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codeforces/762/d.cc

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+#include <bits/stdc++.h>  // {{{
+
+#include <version>
+#ifdef __cpp_lib_ranges_enumerate
+#include <ranges>
+namespace rv = std::views;
+namespace rs = std::ranges;
+#endif
+
+// https://codeforces.com/blog/entry/96344
+
+#pragma GCC optimize("O2,unroll-loops")
+#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
+
+using namespace std;
+
+using i32 = int32_t;
+using u32 = uint32_t;
+using i64 = int64_t;
+using u64 = uint64_t;
+using f64 = double;
+using f128 = long double;
+
+#if __cplusplus >= 202002L
+template <typename T>
+constexpr T MIN = std::numeric_limits<T>::min();
+
+template <typename T>
+constexpr T MAX = std::numeric_limits<T>::max();
+
+template <typename T>
+[[nodiscard]] static T sc(auto&& x) {
+  return static_cast<T>(x);
+}
+
+template <typename T>
+[[nodiscard]] static T sz(auto&& x) {
+  return static_cast<T>(x.size());
+}
+#endif
+
+static void NO() {
+  std::cout << "NO\n";
+}
+
+static void YES() {
+  std::cout << "YES\n";
+}
+
+template <typename T>
+using vec = std::vector<T>;
+
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+#define ff first
+#define ss second
+
+#ifdef LOCAL
+#define db(...) std::print(__VA_ARGS__)
+#define dbln(...) std::println(__VA_ARGS__)
+#else
+#define db(...)
+#define dbln(...)
+#endif
+//  }}}
+
+bitset<100000 + 1> friends;
+void solve() {
+  /*
+     binary search on alpha
+
+     how to know if i can choose at least n - 1 shops to give each guy a present
+     basically, choose, out of all m shops, n shops, one gives each guy a
+present (in the worst)
+
+     hm - must dynamically, per bsearch query, filter arrays
+
+     consider each array: if someone unset can be set, + 1 to count, update max
+     if already set, take max of large value
+
+challenge: n - 1 shops, not  all n
+ take a step back:
+
+ we have m arrays, each which set values offriend individually
+
+ consider each friend separately - have multiple values of joy set to; filter to
+>= mid alphaq
+
+ not nec. choose ones that set most -> greedy
+
+ ok - one shop per friend - per friend, iterate - find shop that sets their joy
+>= alpha
+
+ now, either < n (bad) or n shops - consider each friend as the "substitute"
+candidate
+
+ in other words, consider each friend, and iter AGAIN thru the shit - can we
+find ANOTHER diff array setting this guy, as well as setting another friend?
+
+ if so, done!
+     */
+
+  u32 m, n;
+  cin >> m >> n;
+
+  vec<vec<u64>> p(m, vec<u64>(n));
+  u64 maxp = 0;
+  for (auto& row : p) {
+    for (auto& e : row) {
+      cin >> e;
+      maxp = max(maxp, e);
+    }
+  }
+
+  u64 l = 1, r = maxp;
+
+  auto ok = [&](u64 alpha) {
+    friends.reset();
+    bool both_covered = false;
+
+    for (auto& shop : p) {
+      u32 shop_count = 0;
+      for (u32 i = 0; i < n; ++i) {
+        if (shop[i] >= alpha) {
+          ++shop_count;
+          friends.set(i);
+        }
+      }
+      both_covered |= shop_count > 1;
+    }
+
+    return friends.count() == n && both_covered;
+  };
+
+  while (l <= r) {
+    u64 alpha = l + (r - l) / 2;
+
+    if (ok(alpha)) {
+      l = alpha + 1;
+    } else {
+      r = alpha - 1;
+    }
+  }
+
+  println("{}", r);
+}
+
+int main() {  // {{{
+  std::cin.exceptions(std::cin.failbit);
+
+#ifdef LOCAL
+  std::cerr.rdbuf(std::cout.rdbuf());
+  std::cout.setf(std::ios::unitbuf);
+  std::cerr.setf(std::ios::unitbuf);
+#else
+  std::cin.tie(nullptr)->sync_with_stdio(false);
+#endif
+
+  u32 tc = 1;
+  std::cin >> tc;
+
+  for (u32 t = 0; t < tc; ++t) {
+    solve();
+  }
+
+  return 0;
+}
+// }}}