给定一个由非负整数组成的数组arr [] ，任务是打印给定数组中最长子序列的长度，该数组的每个元素的位数之和是一个复合数字。
例子：
Input: arr[] = {13, 55, 7, 3, 5, 21, 233, 144, 89}
Output: 4
Explanation:Following array elements have sum of digits equal to a composite number:
- 13 -> 1 + 3 = 4
- 55 -> 5 + 5 = 10
- 233 -> 2 + 3 + 3 = 8
- 144 -> 1 + 4 + 4 = 9
Therefore, the required longest subsequence is {13, 55, 233, 144} of length 4.
Input: arr[] = {34, 13, 11, 8, 3, 55, 23}
Output: 3
Explanation: Following array elements have sum of digits equal to a composite number:
- 13 -> 1 + 3 = 4
- 8 -> 8 = 8
- 55 -> 5 + 5 = 10
Therefore, the required longest subsequence is {13, 8, 55} of length 3.
方法：请按照以下步骤解决问题：
- 遍历给定的数组。
- 对于每个数组元素，检查其数字之和是否为素数或其数字之和等于1 。
- 如果其数字的总和为质数，则转到下一个数组元素。否则，将所需子序列的长度增加1 。
- 最后，在遍历数组后，打印获得的子序列的长度。
下面是上述方法的实现：
C++
// C++ implenetation of the
// above approach
#include
using namespace std;
#define N 100005
// Function to generate prime numbers
// using Sieve of Eratosthenes
void SieveOfEratosthenes(bool prime[],
int p_size)
{
// Set 0 and 1 as non-prime
prime[0] = false;
prime[1] = false;
for (int p = 2; p * p <= p_size; p++) {
// If p is a prime
if (prime[p]) {
// Set all multiples of p as non-prime
for (int i = p * 2; i <= p_size; i += p)
prime[i] = false;
}
}
}
// Function to find the digit sum
// of a given number
int digitSum(int number)
{
// Stores the sum of digits
int sum = 0;
while (number > 0) {
// Extract digits and
// add to the sum
sum += (number % 10);
number /= 10;
}
// Return the sum
// of the digits
return sum;
}
// Function to find the longest subsequence
// with sum of digits of each element equal
// to a composite number
void longestCompositeDigitSumSubsequence(
int arr[], int n)
{
int count = 0;
bool prime[N + 1];
memset(prime, true, sizeof(prime));
SieveOfEratosthenes(prime, N);
for (int i = 0; i < n; i++) {
// Calculate sum of digits
// of current array element
int res = digitSum(arr[i]);
// If sum of digits
// equal to 1
if (res == 1) {
continue;
}
// If sum of digits is
// a prime
if (!prime[res]) {
count++;
}
}
cout << count << endl;
}
// Driver Code
int main()
{
int arr[] = { 13, 55, 7, 3, 5, 1,
10, 21, 233, 144, 89 };
int n = sizeof(arr)
/ sizeof(arr[0]);
// Function call
longestCompositeDigitSumSubsequence(
arr, n);
return 0;
} Java
// Java implenetation of the
// above approach
import java.util.*;
class GFG{
static int N = 100005;
// Function to generate prime numbers
// using Sieve of Eratosthenes
static void SieveOfEratosthenes(boolean []prime,
int p_size)
{
// Set 0 and 1 as non-prime
prime[0] = false;
prime[1] = false;
for(int p = 2; p * p <= p_size; p++)
{
// If p is a prime
if (prime[p])
{
// Set all multiples of p as non-prime
for(int i = p * 2; i <= p_size; i += p)
prime[i] = false;
}
}
}
// Function to find the digit sum
// of a given number
static int digitSum(int number)
{
// Stores the sum of digits
int sum = 0;
while (number > 0)
{
// Extract digits and
// add to the sum
sum += (number % 10);
number /= 10;
}
// Return the sum
// of the digits
return sum;
}
// Function to find the longest subsequence
// with sum of digits of each element equal
// to a composite number
static void longestCompositeDigitSumSubsequence(int []arr,
int n)
{
int count = 0;
boolean []prime = new boolean[N + 1];
for(int i = 0; i <= N; i++)
prime[i] = true;
SieveOfEratosthenes(prime, N);
for(int i = 0; i < n; i++)
{
// Calculate sum of digits
// of current array element
