【数据结构】二叉树--链式结构的实现 (遍历)

目录

一 二叉树的遍历

1 构建一个二叉树

2 前序遍历

3 中序遍历

4 后续遍历

5 层序 

6 二叉树销毁

二 应用(递归思想)

1 二叉树节点个数

2 叶子节点个数

3 第K层的节点个数

4 二叉树查找值为x的节点

5 判断是否是二叉树

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一 二叉树的遍历

学习二叉树结构，最简单的方式就是遍历。所谓二叉树遍历(Traversal)是按照某种特定的规则，依次对二叉 树中的节点进行相应的操作，并且每个节点只操作一次。访问结点所做的操作依赖于具体的应用问题。 遍历 是二叉树上最重要的运算之一，也是二叉树上进行其它运算的基础

二叉树是： 1. 空树  2. 非空：根节点，根节点的左子树、根节点的右子树组成的。

前序、中序以及后序遍历： 

按照规则，二叉树的遍历有：前序/中序/后序的递归结构遍历：

1. 前序遍历(Preorder Traversal 亦称先序遍历)——访问根结点的操作发生在遍历其左右子树之前。

2. 中序遍历(Inorder Traversal)——访问根结点的操作发生在遍历其左右子树之中（间）。

3. 后序遍历(Postorder Traversal)——访问根结点的操作发生在遍历其左右子树之后。

由于被访问的结点必是某子树的根，所以N(Node）、L(Left subtree）和R(Right subtree）又可解释为 根、根的左子树和根的右子树。NLR、LNR和LRN分别又称为先根遍历、中根遍历和后根遍历。

代码实现:

1 构建一个二叉树

typedef struct BinaryTreeNode
{struct BinaryTreeNode* left;struct BinaryTreeNode* right;int val;
}BTNode;BTNode* BuyNode(int x)
{BTNode* node = (BTNode*)malloc(sizeof(BTNode));if (node == NULL){perror("malloc fail");exit(-1);}node->left = NULL;node->right = NULL;node->val = x;return node;
}int main()
{BTNode* node1 = BuyNode(1);BTNode* node2 = BuyNode(2);BTNode* node3 = BuyNode(3);BTNode* node4 = BuyNode(4);BTNode* node5 = BuyNode(5);BTNode* node6 = BuyNode(6);node1->left = node2;node1->right = node4;node2->left = node3;node4->left = node5;node4->right = node6;PrevOrder(node1);printf("\n");InOrder(node1);printf("\n");PostOrder(node1);printf("\n");return 0;
}

 2 前序遍历

//前序遍历
void PrevOrder(BTNode* root)
{if (root == NULL){printf("NULL ");return;}printf("%d ", root->val);PrevOrder(root->left);PrevOrder(root->right);
}

3 中序遍历

//中序遍历
void InOrder(BTNode* root)
{if (root == NULL){printf("NULL ");return;}InOrder(root->left);printf("%d ", root->val);InOrder(root->right);
}

 4 后续遍历

//后序遍历
void PostOrder(BTNode* root)
{if (root == NULL){printf("NULL ");return;}PostOrder(root->left);PostOrder(root->right);printf("%d ", root->val);
}

5 层序 

void QueueInit(Que* pq)
{assert(pq);pq->head = pq->tail = NULL;pq->size = 0;
}void QueuePush(Que* pq, QDataType x)
{assert(pq);QNode* newnode = (QNode*)malloc(sizeof(QNode));if (newnode == NULL){perror("malloc fail");exit(-1);}newnode->next = NULL;newnode->val = x;if (pq->tail == NULL){pq->head = pq->tail = newnode;}else{pq->tail->next = newnode;pq->tail = newnode;}pq->size++;}bool QueueEmpty(Que* pq)
{assert(pq);return pq->head == NULL;
}void QueuePop(Que* pq)
{assert(pq);assert(!QueueEmpty(pq));if (pq->head->next == NULL){free(pq->head);pq->head = pq->tail = NULL;}else{QNode* next = pq->head->next;free(pq->head);pq->head = next;}pq->size--;
}QDataType QueueFront(Que* pq)
{assert(pq);assert(!QueueEmpty(pq));return pq->head->val;
}void LevelOrder(BTNode* root)
{Que q;QueueInit(&q);if (root){QueuePush(&q, root);}while (!QueueEmpty(&q)){BTNode* front = QueueFront(&q);printf("%d ", front->val);if (front->left){QueuePush(&q, front->left);}if (front->right){QueuePush(&q, front->right);}QueuePop(&q);}
}

