《Cracking the Coding Interview》——第4章：树和图——题目6

2014-03-19 04:16

题目：找出一棵二叉搜索树中的中序遍历后继节点，每个节点都有指针指向其父节点。

解法1：分两种情况：向下走时，先右后左；向上走时，先左后右。如果目标节点有右子树，就向右下走，否则往左上走。话说，如果没有父指针的话，还是一口气进行各中序遍历，求出所有结果比较有效率。

代码：

// 4.6 Find the inorder successor of a node in the binary tree.
// online algorithm with parent pointer.
#include <cstdio>
#include <unordered_map>
using namespace std;

struct TreeNode {
    int val;
    TreeNode *left;
    TreeNode *right;
    TreeNode *parent;
    
    TreeNode(int _val = 0): val(_val), left(nullptr), right(nullptr), parent(nullptr) {};
};

void constructBinaryTree(TreeNode *&root)
{
    int val;
    
    scanf("%d", &val);
    if (val <= 0) {
        root = nullptr;
    } else {
        root = new TreeNode(val);

        constructBinaryTree(root->left);
        constructBinaryTree(root->right);
        if (root->left != nullptr) {
            root->left->parent = root;
        }
        if (root->right != nullptr) {
            root->right->parent = root;
        }
    }
}

TreeNode *inorderSuccessor(TreeNode *node)
{
    if (node == nullptr) {
        return nullptr;
    }
    
    TreeNode *result;
    if (node->right != nullptr) {
        result = node->right;
        while (result->left != nullptr) {
            result = result->left;
        }
        
        return result;
    } else {
        result = node;
        while(true) {
            if (result->parent == nullptr) {
                return nullptr;
            } else if (result == result->parent->left) {
                return result->parent;
            } else {
                result = result->parent;
            }
        }
    }
}

void inorderTraversal(TreeNode *root)
{
    if (root == nullptr) {
        return;
    }
    
    inorderTraversal(root->left);
    TreeNode *next_node = inorderSuccessor(root);
    if (next_node != nullptr) {
        printf("%d %d\n", root->val, next_node->val);
    } else {
        printf("%d #\n", root->val);
    }
    inorderTraversal(root->right);
}

void clearBinaryTree(TreeNode *&root) {
    if (root == nullptr) {
        return;
    } else {
        clearBinaryTree(root->left);
        clearBinaryTree(root->right);
        delete root;
        root = nullptr;
    }
}

int main()
{
    TreeNode *root;
    
    while (true) {
        constructBinaryTree(root);
        if (root == nullptr) {
            break;
        }
        
        inorderTraversal(root);
        
        clearBinaryTree(root);
    }
    
    return 0;
}

解法2：一次性进行中序遍历的离线做法。

代码：

// 4.6 Find the inorder successor of a node in the binary tree.
// offline algorithm with inorder traversal.
#include <cstdio>
#include <unordered_map>
using namespace std;

struct TreeNode {
    int val;
    TreeNode *left;
    TreeNode *right;
    TreeNode *parent;
    
    TreeNode(int _val = 0): val(_val), left(nullptr), right(nullptr), parent(nullptr) {};
};

void constructBinaryTree(TreeNode *&root)
{
    int val;
    
    scanf("%d", &val);
    if (val <= 0) {
        root = nullptr;
    } else {
        root = new TreeNode(val);

        constructBinaryTree(root->left);
        constructBinaryTree(root->right);
        if (root->left != nullptr) {
            root->left->parent = root;
        }
        if (root->right != nullptr) {
            root->right->parent = root;
        }
    }
}

void inorderTraversal(TreeNode *root, vector<TreeNode *> &inorder_list)
{
    if (root == nullptr) {
        return;
    }
    inorderTraversal(root->left, inorder_list);
    inorder_list.push_back(root);
    inorderTraversal(root->right, inorder_list);
}

TreeNode *inorderSuccessor(TreeNode *node, unordered_map<TreeNode *, TreeNode *> &dict)
{
    if (dict.find(node) == dict.end()) {
        return nullptr;
    } else {
        return dict[node];
    }
}

void clearBinaryTree(TreeNode *&root) {
    if (root == nullptr) {
        return;
    } else {
        clearBinaryTree(root->left);
        clearBinaryTree(root->right);
        delete root;
        root = nullptr;
    }
}

int main()
{
    TreeNode *root;
    unordered_map<TreeNode *, TreeNode *> dict;
    vector<TreeNode *> inorder_list;
    int i;
    
    while (true) {
        constructBinaryTree(root);
        if (root == nullptr) {
            break;
        }
        
        inorderTraversal(root, inorder_list);
        for (i = 0; i < (int)inorder_list.size() - 1; ++i) {
            dict[inorder_list[i]] = inorder_list[i + 1];
        }
        dict[inorder_list[i]] = nullptr;
        
        TreeNode *next_node;
        for (i = 0; i < (int)inorder_list.size(); ++i) {
            next_node = inorderSuccessor(inorder_list[i], dict);
            if (next_node != nullptr) {
                printf("%d %d\n", inorder_list[i]->val, next_node->val);
            } else {
                printf("%d #\n", inorder_list[i]->val);
            }
        }
        
        inorder_list.clear();
        dict.clear();
        clearBinaryTree(root);
    }
    
    return 0;
}