Why am I getting "unknown signal 11" with this knapsack problem solver? - c++

Question

Task
Given n gold bars, find the maximum weight of gold that fits into bag of capacity W
Input
first line contains the capacity W of the knapsack and the number n of bars of gold. The next line contains n integers
Output
The max weight of gold that fits into a knapsack of capacity W.
Constraints
1 <= W <= 10000; 1<= n <= 300; 0 <= w0, w1, w2, ... , w(n-1) <= 100000
Code
#include <iostream>
#include <vector>
using std::vector;
int optimal_weight(int W, vector<int> w) {
int n = w.size() + 1;
int wt = W + 1;
int array [n][wt];
int val = 0;
for(int i = 0; i < wt; i++) array [0][i] = 0;
for(int i = 0; i < n; i++) array [i][0] = 0;
for(int i = 1; i< n; i++) {
for(int j = 1; j < wt; j++ ){
array[i][j] = array [i-1][j];
if (w[i-1] <= j) {
val = array[i-1][j - w[i-1]] + w[i-1];
if(array[i][j] < val) array[i][j] = val;
}
}
}
//printing the grid
// for(int i=0; i < n; i++) {
// for(int j=0; j < wt; j++) {
// cout<<array[i][j]<<" ";
// }
// cout<<endl;
// }
// cout<<endl;
return array [n-1][wt-1];
}
int main() {
int n, W;
std::cin >> W >> n;
vector<int> w(n);
for (int i = 0; i < n; i++) {
std::cin >> w[i];
}
std::cout << optimal_weight(W, w) << '\n';
}
The above code works fine for smaller inputs, but gives an unknown signal 11 error on the platform I wish to submit to. My best guess is of a possible segmentation fault, but I have been unable to debug it since quite some time now. Any help is much appreciated!

Answer 1

First note that your code doesn't work. That is, it doesn't compile when you adhere strictly to the C++ language standard, as C++ does not support variable-length arrays. (as noted by #Evg in a comment; some compilers offer this as an extension.)
The main reason for excluding those from C++ is probably why you're experiencing issues for larger problem sizes: the danger of stack overflows, the namesake of this website (as noted by #huseyinturgulbuyukisik in a comment). Variable-length arrays are allocated on the stack, whose size is limited. When you exceed it, you might attempt to write to a segment of memory that is not allocated to your process, triggering Linux signal 11, also known as SIGSEGV - the segmentation violation signal.
Instead of stack-based allocation, you should allocate your memory on the heap. A straightforward way to do so would be using the std::vector container (whose default allocator does indeed allocate on the heap). Thus, you would write:
std::vector<int> vec(n * wt);
and instead of array[i][j] you'd use vec[i * wt + j].
Now, this is not as convenient as using array[x][y]; for the extra convenience you can, for example, write a helper lambda, to access individual elements, e.g.
auto array_element = [&vec, wt](int x, int y) { return vec[x * wt + y]; }
with this lambda function available, you can now write statements such as array_element(i,j) = array_element(i-1,j);
or use a multi-dimensional container (std::vector<std::vector<int>> would work but it's ugly and wasteful IMHO; unfortunately, the standard library doesn't have a single-allocation multi-dimensional equivalent of that).
Other suggestions, not regarding a solution to your signal 11 issue:
Use more descriptive variable names, e.g. weight instead of wt and capacity instead of W. I'd also considersub_solutions_table or solutions_table instead of array, and might also rename i and j according to the semantics of the dynamic solution table.
You never actually need more than 2 rows of the solutions table; why not just allocate one row for the current iteration and one row for the previous iteration, and have appropriate pointers switch between them?

Answer 2

Replace
vector< vector< int> > k(n + 1,vector< int>(W + 1));
with
int array[n][w];