Algorithm (Greedy)

1. We denote the big matrix as $M$, sidelength as $\ell$ We focus on the first square sub-matrix $A$. Note that if we can put $1$ at $A_{ij},$ then by copy and translation of $A$, $M_{a,b}=1$ for all $a\mod\ell=i$ and $b\mod\ell=j$.
2. Let $\mathcal{C}(i,j)$ be the set of all possible $M_{a,b}$’s to be assigned $1$ when $A_{ij}$ is $1$. Then the solution is then $$\sum_{k=1}^{\texttt{maxOnes}}\texttt{sortedList}\{|\mathcal{C}(i,j)|\}[k].$$
3. This could be solved using a priority queue or a vector. The implementation is standard.

Code

class Solution {
 public:
  int maximumNumberOfOnes(int width, int height, int sideLength, int maxOnes) {

    const auto buildQ = [&](priority_queue<int, std::vector<int>, std::greater<int>> self = {}) {
      for (int r = 0; r < sideLength; ++r)
        for (int c = 0; c < sideLength; ++c) {
          const auto V = (height - 1 - c) / sideLength + 1;
          const auto H = (width - 1 - r) / sideLength + 1;
          self.emplace(V * H);
          if (size(self) > maxOnes)
            self.pop();
        }
      return self;
    };

    const auto solution = [Q = buildQ()](int acc = 0) mutable {
      while (not empty(Q)) {
        acc += Q.top();
        Q.pop();
      }
      return acc;
    }();

    return solution;
  }
};