Codeforces: 2066D2

Club of Young Aircraft Builders (hard version)

Author: Macesuted

Codeforces/2066D2.cpp

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+/**
+ * @file 2066D2.cpp
+ * @author Macesuted ([email protected])
+ * @date 2025-02-17
+ *
+ * @copyright Copyright (c) 2025
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#ifndef LOCAL
+#define endl '\n'
+#endif
+
+bool mem1;
+
+#define maxn 105
+#define maxm 10005
+#define mod 1'000'000'007
+
+int a[maxm], pre[maxm], cnt[maxn], lst[maxn], f[maxn][maxm];
+int64_t fac[maxm], ifac[maxm];
+
+int64_t qpow(int64_t a, int64_t x) {
+    int64_t ans = 1;
+    while (x) {
+        if (x & 1) ans = ans * a % mod;
+        a = a * a % mod, x >>= 1;
+    }
+    return ans;
+}
+int64_t inv(int64_t a) { return qpow(a, mod - 2); }
+int64_t C(int n, int m) { return fac[n] * ifac[m] % mod * ifac[n - m] % mod; }
+
+void solve(void) {
+    int n, c, m;
+    cin >> n >> c >> m;
+
+    for (int i = 1; i <= n; i++) cnt[i] = lst[i] = 0;
+    for (int i = 1; i <= m; i++) {
+        cin >> a[i];
+        if (a[i]) cnt[a[i]]++, lst[a[i]] = i;
+    }
+
+    if (cnt[n] > c) return cout << 0 << endl, void();
+
+    for (int i = 1; i <= n; i++)
+        for (int j = 0; j <= m; j++) f[i][j] = 0;
+
+    f[0][0] = 1;
+    for (int i = 1; i <= n; i++) {
+        for (int j = 1; j <= m; j++) pre[j] = pre[j - 1] + (a[j] <= i);
+        for (int j = 0; j <= m; j++)
+            if (f[i - 1][j])
+                for (int k = (i == n ? c : cnt[i]); k <= c; k++)
+                    if (lst[i] <= c + j && j + k <= m && k <= pre[min(m, c + j)] - j)
+                        f[i][j + k] = (f[i][j + k] + f[i - 1][j] * C(pre[min(m, c + j)] - j - cnt[i], k - cnt[i])) % mod;
+    }
+
+    // for (int i = 1; i <= n; i++) {
+    //     for (int j = 0; j <= m; j++) cerr << f[i][j] << ' ';
+    //     cerr << endl;
+    // }
+
+    cout << f[n][m] << endl;
+
+    return;
+}
+
+bool mem2;
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr);
+#ifdef LOCAL
+    cerr << "Memory Cost: " << abs(&mem1 - &mem2) / 1024. / 1024. << "MB" << endl;
+#endif
+
+    fac[0] = ifac[0] = 1;
+    for (int i = 1; i < maxm; i++) fac[i] = fac[i - 1] * i % mod;
+    ifac[maxm - 1] = inv(fac[maxm - 1]);
+    for (int i = maxm - 2; i; i--) ifac[i] = ifac[i + 1] * (i + 1) % mod;
+
+    int _ = 1;
+    cin >> _;
+    while (_--) solve();
+
+#ifdef LOCAL
+    cerr << "Time Cost: " << clock() * 1000. / CLOCKS_PER_SEC << "MS" << endl;
+#endif
+    return 0;
+}