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