打印 N 加上质数形成的最近质数
原文:https://www . geesforgeks . org/print-最接近的质数-通过将质数加到-n 形成/
给定一个数 n，任务是如果这个数不是素数，则打印最近的素数，方法是从 2 开始依次添加素数，使其成为素数。 例:
输入: N = 8 输出: 13 8 不是素数，所以加上第一个素数得到 10 10 不是素数，因此加上第二个素数，即 3 得到 13，即素数。 输入: N = 45 输出: 47
逼近使用厄拉多塞的筛，在is prime【】列表中用 1 标记质数索引，并将所有质数存储在一个列表prime【】中。继续把质数按顺序加到 N 上，直到它变成质数。 以下是上述方法的实施:
C++
// C++ program to print the
// nearest prime number by
// sequentially adding the
// prime numbers
#include<bits/stdc++.h>
using namespace std;
// Function to store prime
// numbers using prime sieve
void prime_sieve(int MAX, vector<int> &isprime,
vector<int> &prime)
{
// iterate for all
// the numbers
int i = 2;
while (i * i <= MAX)
{
// If prime[p] is not changed,
// then it is a prime
if (isprime[i] == 1)
{
// append the prime
// to the list
prime.push_back(i);
// Update all multiples of p
for (int j = i * 2; j < MAX; j += i)
{
isprime[j] = 0;
}
}
i += 1;
}
}
// Function to print
// the nearest prime
int printNearest(int N)
{
int MAX = 1e6;
// store all the
// index with 1
vector<int> isprime(MAX, 1);
// 0 and 1 are not prime
isprime[0] = isprime[1] = 0;
// list to store
// prime numbers
vector<int> prime;
// variable to
// add primes
int i = 0;
// call the sieve function
prime_sieve(MAX, isprime, prime);
// Keep on adding prime
// numbers till the nearest
// prime number is achieved
while (!isprime[N])
{
N += prime[i];
i += 1;
}
// return the
// nearest prime
return N ;
}
// Driver Code
int main()
{
int N = 8;
printf("%d", printNearest(N));
return 0;
}
// This code is contributed
// by Harshit Saini
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to print the
// nearest prime number by
// sequentially adding the
// prime numbers
import java.util.*;
class GFG
{
// Function to store prime
// numbers using prime sieve
static void prime_sieve(int MAX, int []isprime,
Vector<Integer> prime)
{
// iterate for all
// the numbers
int i = 2;
while (i * i <= MAX)
{
// If prime[p] is not changed,
// then it is a prime
if (isprime[i] == 1)
{
// append the prime
// to the list
prime.add(i);
// Update all multiples of p
for (int j = i * 2;
j < MAX; j += i)
{
isprime[j] = 0;
}
}
i += 1;
}
}
// Function to print
// the nearest prime
static int printNearest(int N)
{
int MAX = (int) 1e6;
// store all the
// index with 1 except 0,1 index
int [] isprime = new int[MAX];
for(int i = 2; i < MAX; i++)
isprime[i] = 1;
// list to store
// prime numbers
Vector<Integer> prime = new Vector<Integer>();
// variable to add primes
int i = 0;
// call the sieve function
prime_sieve(MAX, isprime, prime);
// Keep on adding prime
// numbers till the nearest
// prime number is achieved
while (isprime[N] == 0)
{
N += prime.get(i);
i += 1;
}
// return the
// nearest prime
return N ;
}
// Driver Code
public static void main(String[] args)
{
int N = 8;
System.out.printf("%d", printNearest(N));
}
}
// This code is contributed by Rajput-Ji
Python 3
# Python3 program to print the nearest prime
# number by sequentially adding the prime numbers
# Function to store prime numbers using prime sieve
def prime_sieve(MAX, isprime, prime):
# iterate for all the numbers
i = 2
while (i * i <= MAX):
# If prime[p] is not changed,
# then it is a prime
if (isprime[i] == 1):
# append the prime to the list
prime.append(i)
# Update all multiples of p
for j in range(i * 2, MAX, i):
isprime[j] = 0
i += 1
# Function to print the nearest prime
def printNearest(N):
MAX = 10**6
# store all the index with 1
isprime = [1] * MAX
# 0 and 1 are not prime
isprime[0] = isprime[1] = 0
# list to store prime numbers
prime = []
# variable to add primes
i = 0
# call the sieve function
prime_sieve(MAX, isprime, prime)
# Keep on adding prime numbers
# till the nearest prime number
# is achieved
while not isprime[N]:
N += prime[i]
i += 1
# return the nearest prime
return N
# Driver Code
N = 8
print(printNearest(N))
C
// C# program to print the
// nearest prime number by
// sequentially adding the
// prime numbers
using System;
using System.Collections.Generic;
class GFG
{
// Function to store prime
// numbers using prime sieve
static void prime_sieve(int MAX, int []isprime,
List<int> prime)
{
// iterate for all the numbers
int i = 2;
while (i * i <= MAX)
{
// If prime[p] is not changed,
// then it is a prime
if (isprime[i] == 1)
{
// append the prime to the list
prime.Add(i);
// Update all multiples of p
for (int j = i * 2;
j < MAX; j += i)
{
isprime[j] = 0;
}
}
i += 1;
}
}
// Function to print
// the nearest prime
static int printNearest(int N)
{
int MAX = (int) 1e6;
int i = 0;
// store all the
// index with 1 except 0,1 index
int [] isprime = new int[MAX];
for(i = 2; i < MAX; i++)
isprime[i] = 1;
// list to store
// prime numbers
List<int> prime = new List<int>();
// variable to add primes
i = 0;
// call the sieve function
prime_sieve(MAX, isprime, prime);
// Keep on adding prime
// numbers till the nearest
// prime number is achieved
while (isprime[N] == 0)
{
N += prime[i];
i += 1;
}
// return the
// nearest prime
return N;
}
// Driver Code
public static void Main(String[] args)
{
int N = 8;
Console.Write("{0}", printNearest(N));
}
}
// This code is contributed by Princi Singh
java 描述语言
<script>
// Javascript program to print the
// nearest prime number by
// sequentially adding the
// prime numbers
// Function to store prime
// numbers using prime sieve
function prime_sieve(MAX, isprime, prime)
{
// iterate for all
// the numbers
var i = 2;
while (i * i <= MAX)
{
// If prime[p] is not changed,
// then it is a prime
if (isprime[i] == 1)
{
// append the prime
// to the list
prime.push(i);
// Update all multiples of p
for (var j = i * 2; j < MAX; j += i)
{
isprime[j] = 0;
}
}
i += 1;
}
}
// Function to print
// the nearest prime
function printNearest(N)
{
var MAX = 1e6;
// store all the
// index with 1
var isprime = Array(MAX).fill(1);
// 0 and 1 are not prime
isprime[0] = isprime[1] = 0;
// list to store
// prime numbers
var prime = [];
// variable to
// add primes
var i = 0;
// call the sieve function
prime_sieve(MAX, isprime, prime);
// Keep on adding prime
// numbers till the nearest
// prime number is achieved
while (!isprime[N])
{
N += prime[i];
i += 1;
}
// return the
// nearest prime
return N ;
}
// Driver Code
var N = 8;
document.write( printNearest(N));
// This code is contributed by rrrtnx.
</script>
Output:
13
时间复杂度:O(N * log(logN)) T3】辅助空间: O(N)
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