Change Grid to use vector not string.

This is another optimisation, as it improves memory layout and we are
not using a reference counted string.

On a M1 Macbook Air this brings runtime for solving the 9 cell down to
under 3m30s.  Which is about a 15% performance improvement.

main.cc

@@ -4,7 +4,6 @@
 
 #include <cassert>
 #include <utility>
-#include <string>
 #include <string_view>
 #include <vector>
 #include <iostream>
@@ -44,11 +43,11 @@ struct Grid {
   Grid(int length) : grid_(length * length, '.'), length_(length) {
   }
 
-  Grid(Grid const &other) = default;
+  Grid(Grid const &other) = delete;
 
   Grid(Grid &&other) noexcept = default;
 
-  Grid &operator=(Grid const &other) = default;
+  Grid &operator=(Grid const &other) = delete;
 
   Grid &operator=(Grid &&other) noexcept = default;
 
@@ -113,7 +112,8 @@ struct Grid {
 
   auto output() const {
     for (auto i = 0; i < length_; ++i) {
-      std::cout << grid_.substr(i * length_, length_) << '\n';
+      std::cout <<
+          std::string_view(grid_.data() + i * length_, length_) << '\n';
     }
   }
 
@@ -137,6 +137,7 @@ struct Grid {
       if (grid_[b + y(pos) * length_] != '.') { break; }
       ++b;
     }
+    // Check that this length fits vertically as well.
     auto len = b - x(pos);
     auto ye = std::min(y(pos) + len, length_);
     return ye - y(pos);
@@ -146,15 +147,16 @@ struct Grid {
    *  added.
    */
   auto next_pos(Pos const &pos, int n) const noexcept -> Pos {
-    const auto p = x(pos) + n + y(pos) * length_;
+    auto const b = grid_.begin() + x(pos) + n + y(pos) * length_;
-      const auto next_p = grid_.find('.', p);
+    auto const p = std::find(b, grid_.end(), '.');
-      if (next_p == std::string::npos) {
+    if (p == grid_.end()) {
-        return std::make_pair(0, length_);
+      return std::make_pair(0, length_);
-      }
+    }
-      return std::make_pair(next_p % length_, next_p / length_);
+    auto const v = p - grid_.begin();
+    return std::make_pair(v % length_, v / length_);
   }
 
-  std::string grid_;
+  std::vector<char> grid_;
   int length_;
 };
 
@@ -174,6 +176,7 @@ auto find_solution_impl(Grid &grid, int n, Pos const &pos, Avail &avail_sqs) ->
    * If we know a square of side length N will fit then we know a square of side length
    * N - 1 will fit.
    */
+  assert(x(pos) + grid.largest_square(pos, n) <= grid.length());
   for (auto idx = grid.largest_square(pos, n); idx != 0; --idx) {
     if (avail_sqs[idx] == 0) { continue; }