如何从 c++ 中的数组中获取最长的素数序列

Question

I'm trying to get the longest(largest) sequence of consecutive prime numbers from an array..

On first test with 10 elements in the array works, but when i tried with 15 elements like: 3, 5, 7, 8, 9, 11, 13, 17, 19, 20, 23, 29, 31, 37, 41 it spit out 4, which is incorrect.

#include <iostream>
using namespace std;

int main()
{
    int bar[100];
    int x, j = 0;

    int maxseq = 0;
    int longestseqstart = 0;
    cout << "How big is the array? =";
    cin >> x;
    for (int i = 0; i < x; i++) {
        cout << "bar[" << i << "]=";
        cin >> bar[i];
    }
    for (int i = 1; i < x - 1; i = j) {
        int startseq = i;
        int seq = 0;

        j = i + 1;
        bool prim = true;
        int a = bar[i];
        for (int d = 2; d <= a / 2; d++) {
            if (a % d == 0) {
                prim = false;
            }
        }
        while (j < x && prim) {
            seq++;
            if (seq > maxseq) {
                maxseq = seq;
                longestseqstart = i;
            }
            int a = bar[j];
            for (int d = 2; d <= a / 2; d++) {
                if (a % d == 0) {
                    prim = false;
                }
            }
            j++;
        }
    }

    cout << "The longest sequence is: ";
    cout << maxseq;

    return 0;
}

Answer 1

You are checking twice for prime numbers and you are using a nested loop. That's not necessary. It's enough to read all numbers, check each number, increment the count if it's a prime number and store the maximum sequence length.

#include <iostream>
#include <vector>
using namespace std;

bool isPrime(int a) {
    bool prim = true;
    for (int d = 2; d*d <= a; ++d) {
        if (a % d == 0) {
            prim = false;
        }
    }
    return prim;
}

int main()
{
    int x;

    int longestseqstart = 0;
    cout << "How big is the array? =";
    cin >> x;
    std::vector<int> bar(x);
    for (int i = 0; i < x; i++) {
        cout << "bar[" << i << "]=";
        cin >> bar[i];
    }

    unsigned int count = 0;
    unsigned int maxseq = 0;
    for (const auto &el : bar) {
        if (isPrime(el)) {
            ++count;
            if (count > maxseq) maxseq = count;
        } else count = 0;
    }
    cout << "The longest sequence is: ";
    cout << maxseq;

    return 0;
}

Of course you can avoid the usage of std::vector and functions with

#include <iostream>
using namespace std;

int main()
{
    int x;

    int longestseqstart = 0;
    cout << "How big is the array? =";
    cin >> x;
    int bar[100];
    for (int i = 0; i < x; i++) {
        cout << "bar[" << i << "]=";
        cin >> bar[i];
    }

    unsigned int count = 0;
    unsigned int maxseq = 0;
    for (unsigned int i = 0; i < x; ++i) {
        int a = bar[i];
        bool prim = true;
        for (int d = 2; d*d <= a; ++d) {
            if (a % d == 0) {
                prim = false;
            }
        }
        if (prim) {
            ++count;
            if (count > maxseq) maxseq = count;
        } else count = 0;
    }
    cout << "The longest sequence is: ";
    cout << maxseq;

    return 0;
}

Answer 2

The algorithm looks basically OK. The issue is mostly one of organization: the way the inner loop block is set up means that a run of primes will be short by 1 because the longest sequence is only updated at the beginning of the inner loop, missing the final prime.

A couple of minimal failing examples are:

How big is the array? =1
bar[0]=13
The longest sequence is: 0

How big is the array? =2
bar[0]=5
bar[1]=6
The longest sequence is: 0

Note that there's a repeated prime check in two places. This should not be. If we move all of the prime logic into the loop and test for a new longest sequence only after finishing the entire run, we'll have a clear, accurate algorithm:

#include <iostream>

int is_prime(int n) {
    for (int i = 2; i <= n / 2; i++) {
        if (n % i == 0) {
            return false;
        }
    }

    return true;
}

int main() {
    int nums[100];
    int n;
    std::cout << "How big is the array? =";
    std::cin >> n;

    for (int i = 0; i < n; i++) {
        std::cout << "nums[" << i << "]=";
        std::cin >> nums[i];
    }

    int longest = 0;

    for (int i = 0, start = 0; i < n; i++) {
        for (start = i; i < n && is_prime(nums[i]); i++);

        longest = std::max(longest, i - start);
    }

    std::cout << "The longest sequence is: " << longest;
    return 0;
}

In this rewrite I...

