JZ-C-50

剑指offer第五十题：树中两个结点的最低公共祖先：这里的树是普通树，且没有指向父结点的指针。

  1 //============================================================================
  2 // Name        : JZ-C-50.cpp
  3 // Author      : Laughing_Lz
  4 // Version     :
  5 // Copyright   : All Right Reserved
  6 // Description : 树中两个结点的最低公共祖先：这里的树是普通树，且没有指向父结点的指针。
  7 //============================================================================
  8
  9 #include <iostream>
 10 #include <stdio.h>
 11 #include "Tree.h"
 12 #include <list>
 13 using namespace std;
 14
 15 using namespace std;
 16 /**
 17  * 获得从树的根结点到某结点的路径
 18  */
 19 bool GetNodePath(TreeNode* pRoot, TreeNode* pNode, list<TreeNode*>& path) {
 20     if (pRoot == pNode)
 21         return true;
 22
 23     path.push_back(pRoot);
 24
 25     bool found = false;
 26
 27     vector<TreeNode*>::iterator i = pRoot->m_vChildren.begin(); //这里的树为普通树，甚至不是二叉树。所以这里按照前序遍历子树即可。
 28     while (!found && i < pRoot->m_vChildren.end()) {
 29         found = GetNodePath(*i, pNode, path);
 30         ++i;
 31     }
 32
 33     if (!found)
 34         path.pop_back();
 35
 36     return found;
 37 }
 38 /**
 39  * 获得两条路径的最后一个公共结点。
 40  */
 41 TreeNode* GetLastCommonNode(const list<TreeNode*>& path1,
 42         const list<TreeNode*>& path2) {
 43     list<TreeNode*>::const_iterator iterator1 = path1.begin();
 44     list<TreeNode*>::const_iterator iterator2 = path2.begin();
 45
 46     TreeNode* pLast = NULL;
 47
 48     while (iterator1 != path1.end() && iterator2 != path2.end()) {
 49         if (*iterator1 == *iterator2)
 50             pLast = *iterator1; //遍历完两条路径，得到最后一个公共结点。
 51
 52         iterator1++;
 53         iterator2++;
 54     }
 55
 56     return pLast;
 57 }
 58
 59 TreeNode* GetLastCommonParent(TreeNode* pRoot, TreeNode* pNode1,
 60         TreeNode* pNode2) {
 61     if (pRoot == NULL || pNode1 == NULL || pNode2 == NULL)
 62         return NULL;
 63
 64     list<TreeNode*> path1;
 65     GetNodePath(pRoot, pNode1, path1);
 66
 67     list<TreeNode*> path2;
 68     GetNodePath(pRoot, pNode2, path2);
 69
 70     return GetLastCommonNode(path1, path2);
 71 }
 72
 73 // ====================测试代码====================
 74
 75 void Test(char* testName, TreeNode* pRoot, TreeNode* pNode1, TreeNode* pNode2,
 76         TreeNode* pExpected) {
 77     if (testName != NULL)
 78         printf("%s begins: \n", testName);
 79
 80     TreeNode* pResult = GetLastCommonParent(pRoot, pNode1, pNode2);
 81
 82     if ((pExpected == NULL && pResult == NULL)
 83             || (pExpected != NULL && pResult != NULL
 84                     && pResult->m_nValue == pExpected->m_nValue))
 85         printf("Passed.\n");
 86     else
 87         printf("Failed.\n");
 88 }
 89
 90 // 形状普通的树
 91 //              1
 92 //            /    93 //           2     3
 94 //       /        95 //      4         5
 96 //     / \      / |   97 //    6   7    8  9  10
 98 void Test1() {
 99     TreeNode* pNode1 = CreateTreeNode(1);
100     TreeNode* pNode2 = CreateTreeNode(2);
101     TreeNode* pNode3 = CreateTreeNode(3);
102     TreeNode* pNode4 = CreateTreeNode(4);
103     TreeNode* pNode5 = CreateTreeNode(5);
104     TreeNode* pNode6 = CreateTreeNode(6);
105     TreeNode* pNode7 = CreateTreeNode(7);
106     TreeNode* pNode8 = CreateTreeNode(8);
107     TreeNode* pNode9 = CreateTreeNode(9);
108     TreeNode* pNode10 = CreateTreeNode(10);
109
110     ConnectTreeNodes(pNode1, pNode2);
111     ConnectTreeNodes(pNode1, pNode3);
112
113     ConnectTreeNodes(pNode2, pNode4);
114     ConnectTreeNodes(pNode2, pNode5);
115
116     ConnectTreeNodes(pNode4, pNode6);
117     ConnectTreeNodes(pNode4, pNode7);
118
119     ConnectTreeNodes(pNode5, pNode8);
120     ConnectTreeNodes(pNode5, pNode9);
121     ConnectTreeNodes(pNode5, pNode10);
122
123     Test("Test1", pNode1, pNode6, pNode8, pNode2);
124 }
125
126 // 树退化成一个链表
127 //               1
128 //              /
129 //             2
130 //            /
131 //           3
132 //          /
133 //         4
134 //        /
135 //       5
136 void Test2() {
137     TreeNode* pNode1 = CreateTreeNode(1);
138     TreeNode* pNode2 = CreateTreeNode(2);
139     TreeNode* pNode3 = CreateTreeNode(3);
140     TreeNode* pNode4 = CreateTreeNode(4);
141     TreeNode* pNode5 = CreateTreeNode(5);
142
143     ConnectTreeNodes(pNode1, pNode2);
144     ConnectTreeNodes(pNode2, pNode3);
145     ConnectTreeNodes(pNode3, pNode4);
146     ConnectTreeNodes(pNode4, pNode5);
147
148     Test("Test2", pNode1, pNode5, pNode4, pNode3);
149 }
150
151 // 树退化成一个链表，一个结点不在树中
152 //               1
153 //              /
154 //             2
155 //            /
156 //           3
157 //          /
158 //         4
159 //        /
160 //       5
161 void Test3() {
162     TreeNode* pNode1 = CreateTreeNode(1);
163     TreeNode* pNode2 = CreateTreeNode(2);
164     TreeNode* pNode3 = CreateTreeNode(3);
165     TreeNode* pNode4 = CreateTreeNode(4);
166     TreeNode* pNode5 = CreateTreeNode(5);
167
168     ConnectTreeNodes(pNode1, pNode2);
169     ConnectTreeNodes(pNode2, pNode3);
170     ConnectTreeNodes(pNode3, pNode4);
171     ConnectTreeNodes(pNode4, pNode5);
172
173     TreeNode* pNode6 = CreateTreeNode(6);
174
175     Test("Test3", pNode1, pNode5, pNode6, NULL);
176 }
177
178 // 输入NULL
179 void Test4() {
180     Test("Test4", NULL, NULL, NULL, NULL);
181 }
182
183 int main(int argc, char** argv) {
184     Test1();
185     Test2();
186     Test3();
187     Test4();
188
189     return 0;
190 }