二叉树相关面试题

树的先序遍历（非递归版本）

void TreePreOrderByLoop(TreeNode* root){
    if(root == NULL)
        return;
    //1.先将根节点入栈
    SeqStack stack;
    SeqStackInit(&stack);
    SeqStackPush(&stack,root);
    //2.循环开始，若栈为空，循环结束
    TreeNode* cur = NULL;
    while(GetTop(&stack,&cur)){
        //取栈顶元素为当前元素
        //出栈
        SeqStackPop(&stack);
        //访问当前元素
        printf("%c ",cur->data);
        //将当前的右子树入栈
        if(cur->rchild != NULL)
            SeqStackPush(&stack,cur->rchild);
        //将当前元素的左子树入栈
        if(cur->lchild != NULL)
            SeqStackPush(&stack,cur->lchild);
    }
    return;
}

树的中序遍历（非递归版本）

void TreeInOrderByLoop(TreeNode* root){
    if(root == NULL)
        return;
    SeqStack stack;
    SeqStackInit(&stack);
    //1.定义一个cur指针指向根节点
    TreeNode* cur = root;
    while(1){
    //循环判定cur是否为空，若不为空，cur入栈，cur指向cur->lchild
        while(cur != NULL){
            SeqStackPush(&stack,cur);
            cur = cur->lchild;
        }
    //若cur为空，取栈顶元素，访问，出栈
    TreeNode* top = NULL;
    int ret = GetTop(&stack,&top);
    if(ret == 0){
        printf("\n");
        return;
    }
    printf("%c ",top->data);
    SeqStackPop(&stack);
    //让cur指向栈顶元素的右子树，重复循环判空过程
    cur = top->rchild;
    }
    return ;
}

树的后序遍历（非递归版本）

void TreePostOrderByLoop(TreeNode* root){
    if(root == NULL)
        return;
    SeqStack stack;
    SeqStackInit(&stack);
    //定义cur指向root
    TreeNode* cur = root;
    TreeNode* pre = NULL;
    //循环判定cur是否为空，若不为空，将cur入栈，cur指向cur->lchild
    while(1){
        while(cur != NULL){
            SeqStackPush(&stack,cur);
            cur = cur->lchild;
        }
    //若cur为空，循环取栈顶元素
    TreeNode* top = NULL;
    int ret = GetTop(&stack,&top);
    if(ret == 0){
        printf("\n");
        return;
    }
    //对栈顶元素进行判定
    //a.若top的rchild和访问的上一个元素是同一元素
    //或top->rchild为空
    //访问栈顶元素，并出栈
    if(top->rchild == NULL || top->rchild == pre){
        printf("%c ",top->data);
        SeqStackPop(&stack);
        pre = top;
    }
    //若不满足上面的条件，cur指向top->rchild
    else{
        cur = top->rchild;
    }
    }
    return;
}

求二叉树的镜像（翻转）

递归版本：

void Swap(TreeNode** a,TreeNode** b){
    TreeNode* tmp = *a;
    *a = *b;
    *b = tmp;
}

void TreeMirror(TreeNode* root){
    if(root == NULL)
        return;
    Swap(&root->lchild,&root->rchild);
    TreeMirror(root->lchild);
    TreeMirror(root->rchild);
    return;
}

非递归版本：

void TreeMirrorByLoop(TreeNode* root){
    //层序遍历实现
    if(root == NULL)
        return;
    SeqQueue q;
    SeqQueueInit(&q);
    SeqQueuePush(&q,root);
    TreeNode* cur = NULL;
    while(SeqQueueFront(&q,&cur)){
        Swap(&cur->lchild,&cur->rchild);
        SeqQueuePop(&q);
        if(cur->lchild != NULL){
            SeqQueuePush(&q,cur->lchild);
        }
        if(cur->rchild != NULL){
            SeqQueuePush(&q,cur->rchild);
        }
    }
    return;
}

