#include // {{{ // 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 constexpr T MIN = std::numeric_limits::min(); template constexpr T MAX = std::numeric_limits::max(); template [[nodiscard]] static T sc(auto &&x) { return static_cast(x); } template [[nodiscard]] static T sz(auto &&x) { return static_cast(x.size()); } #endif static void NO() { std::cout << "NO\n"; } static void YES() { std::cout << "YES\n"; } #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 // }}} vector> trace(251); void solve() { /* - # cows patient 0 - k bounds 1. sort by time to "sim" interactions - say x and y shake; unless wek one is sick, wedk consequences (i.e. who gets sick) - only ONE starts out - guess ONE cow is patient zero, run sim - guess all k from 0 to 251?, taking min of low bound, max of high bound k = 250 -> infinity bsearch <- no (if can achieve state w/ k=i, doesn't mean k=i-1, nor k=i+1) NOTE: only candidates for patient zero are initial set 0s, since cows stay sick */ u32 n, t; cin >> n >> t; string state; cin >> state; state = '0' + state; u32 t_; for (u32 i = 0; i < t; ++i) { cin >> t_; cin >> trace[t_].ff >> trace[t_].ss; // NOTE: forgot the one-indexin } u32 lb = numeric_limits::max(), ub = 0; u32 count = 0; /* a bunch of cows shake hooves because the gay USACO (usa computing olympiad) just decided to theme everything cows and for some K, a cow can only transmit what you have (STDs) after at most K hooveshakes but i misread it as saying that if they contract what you have (an STD) they can only transmit the STD up to K days later not after they have sex k times (which is what you do, let k approach infinity) ok. then, after that, i missed k=0 basecase then, after that basically, i only counted when someone transmitted an std & infecting someone instead, i should've counted the cow having sex with ANYONE, even if they already have an std, it still counts as a handshake core note: once realize wrong, reexamine entire problem solution (has rpercussions) rather than what u see is wrong */ for (u32 i = 1; i <= n; ++i) { bool zero = false; for (u32 k = 0; k <= 250; ++k) { vector shakes(n + 1, 0); string cur_state(n + 1, '0'); cur_state[i] = '1'; for (t_ = 1; t_ <= 250; ++t_) { auto [a, b] = trace[t_]; if (a == 0) { continue; } if (cur_state[a] == '1') { ++shakes[a]; } if (cur_state[b] == '1') { ++shakes[b]; } if (cur_state[a] == '0' && cur_state[b] == '1' && shakes[b] <= k) { cur_state[a] = '1'; } else if (cur_state[b] == '0' && cur_state[a] == '1' && shakes[a] <= k) { cur_state[b] = '1'; } } if (cur_state == state) { zero = true; lb = min(lb, k); ub = max(ub, k); } } count += zero; } cout << count << ' ' << lb << ' ' << (ub == 250 ? "Infinity" : to_string(ub)) << '\n'; } int main() { // {{{ cin.tie(nullptr)->sync_with_stdio(false); cin.exceptions(cin.failbit); #define PROBLEM_NAME "tracing" #ifdef LOCAL freopen("io/" PROBLEM_NAME ".in", "r", stdin); freopen("io/" PROBLEM_NAME ".out", "w", stdout); #else freopen(PROBLEM_NAME ".in", "r", stdin); freopen(PROBLEM_NAME ".out", "w", stdout); #endif solve(); return 0; } // }}}