Submission #1202724

#	Time	Username	Problem	Language	Result	Execution time	Memory
1202724		tin_le	Snake Escaping (JOI18_snake_escaping)	C++20	12 / 100	179 ms	21196 KiB

snake_escaping

//████████╗██╗███╗░░██╗  ██╗░░░░░███████╗
//╚══██╔══╝██║████╗░██║  ██║░░░░░██╔════╝
//░░░██║░░░██║██╔██╗██║  ██║░░░░░█████╗░░
//░░░██║░░░██║██║╚████║  ██║░░░░░██╔══╝░░
//░░░██║░░░██║██║░╚███║  ███████╗███████╗
//░░░╚═╝░░░╚═╝╚═╝░░╚══╝  ╚══════╝╚══════╝
//   __________________
//  | ________________ |
//  ||          ____  ||
//  ||   /\    |      ||
//  ||  /__\   |      ||
//  || /    \  |____  ||
//  ||________________||
//  |__________________|
//  \###################\
//   \###################\
//    \        ____       \
//     \_______\___\_______\
// An AC a day keeps the doctor away.

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <ctime>
#include <cassert>
#include <complex>
#include <string>
#include <cstring>
#include <chrono>
#include <random>
#include <bitset>
#include <iomanip>
#include <functional>
#include <numeric>
#include <stack>
#include <array>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;
template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define vt vector
#define all(x) begin(x), end(x)
#define allr(x) rbegin(x), rend(x)
#define ub upper_bound
#define lb lower_bound
#define db double
#define ld long db
#define ll long long
#define ull unsigned long long
#define vll vt<ll>  
#define vvll vt<vll>
#define pll pair<ll, ll>    
#define vpll vt<pll>
#define vvpll vt<vpll>
#define vc vt<char> 
#define vvc vt<vc>
#define vi vt<int>
#define vvi vt<vi>
#define vvvi vt<vvi>
#define pii pair<int, int>
#define vpii vt<pii>
#define vs vt<string>
#define vvs vt<vs>
#define vb vt<bool>
#define vvb vt<vb>
#define vvpii vt<vpii>
#define vd vt<db>
#define ar(x) array<int, x>
#define var(x) vt<ar(x)>
#define vvar(x) vt<var(x)>
#define al(x) array<ll, x>
#define vall(x) vt<al(x)>
#define vvall(x) vt<vall(x)>
#define mset(m, v) memset(m, v, sizeof(m))
#define pb push_back
#define ff first
#define ss second
#define sv string_view
#define MP make_pair
#define MT make_tuple
#define rsz resize
#define sum(x) (ll)accumulate(all(x), 0LL)
#define srt(x) sort(all(x))
#define srtR(x) sort(allr(x))
#define srtU(x) sort(all(x)), (x).erase(unique(all(x)), (x).end())
#define SORTED(x) is_sorted(all(x))
#define rev(x) reverse(all(x))
#define MAX(a) *max_element(all(a)) 
#define MIN(a) *min_element(all(a))
#define ROTATE(a, p) rotate(begin(a), begin(a) + p, end(a))
#define i128 __int128

//SGT DEFINE
#define lc i * 2 + 1
#define rc i * 2 + 2
#define lp lc, left, middle
#define rp rc, middle + 1, right
#define entireTree 0, 0, n - 1
#define midPoint left + (right - left) / 2
#define pushDown push(i, left, right)
#define iter int i, int left, int right

