If you encounter a node that is not second-degree, then if the tree is a complete tree, all leaves behind this node must be.
There are special circumstances. When this tree has only two nodes, the root must have a degree less than 2, and the other node must be leaves, but this tree is not a complete tree.
Therefore, when the number of nodes is greater than 2, the general method can be used, and when there are only two nodes, it is best to output directly as a special case.
As for the sequence traversal, queues can be used. When visiting a node, put its left child into the end of the team, and then put the right child into the end of the team. The nodes of the upper layer must be in front of the lower layer in the queue, and are arranged from left to right.
The code includes the establishment of the tree, the use of the queue, and the output of the sequence. In the function of layer sequence output, two bool variables are used to judge the completeness by the way.
//输入大小
//输入数字
// 生成树
// 进行层序遍历
// 如果某一个结点的没有两个子树
//那么接下去的结点都不能有两个子树
#define _CRT_SECURE_NO_WARNINGS
#include<stdlib.h>
#include<stdio.h>
#include<stdbool.h>
static int n;
//标记树的完全性
static bool sign1 = false;
static bool sign2 = false;
struct TNode{
int value;
struct TNode* Left;
struct TNode* Right;
};
struct TNode* insert(struct TNode* root, int data) {
//新建叶子
if (root == NULL) {
root = (malloc)(sizeof(struct TNode));
root->value = data;
root->Left = NULL;
root->Right = NULL;
return root;
}
else {
if (data > root->value) {
root->Left = insert(root->Left, data);
}
else {
root->Right = insert(root->Right, data);
}
}
return root;
}
//队列及操作
struct Queue {
struct TNode* array[30];
int front;
int top;
int count;
}q;
void initialQueue() {
q.front = q.top = 0;
q.count = 0;
}
void push(struct TNode* data) {
q.array[q.top] = data;
q.top++;
q.count++;
}
struct TNode* pop() {
struct TNode* data = q.array[q.front];
q.front++;
q.count--;
return data;
}
struct TNode* front() {
return q.array[q.front];
}
bool isEmpty() {
return q.count == 0;
}
//队列方式实现层序输出
void levelOut(struct TNode* root) {
//加入根结点
push(root);
while (!isEmpty()) {
struct TNode* tempFront = pop();
if (tempFront->Left != NULL) {
push(tempFront->Left);
}
if (tempFront->Right != NULL) {
push(tempFront->Right);
}
//输出控制.........
if (!isEmpty())
printf("%d ", tempFront->value);
else
printf("%d", tempFront->value);
//... ......
//判断完全性
//有一个不为二度的结点 则后面的都要是叶子
if (sign1== false&&(!(tempFront->Left != NULL && tempFront->Right != NULL))) {
sign1 = true;
continue;
}
if (sign1 == true) {
if (!(tempFront->Left == NULL && tempFront->Right == NULL)) {
sign2 = true;
}
}
//特别讨论只有两个结点的情况
if (n == 2) {
sign2 = true;
}
}
printf("\n");
}
//在层序输出时做好标记
int main() {
struct TNode* treeRoot = NULL;
scanf("%d", &n);
//导入结点
for (int i = 0; i < n; i++) {
int toInsert;
scanf("%d", &toInsert);
treeRoot= insert(treeRoot, toInsert);
}
levelOut(treeRoot);
if (!sign2) {
printf("YES");
}
else {
printf("NO");
}
return 0;
}