从给定数组打印前 K 个不同的 Moran 数

给定一个由N 个不同的正整数组成的数组arr[] ，任务是打印给定数组中的前K 个不同的莫兰数。

A number N is a Moran number if N divided by the sum of its digits gives a prime number. 
Examples: 18, 21, 27, 42, 45

例子：

Input: arr[] = {192, 21, 18, 138, 27, 42, 45}, K = 4 
Output: 21, 27, 42, 45 
Explanation:

• The sum of digits of the integer 21 is 2 + 1 = 3. Therefore, dividing 21 by its sum of digits = 21 / 3 = 7, which is a prime number.
• The sum of digits of the integer 27 is 2 + 7 = 9. Therefore, dividing 27 by its sum of digits results in 27 / 9 = 3, which is a prime number.
• The sum of digits of the integer 42 is 4 + 2 = 6. Therefore, dividing 42 by its sum of digits results in 42 / 6 = 7, which is a prime number.
• The sum of digits of the integer 45 is 4 + 5 = 9. Therefore, dividing 45 by its sum of digits results in 45 / 9 = 5, which is a prime number.

Input: arr[]={127, 186, 198, 63, 27, 91}, K = 3 
Output: 27, 63, 198

方法：按照下面给出的步骤解决问题：

1. 对数组进行排序
2. 遍历排序后的数组，对于每个元素，检查它是否是莫兰数
3. 如果发现为真，则将元素插入 Set 并递增计数器，直到达到K 。
4. 当集合的大小等于K时打印集合中的元素。

下面是上述方法的实现：

C++

#include 
#include 
#include 
using namespace std;
 
// Function to calculate the
// sum of digits of a number
int digiSum(int a)
{
    // Stores the sum of digits
    int sum = 0;
    while (a) {
 
        // Add the digit to sum
        sum += a % 10;
 
        // Remove digit
        a = a / 10;
    }
 
    // Returns the sum
    // of digits
    return sum;
}
 
// Function to check if a number
// is prime or not
bool isPrime(int r)
{
    bool s = true;
 
    for (int i = 2; i * i <= r; i++) {
 
        // If r has any divisor
        if (r % i == 0) {
 
            // Set r as non-prime
            s = false;
            break;
        }
    }
    return s;
}
 
// Function to check if a
// number is moran number
bool isMorannumber(int n)
{
    int dup = n;
 
    // Calculate sum of digits
    int sum = digiSum(dup);
 
    // Check if n is divisible
    // by the sum of digits
    if (n % sum == 0) {
 
        // Calculate the quotient
        int c = n / sum;
 
        // If the quotient is prime
        if (isPrime(c)) {
 
            return true;
        }
    }
 
    return false;
}
 
// Function to print the first K
// Moran numbers from the array
void FirstKMorannumber(int a[],
                       int n, int k)
{
    int X = k;
 
    // Sort the given array
    sort(a, a + n);
 
    // Initialise a set
    set s;
 
    // Traverse the array from the end
    for (int i = n - 1; i >= 0
                        && k > 0;
         i--) {
        // If the current array element
        // is a Moran number
        if (isMorannumber(a[i])) {
 
            // Insert into the set
            s.insert(a[i]);
            k--;
        }
    }
 
    if (k > 0) {
        cout << X << " Moran numbers are"
             << " not present in the array" << endl;
        return;
    }
 
    set::iterator it;
    for (it = s.begin(); it != s.end(); ++it) {
        cout << *it << ", ";
    }
    cout << endl;
}
 
// Driver Code
int main()
{
 
    int A[] = { 34, 198, 21, 42,
                63, 45, 22, 44, 43 };
    int K = 4;
 
    int N = sizeof(A) / sizeof(A[0]);
 
    FirstKMorannumber(A, N, K);
 
    return 0;
}

Java

import java.io.*;
import java.util.*;
 
class GFG{
 
// Function to calculate the
// sum of digits of a number
static int digiSum(int a)
{
     
    // Stores the sum of digits
    int sum = 0;
    while (a != 0)
    {
         
        // Add the digit to sum
        sum += a % 10;
 
