The two declarations you've provided represent two different ways of organizing a 2D array.

vector<vector<int>> dp(n, vector<int>((1 << n), -1));

In this declaration:

dp is a 2D vector with n rows.
Each row is a vector of integers initialized to -1.
Each row has 1 << n columns, i.e., 2 raised to the power of n.
This structure is suitable for problems where you want to store information for each combination of n elements. For example, if you're solving a problem related to subsets of n elements, you can use this structure to store information about each subset.

vector<vector<int>> dp((1 << n), vector<int>(n, -1));

In this declaration:

dp is a 2D vector with 1 << n rows.
Each row is a vector of integers initialized to -1.
Each row has n columns.
This structure is suitable for problems where you want to store information for each element in a set of size 1 << n. For example, if you're solving a problem related to permutations or combinations of n elements, you can use this structure to store information about each individual permutation or combination.

In summary, the difference lies in the organization of rows and columns. The first declaration organizes the data by subsets, while the second organizes it by permutations/combinations. Which one to use depends on the specific problem you're trying to solve.

Array access out of bounds: If your code tries to access elements beyond the allocated memory bounds of the array, it can lead to undefined behavior or a segmentation fault. This is more likely to happen if you mistakenly access elements outside the valid range of indices.

even GPT knows about it

vector<vector>dp(n,vector(**(**1<<n,-1**)**)); remove those brackets

Actually, like what the above commenter has said, you declare the vector in the first sol as vector<vector<int>>dp(n,vector<int>((1<<n,-1)));, instead of vector<vector<int>>dp(n,vector<int>((1<<n),-1));. While the difference here is subtle, it is still a fatal error, as you have accidentally declared vector<int>((1<<n,-1)); which makes the compiler very confused and essentially terminate themselves. Why? Because the first argument you put is not an integer (in fact, it is not any STL data structure at all).

Moral of the story: watch out for bracket placement, as they are the reason some codes basically gives WA or RTE.