《剑指offer》第七题：重建二叉树
// 面试题7：重建二叉树 // 题目：输入某二叉树的前序遍历和中序遍历的结果，请重建出该二叉树。假设输 // 入的前序遍历和中序遍历的结果中都不含重复的数字。例如输入前序遍历序列{1, // 2, 4, 7, 3, 5, 6, 8}和中序遍历序列{4, 7, 2, 1, 5, 3, 8, 6}，则重建出 // 图2.6所示的二叉树并输出它的头结点。 #include "BinaryTree.h" #include <exception> #include <cstdio> BinaryTreeNode* ConstructCore(int* startPreorder, int* endPreorder, int* startInorder, int* endInorder); BinaryTreeNode* Construct(int* preorder, int* inorder, int length) { //鲁棒性测试 1.空数组 2.长度小于等于0 if (preorder == nullptr || inorder == nullptr || length <= 0) return nullptr; return ConstructCore(preorder, preorder + length - 1, inorder, inorder + length - 1); } BinaryTreeNode* ConstructCore ( int* startPreorder, int* endPreorder, int* startInorder, int* endInorder ) { //创建根节点 int rootValue = startPreorder[0]; //第一个值为根节点 BinaryTreeNode* root = new BinaryTreeNode(); root->m_nValue = rootValue; root->m_pLeft = root->m_pRight = nullptr; //如无子节点 if (startPreorder == endPreorder) { //且序列有效, 即前序遍历和中序遍历相等, 两种遍历中只有一个根节点 if (startInorder == endInorder && *startPreorder == *startInorder) return root; else throw std::exception("Invalid input."); } //有子节点, 在中序遍历中寻找根节点 int* rootInorder = startInorder; while (rootInorder <= endInorder && *rootInorder != rootValue) ++rootInorder; //如果没找到根节点, 则序列无效 if (rootInorder == endInorder && *rootInorder != rootValue) throw std::exception("Invalid input."); int leftLength = rootInorder - startInorder; int* leftPreorderEnd = startPreorder + leftLength; if (leftLength > 0) //左子节点长度不为0 { //构建左子树 root->m_pLeft = ConstructCore(startPreorder + 1, leftPreorderEnd, startInorder, rootInorder - 1); } if (leftLength < endPreorder - startPreorder) //右子节点长度不为0 { //构建右子树 root->m_pRight = ConstructCore(leftPreorderEnd + 1, endPreorder, rootInorder + 1, endInorder); } return root; }
// ====================测试代码==================== void Test(const char* testName, int* preorder, int* inorder, int length) { if (testName != nullptr) printf("%s begins:\n", testName); printf("The preorder sequence is: "); for (int i = 0; i < length; ++i) printf("%d ", preorder[i]); printf("\n"); printf("The inorder sequence is: "); for (int i = 0; i < length; ++i) printf("%d ", inorder[i]); printf("\n"); try { BinaryTreeNode* root = Construct(preorder, inorder, length); PrintTree(root); DestroyTree(root); } catch (std::exception & exception) { printf("Invalid Input.\n"); } } // 普通二叉树 // 1 // / \ // 2 3 // / / \ // 4 5 6 // \ / // 7 8 void Test1() { const int length = 8; int preorder[length] = { 1, 2, 4, 7, 3, 5, 6, 8 }; int inorder[length] = { 4, 7, 2, 1, 5, 3, 8, 6 }; Test("Test1", preorder, inorder, length); } // 所有结点都没有右子结点 // 1 // / // 2 // / // 3 // / // 4 // / // 5 void Test2() { const int length = 5; int preorder[length] = { 1, 2, 3, 4, 5 }; int inorder[length] = { 5, 4, 3, 2, 1 }; Test("Test2", preorder, inorder, length); } // 所有结点都没有左子结点 // 1 // \ // 2 // \ // 3 // \ // 4 // \ // 5 void Test3() { const int length = 5; int preorder[length] = { 1, 2, 3, 4, 5 }; int inorder[length] = { 1, 2, 3, 4, 5 }; Test("Test3", preorder, inorder, length); } // 树中只有一个结点 void Test4() { const int length = 1; int preorder[length] = { 1 }; int inorder[length] = { 1 }; Test("Test4", preorder, inorder, length); } // 完全二叉树 // 1 // / \ // 2 3 // / \ / \ // 4 5 6 7 void Test5() { const int length = 7; int preorder[length] = { 1, 2, 4, 5, 3, 6, 7 }; int inorder[length] = { 4, 2, 5, 1, 6, 3, 7 }; Test("Test5", preorder, inorder, length); } // 输入空指针 void Test6() { Test("Test6", nullptr, nullptr, 0); } // 输入的两个序列不匹配 void Test7() { const int length = 7; int preorder[length] = { 1, 2, 4, 5, 3, 6, 7 }; int inorder[length] = { 4, 2, 8, 1, 6, 3, 7 }; Test("Test7: for unmatched input", preorder, inorder, length); } int main(int argc, char* argv[]) { Test1(); Test2(); Test3(); Test4(); Test5(); Test6(); Test7(); return 0; }
