二叉树の探索方法には、主に以下の3つの方式があります:

• 先順序探索
• 中順序探索
• 後順序探索

以下に、それぞれの探索方法の実装例を示します:

再帰的探索

class Solution {
public:
    vector<int> result;

    void preorder(BinaryTreeNode<int>* node) {
        if (node == nullptr) return;
        result.push_back(node->value);
        preorder(node->left);
        preorder(node->right);
    }

    void inorder(BinaryTreeNode<int>* node) {
        if (node == nullptr) return;
        inorder(node->left);
        result.push_back(node->value);
        inorder(node->right);
    }

    void postorder(BinaryTreeNode<int>* node) {
        if (node == nullptr) return;
        postorder(node->left);
        postorder(node->right);
        result.push_back(node->value);
    }

    vector<int> getPreorderTraversal(BinaryTreeNode<int>* root) {
        preorder(root);
        return result;
    }
};

非再帰的探索

class Solution {
public:
    vector<int> result;

    void preorderIterative(BinaryTreeNode<int>* root) {
        if (root == nullptr) return;
        stack<BinaryTreeNode<int>*> stack;
        stack.push(root);

        while (!stack.empty()) {
            BinaryTreeNode<int>* current = stack.top();
            stack.pop();
            result.push_back(current->value);
            if (current->right != nullptr) {
                stack.push(current->right);
            }
            if (current->left != nullptr) {
                stack.push(current->left);
            }
        }
    }

    vector<int> getInorderTraversal(BinaryTreeNode<int>* root) {
        if (root == nullptr) return result;
        stack<BinaryTreeNode<int>*> stack;
        BinaryTreeNode<int>* current = root;

        while (current != nullptr || !stack.empty()) {
            if (current != nullptr) {
                stack.push(current);
                current = current->left;
            } else {
                current = stack.top();
                stack.pop();
                result.push_back(current->value);
                current = current->right;
            }
        }
        return result;
    }
};

多様な探索方法

二叉树の探索方法は、応用によってさまざまに変化します:

• 層序探索
• 逆層序探索
• 右側ビュー
• 層ごとの平均値
• 多叉树の層序探索
• 完全二叉树の連結

例:

class Solution {
public:
    vector<vector<int>> levelOrderTraversal(BinaryTreeNode<int>* root) {
        vector<vector<int>> layers;
        if (root == nullptr) return layers;

        queue<BinaryTreeNode<int>*> queue;
        queue.push(root);

        while (!queue.empty()) {
            int levelSize = queue.size();
            vector<int> currentLevel;

            for (int i = 0; i < levelSize; i++) {
                BinaryTreeNode<int>* node = queue.front();
                queue.pop();
                currentLevel.push_back(node->value);

                if (node->left != nullptr) {
                    queue.push(node->left);
                }
                if (node->right != nullptr) {
                    queue.push(node->right);
                }
            }

            layers.push_back(currentLevel);
        }
        return layers;
    }
};

class Solution {
public:
    vector<vector<int>> reverseLevelOrderTraversal(BinaryTreeNode<int>* root) {
        vector<vector<int>> layers;
        if (root == nullptr) return layers;

        queue<BinaryTreeNode<int>*> queue;
        stack<vector<int>> stack;
        queue.push(root);

        while (!queue.empty()) {
            int levelSize = queue.size();
            vector<int> currentLevel;

            for (int i = 0; i < levelSize; i++) {
                BinaryTreeNode<int>* node = queue.front();
                queue.pop();
                currentLevel.push_back(node->value);

                if (node->left != nullptr) {
                    queue.push(node->left);
                }
                if (node->right != nullptr) {
                    queue.push(node->right);
                }
            }
            stack.push(currentLevel);
        }

        while (!stack.empty()) {
            layers.push_back(stack.top());
            stack.pop();
        }
        return layers;
    }
};

高度計算

二叉树の深さを計算するアルゴリズム:

class Solution {
public:
    int calculateDepth(BinaryTreeNode<int>* root) {
        if (root == nullptr) return 0;
        return max(calculateDepth(root->left), calculateDepth(root->right)) + 1;
    }
};

最小深度を計算するアルゴリズム:

class Solution {
public:
    int calculateMinDepth(BinaryTreeNode<int>* root) {
        if (root == nullptr) return 0;
        if (root->left == nullptr && root->right == nullptr) {
            return 1;
        }
        int leftDepth = root->left != nullptr ? calculateMinDepth(root->left) : INT_MAX;
        int rightDepth = root->right != nullptr ? calculateMinDepth(root->right) : INT_MAX;
        return min(leftDepth, rightDepth) + 1;
    }
};