给定一个二叉树，任务是打印该树的所有互素级别。
Any level of a Binary tree is said to be a Co-prime level, if all nodes of this level are co-prime to each other.
例子：
Input:
1
/ \
15 5
/ / \
11 4 15
\ /
2 3
Output:
1
11 4 15
2 3
Explanation:
First, Third and Fourth levels
are co-prime levels.
Input:
7
/ \
21 14
/ \ \
77 16 3
/ \ \ /
2 5 10 11
/
23
Output:
7
77 16 3
23
Explanation:
First, Third and Fifth levels
are co-prime levels.
方法：为了检查某个级别是否为“同等级别”，
- 首先，我们必须使用Eratosthenes筛子存储所有素数。
- 然后，我们必须对二叉树进行级别顺序遍历，并且必须将该级别的所有元素保存到向量中。
- 此向量用于在执行级别顺序遍历时存储树的级别。
- 然后，对于每个级别，检查元素的GCD是否等于1。如果是，则此级别不是“同等优先”，否则打印该级别的所有元素。
下面是上述方法的实现：
C++
// C++ program for printing Co-prime
// levels of binary Tree
#include
using namespace std;
int N = 1000000;
// To store all prime numbers
vector prime;
void SieveOfEratosthenes()
{
// Create a boolean array "prime[0..N]"
// and initialize all entries it as true.
// A value in prime[i] will finally
// be false if i is Not a prime, else true.
bool check[N + 1];
memset(check, true, sizeof(check));
for (int p = 2; p * p <= N; p++) {
// If prime[p] is not changed,
// then it is a prime
if (check[p] == true) {
prime.push_back(p);
// Update all multiples of p
// greater than or equal to
// the square of it
// numbers which are multiples of p
// and are less than p^2
// are already marked.
for (int i = p * p; i <= N; i += p)
check[i] = false;
}
}
}
// 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 Level
// is Co-prime or not
bool isLevelCo_Prime(vector& L)
{
int max = 0;
for (auto x : L) {
if (max < x)
max = x;
}
for (int i = 0;
i * prime[i] <= max / 2;
i++) {
int ct = 0;
for (auto x : L) {
if (x % prime[i] == 0)
ct++;
}
// If not co-prime
if (ct > 1) {
return false;
}
}
return true;
}
// Function to print a Co-Prime level
void printCo_PrimeLevels(vector& Lev)
{
for (auto x : Lev) {
cout << x << " ";
}
cout << endl;
}
// Utility function to get Co-Prime
// Level of a given Binary tree
void findCo_PrimeLevels(
struct Node* node,
struct Node* queue[],
int index, int size)
{
vector Lev;
// Run while loop
while (index < size) {
int curr_size = size;
// Run inner while loop
while (index < curr_size) {
struct Node* temp = queue[index];
Lev.push_back(temp->key);
// 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 (isLevelCo_Prime(Lev)) {
// Function call to print
// prime level
printCo_PrimeLevels(Lev);
}
Lev.clear();
}
}
// 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 Co-Prime levels
// In a given binary tree
void printCo_PrimeLevels(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
findCo_PrimeLevels(node, queue, 0, 1);
}
// Driver Code
int main()
{
/* 10
/ \
48 12
/ \
18 35
/ \ / \
21 29 43 16
/
7
*/
// Create Binary Tree as shown
Node* root = newNode(10);
root->left = newNode(48);
root->right = newNode(12);
root->right->left = newNode(18);
root->right->right = newNode(35);
root->right->left->left = newNode(21);
root->right->left->right = newNode(29);
root->right->right->left = newNode(43);
root->right->right->right = newNode(16);
root->right->right->right->left = newNode(7);
// To save all prime numbers
SieveOfEratosthenes();
// Print Co-Prime Levels
printCo_PrimeLevels(root);
return 0;
} Java
// Java program for printing Co-prime
// levels of binary Tree
import java.util.*;
class GFG{
static int N = 1000000;
// To store all prime numbers
static Vector prime = new Vector();
static void SieveOfEratosthenes()
{
// Create a boolean array "prime[0..N]"
// and initialize all entries it as true.
