给定一棵二叉树，任务是打印这棵树的所有素数级别。
Any level of a Binary tree is said to be a prime level, if all nodes of this level are prime.
例子：
Input:
1
/ \
15 13
/ / \
11 7 29
\ /
2 3
Output: 11 7 29
2 3
Explanation:
Third and Fourth levels are prime levels.
Input:
7
/ \
23 41
/ \ \
31 16 3
/ \ \ /
2 5 17 11
/
23
Output: 7
23 41
2 5 17 11
23
Explanation:
First, Second, Fourth and
Fifth levels are prime levels.
方法：为了检查一个级别是否为 Prime 级别，
- 我们首先需要对二叉树进行层序遍历，得到每一层的节点值。
- 这里使用 Queue 数据结构来存储树的级别，同时进行级别顺序遍历。
- 然后对于每个级别，检查它是否是主要级别。
下面是上述方法的实现：
C++
// C++ program for printing a prime
// levels of binary Tree
#include
using namespace std;
// A Tree node
struct Node {
int key;
struct Node *left, *right;
};
// Utility function to create a new node
Node* newNode(int key)
{
Node* temp = new Node;
temp->key = key;
temp->left = temp->right = NULL;
return (temp);
}
// Function to check whether node
// Value is prime or not
bool isPrime(int n)
{
if (n == 1)
return false;
// Iterate from 2 to sqrt(n)
for (int i = 2; i * i <= n; i++) {
// If it has a factor
if (n % i == 0) {
return false;
}
}
return true;
}
// Function to print a Prime level
void printLevel(struct Node* queue[],
int index, int size)
{
for (int i = index; i < size; i++) {
cout << queue[i]->key << " ";
}
cout << endl;
}
// Function to check whether given level is
// prime level or not
bool isLevelPrime(struct Node* queue[],
int index, int size)
{
for (int i = index; i < size; i++) {
// Check value of node is
// pPrime or not
if (!isPrime(queue[index++]->key)) {
return false;
}
}
// Return true if for loop
// iIterate completely
return true;
}
// Utility function to get Prime
// Level of a given Binary tree
void findPrimeLevels(struct Node* node,
struct Node* queue[],
int index, int size)
{
// Print root node value, if Prime
if (isPrime(queue[index]->key)) {
cout << queue[index]->key << endl;
}
// Run while loop
while (index < size) {
int curr_size = size;
// Run inner while loop
while (index < curr_size) {
struct Node* temp = queue[index];
// Push left child in a queue
if (temp->left != NULL)
queue[size++] = temp->left;
// Push right child in a queue
if (temp->right != NULL)
queue[size++] = temp->right;
// Increament index
index++;
}
// If condition to check, level is
// prime or not
if (isLevelPrime(
queue, index, size - 1)) {
// Function call to print
// prime level
printLevel(queue, index, size);
}
}
}
// Function to find total no of nodes
// In a given binary tree
int findSize(struct Node* node)
{
// Base condition
if (node == NULL)
return 0;
return 1
+ findSize(node->left)
+ findSize(node->right);
}
// Function to find Prime levels
// In a given binary tree
void printPrimeLevels(struct Node* node)
{
int t_size = findSize(node);
// Create queue
struct Node* queue[t_size];
// Push root node in a queue
queue[0] = node;
// Function call
findPrimeLevels(node, queue, 0, 1);
}
// Driver Code
int main()
{
/* 10
/ \
13 11
/ \
19 23
/ \ / \
21 29 43 15
/
7 */
// Create Binary Tree as shown
Node* root = newNode(10);
root->left = newNode(13);
root->right = newNode(11);
root->right->left = newNode(19);
root->right->right = newNode(23);
root->right->left->left = newNode(21);
root->right->left->right = newNode(29);
root->right->right->left = newNode(43);
root->right->right->right = newNode(15);
root->right->right->right->left = newNode(7);
// Print Prime Levels
printPrimeLevels(root);
return 0;
} Python3
# Python3 program for printing a prime
# levels of binary Tree
# A Tree node
class Node:
def __init__(self, key):
self.key = key
self.left = None
self.right = None
# function to create a
# new node
def newNode(key):
temp = Node(key);
return temp;
# Function to check whether
# node Value is prime or not
def isPrime(n):
if (n == 1):
return False;
i = 2
# Iterate from 2
# to sqrt(n)
while(i * i <= n):
# If it has a factor
if (n % i == 0):
return False;
i += 1
return True;
# Function to print a
# Prime level
def printLevel(queue,
index, size):
for i in range(index, size):
print(queue[i].key, end = ' ')
print()
# Function to check whether
# given level is prime level
# or not
def isLevelPrime(queue,
index, size):
for i in range(index, size):
# Check value of node is
# pPrime or not
if (not isPrime(queue[index].key)):
index += 1
return False;
# Return true if for loop
# iIterate completely
return True;
# Utility function to get Prime
# Level of a given Binary tree
def findPrimeLevels(node, queue,
index, size):
# Print root node value, if Prime
if (isPrime(queue[index].key)):
print(queue[index].key)
# Run while loop
while (index < size):
curr_size = size;
# Run inner while loop
while (index < curr_size):
temp = queue[index];
# Push left child in a queue
if (temp.left != None):
queue[size] = temp.left;
size+=1
# Push right child in a queue
if (temp.right != None):
queue[size] = temp.right;
size+=1
# Increament index
index+=1;
# If condition to check, level
# is prime or not
if (isLevelPrime(queue, index,
size - 1)):
# Function call to print
# prime level
printLevel(queue,
index, size);
# Function to find total no
# of nodes In a given binary
# tree
def findSize(node):
# Base condition
if (node == None):
return 0;
return (1 + findSize(node.left) +
findSize(node.right));
# Function to find Prime levels
# In a given binary tree
def printPrimeLevels(node):
t_size = findSize(node);
# Create queue
queue=[0 for i in range(t_size)]
# Push root node in a queue
queue[0] = node;
# Function call
findPrimeLevels(node, queue,
0, 1);
# Driver code
if __name__ == "__main__":
''' 10
/ \
13 11
/ \
19 23
/ \ / \
21 29 43 15
/
7 '''
# Create Binary Tree as shown
root = newNode(10);
root.left = newNode(13);
root.right = newNode(11);
root.right.left = newNode(19);
root.right.right = newNode(23);
root.right.left.left = newNode(21);
root.right.left.right = newNode(29);
root.right.right.left = newNode(43);
root.right.right.right = newNode(15);
root.right.right.right.left = newNode(7);
# Print Prime Levels
printPrimeLevels(root);
# This code is contributed by Rutvik_56输出：
13 11
19 23
7
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