二叉树是采用链表的结构来实现
1.建立头文件
typedef int BTDataType;
typedef struct BinaryTreeNode
{
BTDataType data;
struct BinaryTreeNode* left;
struct BinaryTreeNode* right;
}BTNode;
// 通过前序遍历的数组"ABD##E#H##CF##G##"构建二叉树
BTNode* Creattree(BTDataType* a, int* pi);
// 二叉树销毁
void BinaryTreeDestroy(BTNode* root);
// 二叉树节点个数
int TreeSize(BTNode* root);
// 二叉树叶子节点个数
int TreeLeafSize(BTNode* root);
// 二叉树第k层节点个数
int TreeKLevel(BTNode* root, int k);
// 二叉树查找值为x的节点
BTNode* TreeFind(BTNode* root, BTDataType x);
int TreeHeight(BTNode* root); //树的深度
// 二叉树前序遍历
void PreOrder(BTNode* root);
// 二叉树中序遍历
void InOrder(BTNode* root);
// 二叉树后序遍历
void afOrder(BTNode* root);
// 层序遍历
void TreeLevelOrder(BTNode* root);
// 判断二叉树是否是完全二叉树
int BinaryTreeComplete(BTNode* root);
2.用前序遍历来建立树
BTNode* Creattree(BTDataType* a, int* pi)
{
if (a[*pi] == '#')
{
(*pi)++;
return NULL;
}
BTNode* root = (BTNode*)malloc(sizeof(BTNode));
if (root == NULL)
{
perror("malloc fail");
return NULL;
}
root->data = a[*pi];
(*pi)++;
root->left = Creattree(a, pi);
root->right = Creattree(a, pi);
return root;
}
如果数组a【*pi】不为空,就开辟空间来存储a【*pi】,同时(*pi)++。然后依次根据左子树,右子树来递归建立树,遇到空时返回。
3.树的销毁
void BinaryTreeDestroy(BTNode* root)
{
if (root == NULL)
{
return;
}
BinaryTreeDestroy(root->left);
BinaryTreeDestroy(root->right);
free(root);
}
由于树是链表结构,所以用递归来依次释放节点。
4.前序遍历
// 二叉树前序遍历
void PreOrder(BTNode* root)
{
if (root == NULL)
{
printf("NULL ");
return;
}
printf("%d ", root->data);
PreOrder(root->left);
PreOrder(root->right);
}
在访问左右子树前先打印该节点
5.中序遍历
// 二叉树中序遍历
void InOrder(BTNode* root)
{
if (root == NULL)
{
printf("NULL ");
return;
}
InOrder(root->left);
printf("%d ", root->data);
InOrder(root->right);
}
6.后序遍历
// 二叉树后序遍历
void afOrder(BTNode* root)
{
if (root == NULL)
{
printf("NULL ");
return;
}
afOrder(root->left);
afOrder(root->right);
printf("%d ", root->data);
}
7.二叉树节点个数
int TreeSize(BTNode* root) // 二叉树节点个数
{
return root == NULL ? 0 :
TreeSize(root->left) + TreeSize(root->right) + 1;
}
依然采用递归来计算节点个数
8.叶子结点个数
int TreeLeafSize(BTNode* root) // 二叉树叶子节点个数
{
if (root == NULL)
return 0;
if (root->left == NULL
&& root->right == NULL)
return 1;
return TreeLeafSize(root->left)
+ TreeLeafSize(root->right);
}
只有遇到叶子节点的时候才会返回1,这样左右子树层层返回相加,最后计算出叶子节点个数。
9.树的深度
int TreeHeight(BTNode* root) //树的深度
{
if (root == NULL)
return 0;
int lh = TreeHeight(root->left);
int rh = TreeHeight(root->right);
return lh > rh ? lh + 1 : rh + 1;
}
用lh和rh来比较大小,这样更深一层的树就会显示出来,包含了浅一层的树。
10.第k层的节点个数
// 第K层节点个数
int TreeKLevel(BTNode* root, int k)
{
assert(k > 0);
if (root == NULL)
return 0;
if (k == 1)
return 1;
// 转换成求子树第k-1层
return TreeKLevel(root->left, k - 1)
+ TreeKLevel(root->right, k - 1);
}
11.返回查找节点的位置
// 返回x所在的节点 // 二叉树查找值为x的节点