• avoided using namespace std; .
• removed unnecessary/confusing variables.
• used clear variable names ( bar should only be used in example code when the name doesn't matter).
• moved is_prime to its own function.

But there are outstanding issues with this code. It should...

• use a vector instead of an array. As it stands, it's vulnerable to a buffer overflow attack should the user specify an array length > 100.
• use a faster method of finding primes . We only need to check up to the square root of the number and can skip a lot of numbers such as even numbers after 2. I suspect this is incidental to this exercise but it's worth mentioning.
• move the longest_prime_sequence to a separate function (and possibly user input gathering as well).

Answer 3

I would write the program the following way

#include <iostream>
#include <iterator>
#include <algorithm>

bool is_prime( unsigned int n )
{
    bool prime = n % 2 == 0 ? n == 2 : n != 1;

    for ( unsigned int i = 3; prime && i <= n / i; i += 2 )
    {
        prime = n % i != 0;
    }

    return prime;
}


int main() 
{
    unsigned int a[] =  { 3, 5, 7, 8, 9, 11, 13, 17, 19, 20, 23, 29, 31, 37, 41 };
    const size_t N = sizeof( a ) / sizeof( *a );

    size_t maxseq = 0;

    for ( auto current = std::find_if( a, a + N, is_prime ); 
          current != a + N;
          current = std::find_if( current, a + N, is_prime ) )
    {
        auto first = current;
        current = std::find_if_not( current, a + N, is_prime );

        size_t n = std::distance( first, current );

        if ( maxseq < n ) maxseq = n;
    }

    std::cout << "The longest sequence is: " <<  maxseq << '\n';

    return 0;
}

The program output is

The longest sequence is: 5

I did not use generic functions std::begin( a ) and std::end( a ) because in your program the array can contain less actual elements than the array dimension.

If you do not know yet standard C++ algorithms then the program can be defined the following way

#include <iostream>

bool is_prime( unsigned int n )
{
    bool prime = n % 2 == 0 ? n == 2 : n != 1;

    for ( unsigned int i = 3; prime && i <= n / i; i += 2 )
    {
        prime = n % i != 0;
    }

    return prime;
}


int main() 
{
    unsigned int a[] =  { 3, 5, 7, 8, 9, 11, 13, 17, 19, 20, 23, 29, 31, 37, 41 };
    const size_t N = sizeof( a ) / sizeof( *a );

    size_t maxseq = 0;
    size_t n = 0;

    for ( size_t i = 0; i < N; i++ )
    {
        bool prime = a[i] % 2 == 0 ? a[i] == 2 : a[i] != 1;

        for ( unsigned int j = 3; prime && j <= a[i] / j; j += 2 )
        {
            prime = a[i] % j != 0;
        }

        if ( prime )
        {
            if ( maxseq < ++n ) maxseq = n;
        }
        else
        {
            n = 0;
        }
    }

    std::cout << "The longest sequence is: " <<  maxseq << '\n';

    return 0;
}

The program output is the same as above

The longest sequence is: 5

As for your program then this loop

for (int i = 1; i < x - 1; i = j) {

skips the first element of the array that is bar[0] .

And due to this statement

j = i + 1;

the calculated value of seq one less than it should be because you do not take into account that bar[i] is already prime.

Set initially seq equal to 1.

int seq = 1;

Moreover you incorrectly are determining prime numbers. For example according to your algorithm 1 is prime.

Answer 4

Convert the array to a Boolean array and find longest length. Try this snippet(not optimized):

bool is_prime(int n) {
    for (int i = 2; i < n; i++) {
        if (n%i == 0) return false;
    }
    return true;
}

int main() {
    //Input
    unsigned int bar[15] = { 3, 5, 7, 8, 9, 11, 13, 17, 19, 20, 23, 29, 31, 37, 41 };
    // Convert input to boolean array
    bool boo[15];
    for (int i = 0; i < 15; i++) {
        boo[i] = is_prime(bar[i]);
    }
    //Check the longest boolean array
    int longest = 0;
    for (int i = 0; i < 15; i++) {
        int count = 0;

        while (boo[i + count] && (i+ count) <15) {
            count++;            
        }
        if (longest < count) longest = count;

    }
    //Output
    cout << longest;

    return 0;
}