P3226 [HNOI2012]集合选数

https://www.luogu.com.cn/record/102434789

Luogu/P3226/P3226.cpp

@@ -0,0 +1,76 @@
+#include <iostream>
+#include <algorithm>
+#include <cstring>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e5 + 5,
+          M = 20;
+const int mod = 1e9 + 1;
+
+int n, g[M][M], w[M], f[2][(1 << M) + 5],
+    ans = 1;
+bool vis[N];
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n;
+
+    for (int x = 1; x <= n; x++) {
+        if (vis[x]) continue;
+
+        // === Build ===
+
+        int height = 0,
+            width = 0;
+
+        for (int i = x; i <= n; i *= 2) {
+            height++;
+
+            w[height] = 0;
+
+            for (int j = i; j <= n; j *= 3) {
+                vis[j] = true;
+                w[height]++;
+            }
+
+            width = std::max(width, w[height]);
+        }
+
+        // === DP ===
+
+        f[0][0] = 1;
+
+        for (int i = 1, k = 1; i <= height; i++, k ^= 1) {
+            for (int s = 0; s < 1 << width; s++) {
+                f[k][s] = 0;
+            }
+
+            for (int s = 0; s < 1 << w[i]; s++) {
+                if ((s & (s << 1)) == 0) {
+                    for (int t = 0; t < 1 << w[i - 1]; t++) {
+                        if ((s & t) == 0 && (t & (t << 1)) == 0) {
+                            f[k][s] = (f[k][s] + f[k ^ 1][t]) % mod;
+                        }
+                    }
+                }
+            }
+        }
+
+        int res = 0;
+
+        for (int s = 0; s < 1 << width; s++) {
+            res = (res + f[height & 1][s]) % mod;
+        }
+
+        ans = static_cast<long long>(ans) * res % mod;
+    }
+
+    cout << ans << endl;
+
+    return 0;
+}