int res = digitSum(arr[i]);
// If sum of digits
// equal to 1
if (res == 1)
{
continue;
}
// If sum of digits is
// a prime
if (prime[res] == false)
{
count++;
}
}
System.out.println(count);
}
// Driver Code
public static void main(String[] args)
{
int []arr = { 13, 55, 7, 3, 5, 1,
10, 21, 233, 144, 89 };
int n = arr.length;
// Function call
longestCompositeDigitSumSubsequence(arr, n);
}
}
// This code is contributed by Stream_CipherPython3
# Python3 implenetation of the
# above approach
N = 100005
# Function to generate prime numbers
# using Sieve of Eratosthenes
def SieveOfEratosthenes(prime,
p_size):
# Set 0 and 1 as non-prime
prime[0] = False
prime[1] = False
p = 2
while p * p <= p_size:
# If p is a prime
if (prime[p]):
# Set all multiples of
# p as non-prime
for i in range(p * 2,
p_size + 1, p):
prime[i] = False
p += 1
# Function to find
# the digit sum of
# a given number
def digitSum(number):
# Stores the sum
# of digits
sum = 0
while (number > 0):
# Extract digits and
# add to the sum
sum += (number % 10)
number //= 10
# Return the sum
# of the digits
return sum
# Function to find the longest subsequence
# with sum of digits of each element equal
# to a composite number
def longestCompositeDigitSumSubsequence(arr, n):
count = 0
prime = [True] * (N + 1)
SieveOfEratosthenes(prime, N)
for i in range(n):
# Calculate sum of digits
# of current array element
res = digitSum(arr[i])
# If sum of digits
# equal to 1
if (res == 1):
continue
# If sum of digits is
# a prime
if (not prime[res]):
count += 1
print (count)
# Driver Code
if __name__ == "__main__":
arr = [13, 55, 7, 3, 5, 1,
10, 21, 233, 144, 89]
n = len(arr)
# Function call
longestCompositeDigitSumSubsequence(arr, n)
# This code is contributed by ChitranayalC#
// C# implenetation of the
// above approach
using System.Collections.Generic;
using System;
class GFG{
static int N = 100005;
// Function to generate prime numbers
// using Sieve of Eratosthenes
static void SieveOfEratosthenes(bool []prime,
int p_size)
{
// Set 0 and 1 as non-prime
prime[0] = false;
prime[1] = false;
for(int p = 2; p * p <= p_size; p++)
{
// If p is a prime
if (prime[p])
{
// Set all multiples of p as non-prime
for(int i = p * 2; i <= p_size; i += p)
prime[i] = false;
}
}
}
// Function to find the digit sum
// of a given number
static int digitSum(int number)
{
// Stores the sum of digits
int sum = 0;
while (number > 0)
{
// Extract digits and
// add to the sum
sum += (number % 10);
number /= 10;
}
// Return the sum
// of the digits
return sum;
}
// Function to find the longest subsequence
// with sum of digits of each element equal
// to a composite number
static void longestCompositeDigitSumSubsequence(int []arr,
int n)
{
int count = 0;
bool []prime = new bool[N + 1];
for(int i = 0; i <= N; i++)
prime[i] = true;
SieveOfEratosthenes(prime, N);
for(int i = 0; i < n; i++)
{
// Calculate sum of digits
// of current array element
int res = digitSum(arr[i]);
// If sum of digits
// equal to 1
if (res == 1)
{
continue;
}
// If sum of digits is
// a prime
if (prime[res] == false)
{
count++;
}
}
Console.WriteLine(count);
}
// Driver Code
public static void Main()
{
int []arr = { 13, 55, 7, 3, 5, 1,
10, 21, 233, 144, 89 };
int n = arr.Length;
// Function call
longestCompositeDigitSumSubsequence(arr, n);
}
}
// This code is contributed by Stream_Cipher输出：
4
时间复杂度：O(N)
辅助空间： O(log 10 (maxm))，其中maxm是maxm数组元素