6 二叉树销毁

//二叉树的销毁
void TreeDestroy(BTNode* root)
{if (root == NULL){return;}TreeDestroy(root->left);TreeDestroy(root->right);free(root);}

二 应用(递归思想)

1 二叉树节点个数

int size = 0;
int TreeSize(BTNode* root)
{if (root == NULL){return 0;}else{size++;}TreeSize(root->left);TreeSize(root->right);return size;}

我们还可以改进

int TreeSize(BTNode* root)
{return root == NULL ? 0 : TreeSize(root->left) + TreeSize(root->right) + 1;
}

 2 叶子节点个数

int TreeLeafSize(BTNode* root)
{if (root == NULL){return 0;}if (root->left == NULL && root->right == NULL){return 1;}return TreeLeafSize(root->left) + TreeLeafSize(root->right);
}

3 第K层的节点个数

int TreeKLevel(BTNode* root, int k)
{assert(k > 0);if (root == NULL){return 0;}if (k == 1){return 1;}return TreeKLevel(root->left, k-1) + TreeKLevel(root->right, k-1);
}

 4 二叉树查找值为x的节点

BTNode* TreeFind(BTNode* root, int x)
{if (root == NULL){return NULL;}if (root->val == x){return root;}BTNode* ret = NULL;//从左树找 找到了就返回 不找右树了ret = TreeFind(root->left, x);if (ret){return ret;}//左树没找到 就开始找右树ret = TreeFind(root->right, x);if (ret){return ret;}}

5 判断是否是二叉树

void QueueInit(Que* pq)
{assert(pq);pq->head = pq->tail = NULL;pq->size = 0;
}void QueueDestroy(Que* pq)
{assert(pq);QNode* cur = pq->head;while (cur){QNode* next = cur->next;free(cur);cur = next;}pq->head = pq->tail = NULL;pq->size = 0;
}void QueuePush(Que* pq, QDataType x)
{assert(pq);QNode* newnode = (QNode*)malloc(sizeof(QNode));if (newnode == NULL){perror("malloc fail");exit(-1);}newnode->next = NULL;newnode->val = x;if (pq->tail == NULL){pq->head = pq->tail = newnode;}else{pq->tail->next = newnode;pq->tail = newnode;}pq->size++;}bool QueueEmpty(Que* pq)
{assert(pq);return pq->head == NULL;
}void QueuePop(Que* pq)
{assert(pq);assert(!QueueEmpty(pq));if (pq->head->next == NULL){free(pq->head);pq->head = pq->tail = NULL;}else{QNode* next = pq->head->next;free(pq->head);pq->head = next;}pq->size--;
}QDataType QueueFront(Que* pq)
{assert(pq);assert(!QueueEmpty(pq));return pq->head->val;
}int TreeComplete(BTNode* root)
{Que q;QueInit(&q);if (root != NULL){QueuePush(&q, root);}//找空节点while (!QueueEmpty(&q)){BTNode* front = QueueFront(&q);if (front == NULL){break;}QueuePush(&q, front->left);QueuePush(&q, front->right);QueuePop(&q);}//已经找到空节点while (!QueueEmpty(&q)){BTNode* front = QueueFront(&q);QueuePop(&q);if (front != NULL){QueueDestroy(&q);return false;}}QueueDestroy(&q);return true;
}

二叉树的链式结构的本质思想是递归, 对于递归不了解的小伙伴可以看看我之前的博客, 也可以自己尝试画一下递归展开图,下一节讲OJ题目.实战才最有效!继续加油!