feat(cses): more dp

cses/dynamic-programming/array-description.cc

@@ -0,0 +1,114 @@
+#include <bits/stdc++.h>  // {{{
+
+// https://codeforces.com/blog/entry/96344
+
+#pragma GCC optimize("O2,unroll-loops")
+#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
+
+using namespace std;
+
+using i32 = int32_t;
+using u32 = uint32_t;
+using i64 = int64_t;
+using u64 = uint64_t;
+using d64 = double;
+using d128 = long double;
+template <typename T>
+using vec = std::vector<T>;
+template <typename T, size_t N>
+using arr = std::array<T, N>;
+template <typename T1, typename T2>
+using pai = std::pair<T1, T2>;
+
+template <typename T>
+constexpr T MIN = std::numeric_limits<T>::min();
+
+template <typename T>
+constexpr T MAX = std::numeric_limits<T>::max();
+
+template <typename T>
+[[nodiscard]] static T sc(auto&& x) {
+  return static_cast<T>(x);
+}
+
+template <typename T>
+[[nodiscard]] static T sz(auto&& x) {
+  return static_cast<T>(x.size());
+}
+
+static void NO() {
+  std::cout << "NO\n";
+}
+
+static void YES() {
+  std::cout << "YES\n";
+}
+
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+
+#ifdef LOCAL
+#define db(...) std::print(__VA_ARGS__)
+#define dbln(...) std::println(__VA_ARGS__)
+#else
+#define db(...)
+#define dbln(...)
+#endif
+//  }}}
+
+static constexpr u64 MOD = 1e9 + 7;
+
+void solve() {
+  u32 n, m;
+  cin >> n >> m;
+  vec<i64> a(n);
+  for (auto& e : a)
+    cin >> e;
+
+  vec<i64> prev(m + 1, 0);
+  if (a[0] != 0) {
+    prev[a[0]] = 1;
+  } else {
+    for (u32 i = 1; i <= m; ++i)
+      prev[i] = 1;
+  }
+
+  for (u32 i = 2; i <= n; ++i) {
+    vec<i64> cur(m + 1, 0);
+    if (a[i - 1] == 0) {
+      for (u32 x = 1; x <= m; ++x) {
+        for (i64 delta = -1; delta <= 1; ++delta) {
+          if (1 <= x + delta && x + delta <= m)
+            cur[x] = (cur[x] + prev[x + delta]) % MOD;
+        }
+      }
+    } else {
+      for (i64 delta = -1; delta <= 1; ++delta) {
+        if (1 <= a[i - 1] + delta && a[i - 1] + delta <= m)
+          cur[a[i - 1]] = (cur[a[i - 1]] + prev[a[i - 1] + delta]) % MOD;
+      }
+    }
+    prev = cur;
+  }
+
+  i64 ans = 0;
+  for (auto e : prev) {
+    ans = (ans + e) % MOD;
+  }
+  cout << ans << '\n';
+}
+
+int main() {  // {{{
+  cin.tie(nullptr)->sync_with_stdio(false);
+  cin.exceptions(cin.failbit);
+
+  int tc = 1;
+  // cin >> tc;
+
+  for (int t = 0; t < tc; ++t) {
+    solve();
+  }
+
+  return 0;
+}
+// }}}