BTNode* TreeFind(BTNode* root, BTDataType x)
{
BTNode* lret, * rret;
if (root == NULL)
return NULL;
if (root->data == x)
return root;
// 先去左树找
lret = TreeFind(root->left, x);
if (lret)
return lret;
// 左树没有找到,再到右树找
rret = TreeFind(root->right, x);
if (rret)
return rret;
return NULL;
}
12.二叉树的层序遍历
void TreeLevelOrder(BTNode* root) //二叉树的层序遍历
{
Queue q;
QueueInit(&q);
if (root)
QueuePush(&q, root);
while (!QueueEmpty(&q))
{
BTNode* front = QueueFront(&q);
QueuePop(&q);
printf("%d ", front->data);
// 下一层,入队列
if (front->left)
QueuePush(&q, front->left);
if (front->right)
QueuePush(&q, front->right);
}
printf("\n");
QueueDestroy(&q);
}
其中包含了队列的使用方式
13.判断是不是完全二叉树
// 判断二叉树是否是完全二叉树
int BinaryTreeComplete(BTNode* root)
{
Queue q;
QueueInit(&q);
if (root)
QueuePush(&q, root);
while (!QueueEmpty(&q))
{
BTNode* front = QueueFront(&q);
QueuePop(&q);
if (front == NULL)
{
break;
}
QueuePush(&q, front->left);
QueuePush(&q, front->right);
}
// 遇到空以后,后面全是空,则是完全二叉树
// 遇到空以后,后面存在非空,则不是完全二叉树
while (!QueueEmpty(&q))
{
BTNode* front = QueueFront(&q);
QueuePop(&q);
if (front != NULL)
{
QueueDestroy(&q);
return false;
}
}
QueueDestroy(&q);
return true;
}
也是依次层序遍历,然后在最后一层判断遇到空后是不是一直为空
14.测试
BTNode* CreateTree()
{
BTNode* n1 = (BTNode*)malloc(sizeof(BTNode));
assert(n1);
BTNode* n2 = (BTNode*)malloc(sizeof(BTNode));
assert(n2);
BTNode* n3 = (BTNode*)malloc(sizeof(BTNode));
assert(n3);
BTNode* n4 = (BTNode*)malloc(sizeof(BTNode));
assert(n4);
BTNode* n5 = (BTNode*)malloc(sizeof(BTNode));
assert(n5);
BTNode* n6 = (BTNode*)malloc(sizeof(BTNode));
assert(n6);
BTNode* n7 = (BTNode*)malloc(sizeof(BTNode));
assert(n7);
n1->data = 1;
n2->data = 2;
n3->data = 3;
n4->data = 4;
n5->data = 5;
n6->data = 6;
n7->data = 7;
n1->left = n2;
n1->right = n4;
n2->left = n3;
n2->right = NULL;
n4->left = n5;
//n4->right = n6;
n4->right = NULL;
n3->left = NULL;
n3->right = NULL;
n5->left = NULL;
n5->right = NULL;
//n6->left = NULL;
//n6->right = NULL;
//n3->right = n7;
n2->right = n7;
n7->left = NULL;
n7->right = NULL;
return n1;
}
int main()
{
BTNode* root = CreateTree();
PreOrder(root);
printf("\n");
InOrder(root);
printf("\n");
//count = 0;
//TreeSize(root);
//printf("Tree size:%d\n", count);
//count = 0;
//TreeSize(root);
//printf("Tree size:%d\n", count);
printf("Tree size:%d\n", TreeSize(root));
printf("Tree size:%d\n", TreeSize(root));
printf("Tree size:%d\n", TreeSize(root));
printf("Tree Leaf size:%d\n", TreeLeafSize(root));
printf("Tree Height:%d\n", TreeHeight(root));
printf("Tree K Level:%d\n", TreeKLevel(root, 3));
printf("Tree Find:%p\n", TreeFind(root, 8));
BTNode* ret = TreeFind(root, 7);
ret->data *= 10;
PreOrder(root);
printf("\n");
BinaryTreeDestroy(root);
root = NULL;
return 0;
}
测试结果