        // Remove digit
        a = a / 10;
    }
 
    // Returns the sum
    // of digits
    return sum;
}
 
// Function to check if a number
// is prime or not
static boolean isPrime(int r)
{
    boolean s = true;
 
    for(int i = 2; i * i <= r; i++)
    {
         
        // If r has any divisor
        if (r % i == 0)
        {
             
            // Set r as non-prime
            s = false;
            break;
        }
    }
    return s;
}
 
// Function to check if a
// number is moran number
static boolean isMorannumber(int n)
{
    int dup = n;
 
    // Calculate sum of digits
    int sum = digiSum(dup);
 
    // Check if n is divisible
    // by the sum of digits
    if (n % sum == 0)
    {
         
        // Calculate the quotient
        int c = n / sum;
 
        // If the quotient is prime
        if (isPrime(c))
        {
            return true;
        }
    }
    return false;
}
 
// Function to print the first K
// Moran numbers from the array
static void FirstKMorannumber(int[] a,
                              int n, int k)
{
    int X = k;
 
    // Sort the given array
    Arrays.sort(a);
 
    // Initialise a set
    TreeSet s = new TreeSet();
 
    // Traverse the array from the end
    for(int i = n - 1; i >= 0 && k > 0; i--)
    {
         
        // If the current array element
        // is a Moran number
        if (isMorannumber(a[i]))
        {
             
            // Insert into the set
            s.add(a[i]);
            k--;
        }
    }
 
    if (k > 0)
    {
        System.out.println(X + " Moran numbers are" +
                               " not present in the array");
        return;
    }
 
    for(int value : s)
        System.out.print(value + ", ");
         
    System.out.print("\n");
}
 
// Driver Code
public static void main(String[] args)
{
    int[] A = { 34, 198, 21, 42,
                63, 45, 22, 44, 43 };
    int K = 4;
 
    int N = A.length;
 
    FirstKMorannumber(A, N, K);
}
}
 
// This code is contributed by akhilsaini

Python3

import math
 
# Function to calculate the
# sum of digits of a number
def digiSum(a):
     
    # Stores the sum of digits
    sums = 0
    while (a != 0):
         
        # Add the digit to sum
        sums += a % 10
 
        # Remove digit
        a = a // 10
 
    # Returns the sum
    # of digits
    return sums
 
# Function to check if a number
# is prime or not
def isPrime(r):
     
    s = True
 
    for i in range(2, int(math.sqrt(r)) + 1):
         
        # If r has any divisor
        if (r % i == 0):
 
            # Set r as non-prime
            s = False
            break
 
    return s
 
# Function to check if a
# number is moran number
def isMorannumber(n):
     
    dup = n
 
    # Calculate sum of digits
    sums = digiSum(dup)
 
    # Check if n is divisible
    # by the sum of digits
    if (n % sums == 0):
         
        # Calculate the quotient
        c = n // sums
 
        # If the quotient is prime
        if isPrime(c):
            return True
 
    return False
 
# Function to print the first K
# Moran numbers from the array
def FirstKMorannumber(a, n, k):
     
    X = k
 
    # Sort the given array
    a.sort()
 
    # Initialise a set
    s = set()
 
    # Traverse the array from the end
    for i in range(n - 1, -1, -1):
        if (k <= 0):
            break
 
        # If the current array element
        # is a Moran number
        if (isMorannumber(a[i])):
             
            # Insert into the set
            s.add(a[i])
            k -= 1
 
    if (k > 0):
        print(X, end =' Moran numbers are not '
                       'present in the array')
        return
 
    lists = sorted(s)
    for i in lists:
        print(i, end = ', ')
 
# Driver Code
if __name__ == '__main__':
 
    A = [ 34, 198, 21, 42,
          63, 45, 22, 44, 43 ]
    K = 4
 
    N = len(A)
 
    FirstKMorannumber(A, N, K)
 
# This code is contributed by akhilsaini

C#

using System;
using System.Collections;
using System.Collections.Generic;
 
class GFG{
 
// Function to calculate the
// sum of digits of a number
static int digiSum(int a)
{
     
    // Stores the sum of digits
    int sum = 0;
    while (a != 0)
    {
         
        // Add the digit to sum
        sum += a % 10;
 
