C - Gerald and Giant Chess

https://codeforces.com/contest/559/submission/176493915

Codeforces/559/C/C.cpp

@@ -0,0 +1,59 @@
+#include <iostream>
+#include <algorithm>
+#include <utility>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e5 + 5;
+const int mod = 1e9 + 7;
+
+int h, w, n, f[N];
+int fac[N << 1], inv[N << 1], fac_inv[N << 1];
+std::pair<int, int> a[N];
+
+inline int C(int n, int m) {
+    return static_cast<long long>(fac[n]) * fac_inv[m] % mod * fac_inv[n - m] % mod;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    fac[0] = 1;
+    for (int i = 1; i < N << 1; i++) {
+        fac[i] = static_cast<long long>(fac[i - 1]) * i % mod;
+    }
+
+    inv[0] = inv[1] = 1;
+    for (int i = 2; i < N << 1; 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 << 1; i++) {
+        fac_inv[i] = static_cast<long long>(fac_inv[i - 1]) * inv[i] % mod;
+    }
+
+    cin >> h >> w >> n;
+
+    for (int i = 1, r, c; i <= n; i++) {
+        cin >> a[i].first >> a[i].second;
+    }
+
+    std::sort(a + 1, a + 1 + n);
+
+    a[n + 1] = std::make_pair(h, w);
+    for (int i = 1; i <= n + 1; i++) {
+        f[i] = C(a[i].first + a[i].second - 2, a[i].first - 1);
+
+        for (int j = 1; j < i; j++) {
+            f[i] = (f[i] - static_cast<long long>(f[j]) * C(a[i].first - a[j].first + a[i].second - a[j].second, a[i].first - a[j].first)) % mod;
+        }
+    }
+
+    cout << (f[n + 1] + mod) % mod << endl;
+
+    return 0;
+}