# 数据结构和算法面试题系列—二叉树基础

0 概述

1 定义

typedefstructBTNode{intvalue;structBTNode*left;structBTNode*right;} BTNode;复制代码

2 基本操作

1) 创建结点

/** * 创建BTNode */BTNode *newNode(int value){ BTNode *node= (BTNode*)malloc(sizeof(BTNode));node->value= value;node->left=node->right= NULL; returnnode;

}

2) BST 插入结点

/**

* BST中插入值，递归方法

*//**

* BST中插入结点，递归方法

*/BTNode *bstInsert(BTNode *root,intvalue){if(!root)returnnewNode(value);if(root->value > value) { root->left = bstInsert(root->left, value); }else{ root->right = bstInsert(root->right, value); }returnroot;}/**

* BST中插入结点，非递归方法

*/BTNode *bstInsertIter(BTNode *root,intvalue){ BTNode *node = newNode(value);if(!root)returnnode; BTNode *current = root, *parent=NULL;while(current) {parent= current;if(current->value > value) current = current->left;elsecurrent = current->right; }if(parent->value >= value)parent->left = node;elseparent->right = node;returnroot;}复制代码

3) BST 删除结点

/** * BST中删除结点 */BTNode *bstDelete(BTNode *root, int value){ BTNode *parent = NULL, *current = root; BTNode *node= bstSearchIter(root, &parent, value); if (!node) {

printf("Value not found\n"); return root; } if (!node->left&& !node->right) { // 情况1：待删除结点是叶子结点 if (node!= root) { if (parent->left ==node) {

parent->left = NULL; } else { parent->right = NULL; } } else { root = NULL; } free(node);

} elseif (node->left&&node->right) { // 情况2：待删除结点有两个子结点 BTNode *predecessor = bstMax(node->left); bstDelete(root, predecessor->value);node->value= predecessor->value; } else { // 情况3：待删除结点只有一个子结点 BTNode *child = (node->left) ?node->left:node->right; if (node!= root) { if (node== parent->left) parent->left = child; else parent->right = child; } else { root = child; } free(node);

}

returnroot;}复制代码

4) BST 查找结点

/**

* BST查找结点-递归

*/BTNode *bstSearch(BTNode *root,intvalue){if(!root)returnNULL;if(root->value==value) {returnroot; }elseif(root->value>value) {returnbstSearch(root->left,value); }else{returnbstSearch(root->left,value); }}/**

* BST查找结点-非递归

*/BTNode *bstSearchIter(BTNode *root, BTNode **parent,intvalue){if(!root)returnNULL; BTNode *current = root;while(current && current->value!=value) { *parent = current;if(current->value>value) current = current->left;elsecurrent = current->right; }returncurrent;}复制代码

5）BST 最小值结点和最大值结点

/** * BST最小值结点 */BTNode *bstMin(BTNode *root){if(!root->left)returnroot;returnbstMin(root->left);}/** * BST最大值结点 */BTNode *bstMax(BTNode *root){if(!root->right)returnroot;returnbstMax(root->right);}复制代码

6）二叉树结点数目和高度

/**

* 二叉树结点数目

*/intsize(BTNode *root){if(!root)return0;returnsize(root->left) +size(root->right) +1;}/**

* 二叉树高度

*/intheight(BTNode *root){if(!root)return0;intleftHeight =height(root->left);intrightHeight =height(root->right);intmaxHeight = leftHeight > rightHeight ? leftHeight+1: rightHeight+1;returnmaxHeight;}复制代码

3 二叉树遍历

/**

* 二叉树先序遍历

*/void preOrder(BTNode *root){ if (!root) return;printf("%d ", root->value);preOrder(root->left);preOrder(root->right);}/**

* 二叉树中序遍历

*/void inOrder(BTNode *root){ if (!root) return;inOrder(root->left);printf("%d ", root->value);inOrder(root->right);}/**

* 二叉树后序遍历

*/void postOrder(BTNode *root){ if (!root) return;postOrder(root->left);postOrder(root->right);printf("%d ", root->value);}/**

* 二叉树层序遍历

*/void levelOrder(BTNode *root){ intbtHeight = height(root); int level;for (level =1; level <= btHeight; level++) {levelOrderInLevel(root, level);}}/**

* 二叉树层序遍历辅助函数-打印第level层的结点

*/void levelOrderInLevel(BTNode *root, int level){ if (!root) return;if (level ==1) { printf("%d ", root->value);return;} levelOrderInLevel(root->left, level-1);levelOrderInLevel(root->right, level-1);}复制代码

/*********************//** 二叉树遍历-非递归 **//*********************//** * 先序遍历-非递归 */void preOrderIter(BTNode *root){ if (!root) return; int btSize = size(root); BTNodeStack *stack = stackNew(btSize); push(stack, root); while (!IS_EMPTY(stack)) { BTNode *node= pop(stack); printf("%d ",node->value); if (node->right) push(stack,node->right); if (node->left) push(stack,node->left); } free(stack);}/** * 中序遍历-非递归 */void inOrderIter(BTNode *root){ if (!root) return; BTNodeStack *stack = stackNew(size(root)); BTNode *current = root; while (current || !IS_EMPTY(stack)) { if (current) { push(stack, current); current = current->left; } else { BTNode *node= pop(stack); printf("%d ",node->value); current =node->right; } } free(stack);}/** * 后续遍历-使用一个栈非递归 */void postOrderIter(BTNode *root){ BTNodeStack *stack = stackNew(size(root)); BTNode *current = root; do {  // 移动至最左边结点 while (current) {  // 将该结点右孩子和自己入栈 if (current->right)  push(stack, current->right);  push(stack, current);  // 往左子树遍历 current = current->left;  }  current = pop(stack);  if (current->right && peek(stack) == current->right) {  pop(stack); push(stack, current); current = current->right; } else {  printf("%d ", current->value);  current = NULL;  }  } while (!IS_EMPTY(stack)); }/** * 后续遍历-使用两个栈，更好理解一点。 */void postOrderIterWith2Stack(BTNode *root){ if (!root) return; BTNodeStack *stack = stackNew(size(root)); BTNodeStack *output = stackNew(size(root)); push(stack, root); BTNode *node;

while(!IS_EMPTY(stack)) {node= pop(stack); push(output,node);

if(node->left) push(stack,node->left); if (node->right) push(stack,node->right); } while (!IS_EMPTY(output)) {node= pop(output); printf("%d ",node->value); }}/** * 层序遍历-非递归 */void levelOrderIter(BTNode *root){ if (!root) return; BTNodeQueue *queue = queueNew(size(root)); enqueue(queue, root); while (1) { int nodeCount = QUEUE_SIZE(queue); if (nodeCount ==0) break; while (nodeCount >0) { BTNode *node= dequeue(queue); printf("%d ",node->value); if (node->left) enqueue(queue,node->left); if (node->right) enqueue(queue,node->right); nodeCount--; } printf("\n"); }}