        // Remove digit
        a = a / 10;
    }
 
    // Returns the sum
    // of digits
    return sum;
}
 
// Function to check if a number
// is prime or not
static bool isPrime(int r)
{
    bool s = true;
 
    for(int i = 2; i * i <= r; i++)
    {
         
        // If r has any divisor
        if (r % i == 0)
        {
             
            // Set r as non-prime
            s = false;
            break;
        }
    }
    return s;
}
 
// Function to check if a
// number is moran number
static bool isMorannumber(int n)
{
    int dup = n;
     
    // Calculate sum of digits
    int sum = digiSum(dup);
 
    // Check if n is divisible
    // by the sum of digits
    if (n % sum == 0)
    {
         
        // Calculate the quotient
        int c = n / sum;
 
        // If the quotient is prime
        if (isPrime(c))
        {
            return true;
        }
    }
    return false;
}
 
// Function to print the first K
// Moran numbers from the array
static void FirstKMorannumber(int[] a,
                              int n, int k)
{
    int X = k;
 
    // Sort the given array
    Array.Sort(a);
 
    // Initialise a set
    SortedSet s = new SortedSet();
 
    // Traverse the array from the end
    for(int i = n - 1; i >= 0 && k > 0; i--)
    {
         
        // If the current array element
        // is a Moran number
        if (isMorannumber(a[i]))
        {
             
            // Insert into the set
            s.Add(a[i]);
            k--;
        }
    }
 
    if (k > 0)
    {
        Console.WriteLine(X + " Moran numbers are" +
                              " not present in the array");
        return;
    }
 
    foreach(var val in s)
    {
        Console.Write(val + ", ");
    }
    Console.Write("\n");
}
 
// Driver Code
public static void Main()
{
    int[] A = { 34, 198, 21, 42,
                63, 45, 22, 44, 43 };
    int K = 4;
 
    int N = A.Length;
 
    FirstKMorannumber(A, N, K);
}
}
 
// This code is contributed by akhilsaini

Javascript

 
// Function to calculate the
// sum of digits of a number
function digiSum(a)
{
    // Stores the sum of digits
    let sum = 0;
    while (a) {
 
        // Add the digit to sum
        sum += a % 10;
 
        // Remove digit
        a = Math.floor(a / 10);
    }
 
    // Returns the sum
    // of digits
    return sum;
}
 
// Function to check if a number
// is prime or not
function isPrime(r)
{
    let s = true;
 
    for (let i = 2; i * i <= r; i++) {
 
        // If r has any divisor
        if (r % i == 0) {
 
            // Set r as non-prime
            s = false;
            break;
        }
    }
    return s;
}
 
// Function to check if a
// number is moran number
function isMorannumber(n)
{
    let dup = n;
 
    // Calculate sum of digits
    let sum = digiSum(dup);
 
    // Check if n is divisible
    // by the sum of digits
    if (n % sum == 0) {
 
        // Calculate the quotient
        let c = n / sum;
 
        // If the quotient is prime
        if (isPrime(c)) {
 
            return true;
        }
    }
 
    return false;
}
 
// Function to print the first K
// Moran numbers from the array
function FirstKMorannumber(a, n, k)
{
    let X = k;
 
    // Sort the given array
    a = a.sort((x, y) => x - y)
 
    // Initialise a set
    let s = new Set();
 
    // Traverse the array from the end
    for (let i = n - 1; i >= 0
                        && k > 0;
         i--) {
        // If the current array element
        // is a Moran number
        if (isMorannumber(a[i])) {
 
            // Insert into the set
            s.add(a[i]);
            k--;
        }
    }
 
    if (k > 0) {
        document.write(X + " Moran numbers are"
             + " not present in the array"  + "<br>");
        return;
    }
 
    // Convert the set into array and then sort the array
 
    s = [...s].sort((a, b) => a - b)
 
    for (let it of s) {
        document.write(it + ", ");
    }
    document.write("<br>");
}
 
// Driver Code
 
    let A = [ 34, 198, 21, 42,
                63, 45, 22, 44, 43 ];
    let K = 4;
 
    let N = A.length;
 
    FirstKMorannumber(A, N, K);
 
    // This code is contributed by gfgking
     

输出：

42, 45, 63, 198,

时间复杂度： O(N ^3/2 )
辅助空间： O(N)

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