struct BinaryTreeNode { int m_nValue; BinaryTreeNode* m_pLeft; BinaryTreeNode* m_pRight; }; __declspec( dllexport ) BinaryTreeNode* CreateBinaryTreeNode(int value); __declspec( dllexport ) void ConnectTreeNodes(BinaryTreeNode* pParent, BinaryTreeNode* pLeft, BinaryTreeNode* pRight); __declspec( dllexport ) void PrintTreeNode(const BinaryTreeNode* pNode); __declspec( dllexport ) void PrintTree(const BinaryTreeNode* pRoot); __declspec( dllexport ) void DestroyTree(BinaryTreeNode* pRoot);
#include <cstdio> #include "BinaryTree.h" //新建一个父节点 BinaryTreeNode* CreateBinaryTreeNode(int value) { BinaryTreeNode* pNode = new BinaryTreeNode(); pNode->m_nValue = value; pNode->m_pLeft = nullptr; pNode->m_pRight = nullptr; return pNode; } //父节点连接左右子节点 void ConnectTreeNodes(BinaryTreeNode* pParent, BinaryTreeNode* pLeft, BinaryTreeNode* pRight) { if(pParent != nullptr) { pParent->m_pLeft = pLeft; pParent->m_pRight = pRight; } } //打印当前父节点以及左右子节点 void PrintTreeNode(const BinaryTreeNode* pNode) { if(pNode != nullptr) { printf("value of this node is: %d\n", pNode->m_nValue); if(pNode->m_pLeft != nullptr) printf("value of its left child is: %d.\n", pNode->m_pLeft->m_nValue); else printf("left child is nullptr.\n"); if(pNode->m_pRight != nullptr) printf("value of its right child is: %d.\n", pNode->m_pRight->m_nValue); else printf("right child is nullptr.\n"); } else { printf("this node is nullptr.\n"); } printf("\n"); } //递归调用打印整个二叉树 void PrintTree(const BinaryTreeNode* pRoot) { PrintTreeNode(pRoot); if(pRoot != nullptr) { if(pRoot->m_pLeft != nullptr) PrintTree(pRoot->m_pLeft); if(pRoot->m_pRight != nullptr) PrintTree(pRoot->m_pRight); } } //递归调用删除整个树 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); } }
分析：递归思想。
牛客网又给了vector，代码思路和上面一致，指针改为索引，绝对位置变为相对位置，根据代码量来看指针更方便。
/** * Definition for binary tree * struct TreeNode { * int val; * TreeNode *left; * TreeNode *right; * TreeNode(int x) : val(x), left(NULL), right(NULL) {} * }; */ class Solution { public: TreeNode* reConstructBinaryTree(vector<int> preorder,vector<int> inorder) { int length = int(preorder.size()); if (preorder.empty() || inorder.empty()) return nullptr; return ConstructCore (preorder, inorder, 0, length - 1, 0, length - 1); } TreeNode* ConstructCore (vector<int> preorder, vector<int> inorder, int startPreorder, int endPreorder, int startInorder, int endInorder) { //根节点 TreeNode* root = new TreeNode(preorder[startPreorder]); //无子节点 if (startPreorder == endPreorder) { if (startInorder == endInorder && preorder[startPreorder] == inorder[startInorder]) return root; else printf("Invaild input."); //throw std::exception("Invaild input."); } //有子节点，先寻找中序遍历中根节点位置 int rootInorder = startInorder; while(startInorder <= endInorder && inorder[rootInorder] != root->val) ++rootInorder; //如果没找到 if (startInorder == endInorder && inorder[rootInorder] != root->val) printf("Invaild input."); //throw std::exception("Invaild input."); int leftLength = rootInorder - startInorder; int rightLength = endInorder - rootInorder; int leftPreorderEnd = startPreorder + leftLength; if (leftLength > 0) //左子节点 { root->left = ConstructCore(preorder, inorder, startPreorder + 1, leftPreorderEnd, startInorder, rootInorder - 1); } if (rightLength > 0) //右子节点 { root->right = ConstructCore(preorder, inorder, leftPreorderEnd + 1, endPreorder, rootInorder + 1, endInorder); } return root; } };