判断一棵树是否为完全二叉树

int IsCompleteTree(TreeNode* root){
    if(root == NULL)
        return 0;
    SeqQueue q;
    SeqQueueInit(&q);
    SeqQueuePush(&q,root);
    TreeNode* cur = NULL;
    int start_step_two = 0;
    while(SeqQueueFront(&q,&cur)){
        SeqQueuePop(&q);
        if(start_step_two == 0){
            //阶段一
            if(cur->lchild != NULL && cur->rchild != NULL){
                //同时具备左右子树
                SeqQueuePush(&q,cur->lchild);
                SeqQueuePush(&q,cur->rchild);
            }
            else if(cur->lchild == NULL && cur->rchild != NULL)
                //只有右子树
                return 0;
            else if(cur->lchild != NULL && cur->rchild == NULL){
                //只有左子树
                start_step_two = 1;
                SeqQueuePush(&q,cur->lchild);
            }
            else{//无左右子树
            start_step_two = 1;
        }
    }
    else{//阶段二
        if(cur->lchild == NULL && cur->rchild == NULL);
        else 
            return 0;
    }
    }
    return 1;
}

测试函数：

void TestPreOrderByLoop(){
    PRINT_HEAD;
    TreeNodeType data[] = "abd##eg###c#f##";
    TreeNode* root = TreeCreate(data,sizeof(data)/sizeof(data[0])-1,'#');
    printf("先序遍历为：");
    TreePreOrderByLoop(root);
    printf("\n");
}

void TestInOrderByLoop(){
     PRINT_HEAD;
     TreeNodeType data[] = "abd##eg###c#f##";
     TreeNode* root = TreeCreate(data,sizeof(data)/sizeof(data[0])-1,'#');
     printf("中序遍历为：");
     TreeInOrderByLoop(root);
     printf("\n");

}

void TestPostOrderByLoop(){
     PRINT_HEAD;
     TreeNodeType data[] = "abd##eg###c#f##";
     TreeNode* root = TreeCreate(data,sizeof(data)/sizeof(data[0])-1,'#');
     printf("后序遍历为：");
     TreePostOrderByLoop(root);
     printf("\n");
}

void TestMirror(){
     PRINT_HEAD;
     TreeNodeType data[] = "abd##eg###c#f##";
     TreeNode* root = TreeCreate(data,sizeof(data)/sizeof(data[0])-1,'#');
     TreeMirror(root);
     printf("先序遍历为：");
     TreePreOrderByLoop(root);
     printf("\n");
     printf("中序遍历为：");
     TreeInOrderByLoop(root);
     printf("后序遍历为：");
     TreePostOrderByLoop(root);
     printf("层序遍历为：");
     TreeLevelOrder(root);
     printf("\n");
}

void TestMirrorByLoop(){
     PRINT_HEAD;
     TreeNodeType data[] = "abd##eg###c#f##";
     TreeNode* root = TreeCreate(data,sizeof(data)/sizeof(data[0])-1,'#');
     TreeMirror(root);
     printf("先序遍历为：");
     TreePreOrderByLoop(root);
     printf("\n");
     printf("中序遍历为：");
     TreeInOrderByLoop(root);
     printf("后序遍历为：");
     TreePostOrderByLoop(root);
     printf("层序遍历为：");
     TreeLevelOrder(root);
     printf("\n");
}

void TestIsCompleteTree(){
    PRINT_HEAD;
    TreeNodeType data[] = "abd##eg###c#f##";
    TreeNode* root = TreeCreate(data,sizeof(data)/sizeof(data[0])-1,'#');
    int ret = IsCompleteTree(root);
    printf("ret = %d\n",ret);    
}

int main(){
    TestPreOrderByLoop();
    TestInOrderByLoop();
    TestPostOrderByLoop();
    TestMirror();
    TestMirrorByLoop();
    TestIsCompleteTree();
}

结果演示：

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