNodeA4, NULL, pNodeA5);BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9);BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(2);ConnectBinaryTreeNodes(pNodeB1, NULL, pNodeB2);ConnectBinaryTreeNodes(pNodeB2, NULL, pNodeB3);Test("Test5", pNodeA1, pNodeB1, true);DestoryTree(pNodeA1);DestoryTree(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        //              \//               5void Test6(){BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(9);BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(2);BinaryTreeNode* pNodeA5 = CreateBinaryTreeNode(5);ConnectBinaryTreeNodes(pNodeA1, NULL, pNodeA2);ConnectBinaryTreeNodes(pNodeA2, NULL, pNodeA3);ConnectBinaryTreeNodes(pNodeA3, NULL, pNodeA4);ConnectBinaryTreeNodes(pNodeA4, NULL, pNodeA5);BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9);BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(3);BinaryTreeNode* pNodeB4 = CreateBinaryTreeNode(2);ConnectBinaryTreeNodes(pNodeB1, NULL, pNodeB2);ConnectBinaryTreeNodes(pNodeB2, pNodeB3, pNodeB4);Test("Test6", pNodeA1, pNodeB1, false);DestoryTree(pNodeA1);DestoryTree(pNodeB1);}// 树A为空树void Test7(){BinaryTreeNode* pNodeB1 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeB2 = CreateBinaryTreeNode(9);BinaryTreeNode* pNodeB3 = CreateBinaryTreeNode(3);BinaryTreeNode* pNodeB4 = CreateBinaryTreeNode(2);ConnectBinaryTreeNodes(pNodeB1, NULL, pNodeB2);ConnectBinaryTreeNodes(pNodeB2, pNodeB3, pNodeB4);Test("Test7", NULL, pNodeB1, false);DestoryTree(pNodeB1);}// 树B为空树void Test8(){BinaryTreeNode* pNodeA1 = CreateBinaryTreeNode(8);BinaryTreeNode* pNodeA2 = CreateBinaryTreeNode(9);BinaryTreeNode* pNodeA3 = CreateBinaryTreeNode(3);BinaryTreeNode* pNodeA4 = CreateBinaryTreeNode(2);ConnectBinaryTreeNodes(pNodeA1, NULL, pNodeA2);ConnectBinaryTreeNodes(pNodeA2, pNodeA3, pNodeA4);Test("Test8", pNodeA1, NULL, false);DestoryTree(pNodeA1);}// 树A和树B都为空void Test9(){Test("Test9", NULL, NULL, false);}int main(){Test1();Test2();Test3();Test4();Test5();Test6();Test7();Test8();Test9();system("pause");return 0;}

运行结果：

Test1 passed.Test2 passed.Test3 passed.Test4 passed.Test5 passed.Test6 passed.Test7 passed.Test8 passed.Test9 passed.请按任意键继续. . .