2023 Day 12 Part 2 reworked.

Let's try to assign ### to positions and validate earlier.

2023/puzzle-12-02.cc

@@ -1,6 +1,8 @@
+#include <cassert>
 #include <cstdint>
 #include <cstdlib>
 #include <iostream>
+#include <numeric>
 #include <string>
 #include <string_view>
 #include <utility>
@@ -29,75 +31,79 @@ auto split(std::string_view line) -> std::pair<std::string_view, UIntVec>
   return std::make_pair(pattern, nums);
 }
 
-[[nodiscard]] auto validate_subpattern(std::string_view pattern, std::string_view start,
-                                       UInt num_hashs, UInt gaps) -> bool
+std::unordered_map<std::string, UInt> counts;
+
+auto valid_sequences(std::string_view pattern, UIntVec::const_iterator begin,
+                     UIntVec::const_iterator end) -> UInt;
+
+auto generate_pattern(std::string pattern, UIntVec::const_iterator begin,
+                      UIntVec::const_iterator end) -> UInt
 {
-  if (pattern.size() < start.size()) {
-    return false;
-  }
-  UInt hash_count{0};
-
-  auto pit{pattern.begin()};
-  for (auto sit{start.begin()}; sit != start.end(); ++pit, ++sit) {
-    if (*sit == '#') { ++hash_count; }
-    if (*pit != '?' && *pit != *sit) {
-      return false;
-    }
-  }
-
-  for (; pit != pattern.end(); ++pit) {
-    if (*pit == '#') { ++hash_count; }
-  }
-
-  if (num_hashs < hash_count) {
-    return false;
-  }
-  if (start.size() + (num_hashs - hash_count) + gaps > pattern.size()) {
-    return false;
-  }
-
-  return true;
-}
-
-void generate_pattern(std::string start, UIntVec::const_iterator it, UIntVec::const_iterator end,
-                      std::string_view pattern, UInt hash_count, UInt& count)
-{
-  auto pos = start.size();
-  auto num_hashs = *it++;
-  start += std::string(num_hashs, '#');
-
-  if (it == end) {
-    if (start.size() <= pattern.size()) {
-      start.resize(pattern.size(), '.');
-      if (validate_subpattern(pattern.substr(pos), start.substr(pos), num_hashs, 0)) {
-        ++count;
-        if (count % 1'000'000 == 0) {
-          std::cout << start << '\n';
-        }
-      }
-    }
-    return;
-  }
-
-  start += '.';
-  while (validate_subpattern(pattern.substr(pos), start.substr(pos), hash_count, end - it - 1)) {
-    generate_pattern(start, it, end, pattern, hash_count - num_hashs, count);
-    start += '.';
-  }
-}
-
-auto valid_sequences(std::string_view pattern, UIntVec const& nums) -> UInt
-{
-  UInt count{0};
-  UInt hash_count{0};
-  for (auto num : nums) { hash_count += num; }
-  std::string start;
-  while (validate_subpattern(pattern, start, hash_count, nums.size() - 1)) {
-    generate_pattern(start, nums.begin(), nums.end(), pattern, hash_count, count);
-    start += '.';
+  while (begin != end) {
+    if (pattern.empty()) {
+      // We still have ###s to add but nowhere to put them - this isn't a match.
+      return 0;
     }
 
+    if (pattern[0] == '?') {
+      // We don't know what the first character is so let's try both options recursively.
+      auto new_pattern{pattern};
+      new_pattern[0] = '.';
+      auto count = valid_sequences(new_pattern, begin, end);
+      new_pattern[0] = '#';
+      count += valid_sequences(new_pattern, begin, end);
       return count;
+    }
+
+    if (pattern[0] == '.') {
+      // If the pattern begins with a '.' then we just skip over it.
+      pattern = pattern.substr(1);
+      continue;
+    }
+
+    /* We must have a '#' now. */
+    assert(pattern[0] == '#');
+
+    if (pattern.size() < *begin) {
+      // Not enough space.
+      return 0;
+    }
+
+    for (std::size_t count = 0; count < *begin; ++count) {
+      // Check for dots.
+      if (pattern[count] == '.') { return 0; }
+    }
+
+    // Move along the pattern.
+    pattern = pattern.substr(*begin++);
+
+    if (begin != end) {
+      if (pattern.empty()) { return 0; }
+      if (pattern[0] == '#') { return 0; }
+      pattern = pattern.substr(1);
+    }
+  }
+
+  return pattern.find('#') == std::string_view::npos;
+}
+
+auto valid_sequences(std::string_view pattern, UIntVec::const_iterator begin,
+                     UIntVec::const_iterator end) -> UInt
+{
+  std::string hash = std::string(pattern);
+  for (auto it{begin}; it != end; ++it) {
+    hash += ',';
+    hash += std::to_string(*it);
+  }
+
+  auto it = counts.find(hash);
+  if (it == counts.end()) {
+    bool success;
+    std::tie(it, success) = counts.insert(
+      {hash, generate_pattern(std::string(pattern), begin, end)});
+  }
+
+  return it->second;
 }
 
 auto main() -> int try {
@@ -115,7 +121,7 @@ auto main() -> int try {
       unfolded_nums.insert(unfolded_nums.begin(), nums.begin(), nums.end());
     }
 
-    line_count += valid_sequences(unfolded_pattern, unfolded_nums);
+    line_count += valid_sequences(unfolded_pattern, unfolded_nums.begin(), unfolded_nums.end());
     std::cout << line << ": " << line_count << '\n';
     count += line_count;
   }