Add problem from URI #math #combinatoric

URI/1904.cpp

@@ -0,0 +1,69 @@
+// https://www.urionlinejudge.com.br/judge/en/problems/view/1904
+#include<bits/stdc++.h>
+using namespace std;
+
+#define endl '\n'
+#define D(x) cout << #x << " = " << (x) << endl;
+
+const int mx = 1e7 + 10;
+long long fact[mx];
+
+vector<long long> primes;
+long long cnt_primes[mx];
+vector<long long> criba(mx, true);
+
+// test parity for C(n, k)
+bool calc (long long n, long long k) {
+  return (k & (n - k)) ? 0 : 1;
+}
+
+long long count_primes (long long a, long long b) {
+  return cnt_primes[b] - cnt_primes[a - 1];
+}
+
+void gen_primes () {
+  for (int i = 2; i < mx; ++i) {
+    if (criba[i]) {
+      int j = 2;
+      while (i * j < mx) {
+        criba[i * j] = false;
+        j ++;
+      }
+    }
+  }
+
+  criba[0] = criba[1] = 0;
+}
+
+int main() {
+  gen_primes();
+  long long a, b;
+
+  for (int i = 1; i < mx; ++i) {
+    criba[i] += criba[i - 1];
+  }
+
+  while (cin >> a >> b) {
+    if (a > b) swap(a, b);
+
+    if (a == b) {
+      cout << "?" << endl;
+      continue;
+    }
+
+
+    long long n = b - a;
+    long long r = criba[b] - criba[max(0LL, a - 1)];
+
+    //  |n+r-1|    (n+r-1)!           |n+r-1|       n!
+    //  |     | = ----------    =     |     | = ----------
+    //  |  r  |   r! * (n-1)!         |  n  |   r! * (n-r)!
+    //
+    //  from stars and bars Theorem
+
+    bool ans = calc(n + r - 1, n);
+
+    cout << (ans ? "Alice" : "Bob") << endl;
+  }
+  return 0;
+}