// A value in prime[i] will finally
// be false if i is Not a prime, else true.
boolean []check = new boolean[N + 1];
Arrays.fill(check, true);
for (int p = 2; p * p <= N; p++) {
// If prime[p] is not changed,
// then it is a prime
if (check[p] == true) {
prime.add(p);
// Update all multiples of p
// greater than or equal to
// the square of it
// numbers which are multiples of p
// and are less than p^2
// are already marked.
for (int i = p * p; i <= N; i += p)
check[i] = false;
}
}
}
// A Tree node
static class Node {
int key;
Node left, right;
};
// Utility function to create a new node
static Node newNode(int key)
{
Node temp = new Node();
temp.key = key;
temp.left = temp.right = null;
return (temp);
}
// Function to check whether Level
// is Co-prime or not
static boolean isLevelCo_Prime(Vector L)
{
int max = 0;
for (int x : L) {
if (max < x)
max = x;
}
for (int i = 0;
i * prime.get(i) <= max / 2;
i++) {
int ct = 0;
for (int x : L) {
if (x % prime.get(i) == 0)
ct++;
}
// If not co-prime
if (ct > 1) {
return false;
}
}
return true;
}
// Function to print a Co-Prime level
static void printCo_PrimeLevels(Vector Lev)
{
for (int x : Lev) {
System.out.print(x+ " ");
}
System.out.println();
}
// Utility function to get Co-Prime
// Level of a given Binary tree
static void findCo_PrimeLevels(
Node node,
Node queue[],
int index, int size)
{
Vector Lev = new Vector();
// Run while loop
while (index < size) {
int curr_size = size;
// Run inner while loop
while (index < curr_size) {
Node temp = queue[index];
Lev.add(temp.key);
// 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 (isLevelCo_Prime(Lev)) {
// Function call to print
// prime level
printCo_PrimeLevels(Lev);
}
Lev.clear();
}
}
// Function to find total no of nodes
// In a given binary tree
static int findSize(Node node)
{
// Base condition
if (node == null)
return 0;
return 1
+ findSize(node.left)
+ findSize(node.right);
}
// Function to find Co-Prime levels
// In a given binary tree
static void printCo_PrimeLevels(Node node)
{
int t_size = findSize(node);
// Create queue
Node []queue = new Node[t_size];
// Push root node in a queue
queue[0] = node;
// Function call
findCo_PrimeLevels(node, queue, 0, 1);
}
// Driver Code
public static void main(String[] args)
{
/* 10
/ \
48 12
/ \
18 35
/ \ / \
21 29 43 16
/
7
*/
// Create Binary Tree as shown
Node root = newNode(10);
root.left = newNode(48);
root.right = newNode(12);
root.right.left = newNode(18);
root.right.right = newNode(35);
root.right.left.left = newNode(21);
root.right.left.right = newNode(29);
root.right.right.left = newNode(43);
root.right.right.right = newNode(16);
root.right.right.right.left = newNode(7);
// To save all prime numbers
SieveOfEratosthenes();
// Print Co-Prime Levels
printCo_PrimeLevels(root);
}
}
// This code is contributed by PrinciRaj1992 Python3
# Python3 program for printing
# Co-prime levels of binary Tree
# A Tree node
class Node:
def __init__(self, key):
self.key = key
self.left = None
self.right = None
# Utility function to create
# a new node
def newNode(key):
temp = Node(key)
return temp
N = 1000000
# Vector to store all the
# prime numbers
prime = []
# Function to store all the
# prime numbers in an array
def SieveOfEratosthenes():
# Create a boolean array "prime[0..N]"
# and initialize all the entries in it
# as true. A value in prime[i]
# will finally be false if
# i is Not a prime, else true.
check = [True for i in range(N + 1)]
p = 2
while(p * p <= N):
# If prime[p] is not changed,
# then it is a prime
if (check[p]):
prime.append(p);
