Complete CodeForces 835E The Penguins Game

Author: andreimaximov

README.md

@@ -100,6 +100,7 @@ easily understandable algorithms for learning purposes.
 - [827C DNA Evolution](codeforces/dna-evolution)
 - [830B Cards Sorting](codeforces/cards-sorting)
 - [833B The Bakery](codeforces/the-bakery)
+- [835E The Penguin's Game](codeforces/the-penguins-game)
 
 ## Geeks for Geeks
 

codeforces/the-penguins-game/Makefile

@@ -0,0 +1,13 @@
+CXX := g++
+CXXFLAGS := -std=c++14 -Wall -o out
+
+default: out run
+
+out: main.cpp
+	$(CXX) $(CXXFLAGS) main.cpp
+
+clean:
+	$(RM) out
+
+run:
+	./out

codeforces/the-penguins-game/README.md

@@ -0,0 +1,3 @@
+# README
+
+[http://codeforces.com/problemset/problem/835/E](http://codeforces.com/problemset/problem/835/E)

codeforces/the-penguins-game/main.cpp

@@ -0,0 +1,110 @@
+#include <bits/stdc++.h>
+
+using namespace std;  // NOLINT
+
+// The maximum number of bits we need to represent positions 1 ... n.
+constexpr int MAX_BITS = 10;
+
+int n, x, y;
+
+//
+// Queries the XOR of icicles with positions idxs.
+//
+int query(const vector<int>& idxs) {
+  cout << "? " << idxs.size();
+  for (int i : idxs)
+    cout << " " << i;
+  cout << endl << flush;
+
+  int z;
+  cin >> z;
+  assert(z != -1);
+
+  return z;
+}
+
+//
+// Finds the position of a single special icicle in positions idxs.
+//
+int find_one(const vector<int>& idxs) {
+  assert(!idxs.empty());
+
+  if (idxs.size() == 1) return idxs[0];
+
+  auto mid = idxs.begin() + idxs.size() / 2;
+  vector<int> left(idxs.begin(), mid);
+
+  int z = query(left);
+
+  if ((left.size() % 2 == 0 && z != 0) || (left.size() % 2 == 1 && z == y))
+    return find_one(left);
+
+  vector<int> right(mid, idxs.end());
+  return find_one(right);
+}
+
+//
+// Returns a set of positions with the i'th bit set to 1.
+//
+vector<int> idxs_with_bit(int i) {
+  vector<int> idxs;
+  int mask = 1 << i;
+
+  for (int p = 1; p <= n; p++)
+    if ((mask & p) != 0)
+      idxs.push_back(p);
+
+  return idxs;
+}
+
+//
+// Returns the bits that the positions of the two special icicles differ in.
+//
+vector<int> find_diff_bits() {
+  vector<int> diff;
+
+  for (int i = 1; i <= MAX_BITS; i++) {
+    auto idxs = idxs_with_bit(i - 1);
+
+    if (idxs.empty()) continue;
+
+    auto z = query(idxs);
+
+    if ((idxs.size() % 2 == 0 && z != 0) || (idxs.size() % 2 == 1 && z == y))
+      diff.push_back(i - 1);
+  }
+
+  return diff;
+}
+
+int main() {
+  ios::sync_with_stdio(false);
+
+  cin >> n >> x >> y;
+
+  // 1. Find bits in positions of special icicles that are different.
+  auto bits = find_diff_bits();
+  assert(!bits.empty());
+
+  // 2. Search for single special icicle in a set of positions where a
+  // differing bit is on. This way we guarantee only one special icicle in the
+  // set.
+  auto idxs = idxs_with_bit(bits[0]);
+  int p = find_one(idxs);
+
+  // 3. Reconstruct the other icicle using the bits we know are different.
+  int q = p;
+  for (int i : bits) {
+    // Clear the ith bit of q.
+    q = q & ~(1 << i);
+
+    // Set to inverse of ith bit of p.
+    if ((p & (1 << i)) == 0) q = q | (1 << i);
+  }
+
+  if (p > q) swap(p, q);
+
+  cout << "! " << p << " " << q << endl;
+
+  return 0;
+}