Why I got runtime error while I am using local N instead of global N?

Question

In this code when I use N is globally it works but using the same value as a local variable shows a runtime error. But I can not fix the problem. Actually, why should I use this N globally?

void solve()
{
    long long n;
    cin >> n;

    long long N=210;   /// But when I use this locally it shows runtime error
    long a[N];
    long long dp[N][N];

    for(int i=1; i<=n; i++){
        cin >> a[i];
    }

    sort(a, a+n+1);

    dp[0][0]=0;

    for(int i=1; i<=n; i++)
    {
        dp[i][0]=1e9;

        for(ll j=1; j<=2*n; j++){
            dp[i][j]=min(dp[i][j-1], dp[i-1][j-1]+abs(a[i]-j));
        }
    }

    long long ans=dp[n][2*n];

    cout << ans << '\n';
}

Answer 1

long long N;   /// But when I use this locally it shows runtime error
long a[N];

There are two problems with this:

1. N is uninitialised. The behaviour of the program is undefined since you read the value of an uninitialised object.
2. N is not compile time constant. It cannot be used as the size of an array variable. The program is ill-formed.

If N was global, then it would be zero-initialised, so the first problem would be resolved. However, that would introduce another problem that the size would be zero which isn't allowed for array variables. The non-constant problem also remains.

To properly solve 1. initialise the variable before attempting to use its value.

To properly solve 2. either use compile time constant size or create a dynamic array. The simplest way to do the latter is to use std::vector. There's no need to use a global variable:

std::size_t N;
std::cin >> N;
std::vector<long> a(N);

---

long a[N];
// ...
for(int i=1; i<=n; i++){
    cin >> a[i];
}
sort(a, a+n+1);

There's a potential problem here. If N is less than or equal to n, then this will overflow a and the behaviour of the program will be undefined.

Furthermore, you never initialised a[0] so when std::sort reads it, the behaviour of the program will be undefined.

I recommend using range-based loops to avoid overflows:

for(int& element : a) {
    std::cin >> element;
}
std::ranges::sort(a);