# Update all multiples of p
# greater than or equal to
# the square of it
# numbers which are multiples of p
# and are less than p^2
# are already marked.
for i in range(p * p, N + 1, p):
check[i] = False;
p += 1
# Function to check whether
# Level is Co-prime or not
def isLevelCo_Prime(L):
max = 0;
for x in L:
if (max < x):
max = x;
i = 0
while(i * prime[i] <= max // 2):
ct = 0;
for x in L:
if (x % prime[i] == 0):
ct += 1
# If not co-prime
if (ct > 1):
return False;
i += 1
return True;
# Function to print a
# Co-Prime Level
def printCo_PrimeLevels(Lev):
for x in Lev:
print(x, end = ' ')
print()
# Utility function to get Co-Prime
# Level of a given Binary tree
def findCo_PrimeLevels(node, queue,
index, size):
Lev = []
# Run while loop
while (index < size):
curr_size = size;
# Run inner while loop
while (index < curr_size):
temp = queue[index];
Lev.append(temp.key)
# 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 (isLevelCo_Prime(Lev)):
# Function call to print
# prime level
printCo_PrimeLevels(Lev);
Lev.clear();
# 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 Co-Prime levels
# In a given binary tree
def printCo_PrimeLevel(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
findCo_PrimeLevels(node, queue,
0, 1);
# Driver code
if __name__ == "__main__":
''' 10
/ \
48 12
/ \
18 35
/ \ / \
21 29 43 16
/
7
'''
# Create Binary Tree as shown
root = newNode(10);
root.left = newNode(48);
root.right = newNode(12);
root.right.left = newNode(18);
root.right.right = newNode(35);
root.right.left.left = newNode(21);
root.right.left.right = newNode(29);
root.right.right.left = newNode(43);
root.right.right.right = newNode(16);
root.right.right.right.left = newNode(7);
# To save all prime numbers
SieveOfEratosthenes();
# Print Co-Prime Levels
printCo_PrimeLevel(root);
# This code is contributed by Rutvik_56C#
// C# program for printing Co-prime
// levels of binary Tree
using System;
using System.Collections.Generic;
class GFG{
static int N = 1000000;
// To store all prime numbers
static List prime = new List();
static void SieveOfEratosthenes()
{
// Create a bool array "prime[0..N]"
// and initialize all entries it as true.
// A value in prime[i] will finally
// be false if i is Not a prime, else true.
bool []check = new bool[N + 1];
for(int i = 0; i <= N; i++)
check[i] = true;
for (int p = 2; p * p <= N; p++) {
// If prime[p] is not changed,
// then it is a prime
if (check[p] == true) {
prime.Add(p);
// Update all multiples of p
// greater than or equal to
// the square of it
// numbers which are multiples of p
// and are less than p^2
// are already marked.
for (int i = p * p; i <= N; i += p)
check[i] = false;
}
}
}
// A Tree node
class Node {
public int key;
public Node left, right;
};
// Utility function to create a new node
static Node newNode(int key)
{
Node temp = new Node();
temp.key = key;
temp.left = temp.right = null;
return (temp);
}
// Function to check whether Level
// is Co-prime or not
static bool isLevelCo_Prime(List L)
{
int max = 0;
foreach (int x in L) {
if (max < x)
max = x;
}
for (int i = 0;
i * prime[i] <= max / 2;
i++) {
int ct = 0;
foreach (int x in L) {
if (x % prime[i] == 0)
ct++;
}
// If not co-prime
if (ct > 1) {
return false;
}
}
return true;
}
// Function to print a Co-Prime level
static void printCo_PrimeLevels(List Lev)
{
foreach (int x in Lev) {
Console.Write(x+ " ");
}
Console.WriteLine();
}
// Utility function to get Co-Prime
// Level of a given Binary tree
static void findCo_PrimeLevels(
Node node,
Node []queue,
int index, int size)
{
List Lev = new List();
// Run while loop
while (index < size) {
int curr_size = size;
// Run inner while loop
while (index < curr_size) {
Node temp = queue[index];
Lev.Add(temp.key);
// 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 (isLevelCo_Prime(Lev)) {
// Function call to print
// prime level
printCo_PrimeLevels(Lev);
}
Lev.Clear();
}
}
// Function to find total no of nodes
// In a given binary tree
static int findSize(Node node)
{
// Base condition
if (node == null)
return 0;
return 1
+ findSize(node.left)
+ findSize(node.right);
}
// Function to find Co-Prime levels
// In a given binary tree
static void printCo_PrimeLevels(Node node)
{
int t_size = findSize(node);
// Create queue
Node []queue = new Node[t_size];
// Push root node in a queue
queue[0] = node;
// Function call
findCo_PrimeLevels(node, queue, 0, 1);
}
// Driver Code
public static void Main(String[] args)
{
/* 10
/ \
48 12
/ \
18 35
/ \ / \
21 29 43 16
/
7
*/
// Create Binary Tree as shown
Node root = newNode(10);
root.left = newNode(48);
root.right = newNode(12);
root.right.left = newNode(18);
root.right.right = newNode(35);
root.right.left.left = newNode(21);
root.right.left.right = newNode(29);
root.right.right.left = newNode(43);
root.right.right.right = newNode(16);
root.right.right.right.left = newNode(7);
// To save all prime numbers
SieveOfEratosthenes();
// Print Co-Prime Levels
printCo_PrimeLevels(root);
}
}
// This code is contributed by Rajput-Ji 输出：
10
18 35
21 29 43 16
7