#10232. 「一本通 6.6 练习 3」车的放置

https://loj.ac/s/1643806

LibreOJ/10232/10232.cpp

@@ -0,0 +1,49 @@
+#include <iostream>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 2005;
+const int mod = 1e5 + 3;
+
+int a, b, c, d, k, fac[N], inv[N], fac_inv[N], ans;
+
+inline int C(int n, int m) {
+    return static_cast<long long>(fac[n]) * fac_inv[m] % mod * fac_inv[n - m] % mod;
+}
+
+int f(int n, int m, int k) {
+    if (k > n || k > m) return 0;
+    return static_cast<long long>(C(n, k)) * C(m, k) % mod * fac[k] % mod;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    fac[0] = 1;
+    for (int i = 1; i < N; i++) {
+        fac[i] = static_cast<long long>(fac[i - 1]) * i % mod;
+    }
+
+    inv[0] = inv[1] = 1;
+    for (int i = 2; i < N; i++) {
+        inv[i] = static_cast<long long>(mod - mod / i) * inv[mod % i] % mod;
+    }
+
+    fac_inv[0] = fac_inv[1] = 1;
+    for (int i = 2; i < N; i++) {
+        fac_inv[i] = static_cast<long long>(fac_inv[i - 1]) * inv[i] % mod;
+    }
+
+    cin >> a >> b >> c >> d >> k;
+
+    for (int i = 0; i <= k; i++) {
+        ans = (ans + static_cast<long long>(f(a, b, i)) * f(a + c - i, d, k - i)) % mod;
+    }
+
+    cout << ans << endl;
+
+    return 0;
+}