#define IOS ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)

struct custom {
    static const uint64_t C = 0x9e3779b97f4a7c15; const uint32_t RANDOM = std::chrono::steady_clock::now().time_since_epoch().count();
    size_t operator()(uint64_t x) const { return __builtin_bswap64((x ^ RANDOM) * C); }
    size_t operator()(const std::string& s) const { size_t hash = std::hash<std::string>{}(s); return hash ^ RANDOM; } };
template <class K, class V> using umap = std::unordered_map<K, V, custom>; template <class K> using uset = std::unordered_set<K, custom>;
template<class T> using max_heap = priority_queue<T>;
template<class T> using min_heap = priority_queue<T, vector<T>, greater<T>>;
    
template<typename T, size_t N>
istream& operator>>(istream& is, array<T, N>& arr) {
    for (size_t i = 0; i < N; i++) { is >> arr[i]; } return is;
}

template<typename T, size_t N>
istream& operator>>(istream& is, vector<array<T, N>>& vec) {
    for (auto &arr : vec) { is >> arr; } return is;
}

inline std::ostream& operator<<(std::ostream& os, i128 x) {
    if(x == 0) { os << '0'; return os; } if(x < 0) { os << '-'; x = -x; }
    string s; while (x > 0) { int digit = int(x % 10); s.pb(char('0' + digit)); x /= 10; }
    rev(s); os << s; return os;
}
    
template <typename T1, typename T2>  istream &operator>>(istream& in, pair<T1, T2>& input) {    return in >> input.ff >> input.ss; }
    
template <typename T> istream &operator>>(istream &in, vector<T> &v) { for (auto &el : v) in >> el; return in; }

template<class T>
void output_vector(vt<T>& a, int off_set = 0) {
    int n = a.size();
    for(int i = off_set; i < n; i++) {
        cout << a[i] << (i == n - 1 ? '\n' : ' ');
    }
}

template<typename T, typename Compare>
vi closest_left(const vt<T>& a, Compare cmp) {
    int n = a.size(); vi closest(n); iota(all(closest), 0);
    for (int i = 0; i < n; i++) {
        auto& j = closest[i];
        while(j && cmp(a[i], a[j - 1])) j = closest[j - 1];
    }
    return closest;
}

template<typename T, typename Compare> // auto right = closest_right<int>(a, std::less<int>());
vi closest_right(const vt<T>& a, Compare cmp) {
    int n = a.size(); vi closest(n); iota(all(closest), 0);
    for (int i = n - 1; i >= 0; i--) {
        auto& j = closest[i];
        while(j < n - 1 && cmp(a[i], a[j + 1])) j = closest[j + 1];
    }
    return closest;
}

template<typename T, typename V = string>
vt<pair<T, int>> encode(const V& s) {
    vt<pair<T, int>> seg;
    for(auto& ch : s) {
        if(seg.empty() || ch != seg.back().ff) seg.pb({ch, 1});
        else seg.back().ss++;
    }
    return seg;
}

    
template<typename K, typename V>
auto operator<<(std::ostream &o, const std::map<K, V> &m) -> std::ostream& {
    o << "{"; int i = 0;
    for (const auto &[key, value] : m) { if (i++) o << " , "; o << key << " : " << value; }
    return o << "}";
}

#ifdef LOCAL
#define debug(x...) debug_out(#x, x)
void debug_out(const char* names) { std::cerr << std::endl; }
template <typename T, typename... Args>
void debug_out(const char* names, T value, Args... args) {
    const char* comma = strchr(names, ',');
    std::cerr << "[" << (comma ? std::string(names, comma) : names) << " = " << value << "]";
    if (sizeof...(args)) { std::cerr << ", "; debug_out(comma + 1, args...); }   
    else { std::cerr << std::endl; }
}
template<typename T1, typename T2>
std::ostream& operator<<(std::ostream& o, const std::pair<T1, T2>& p) { return o << "{" << p.ff << " , " << p.ss << "}"; }
auto operator<<(auto &o, const auto &x) -> decltype(end(x), o) {
    o << "{"; int i = 0; for (const auto &e : x) { if (i++) o << " , "; o << e; } return o << "}";
} // remove for leetcode
#include <sys/resource.h>
#include <sys/time.h>
void printMemoryUsage() {
    struct rusage usage;
    getrusage(RUSAGE_SELF, &usage);
    double memoryMB = usage.ru_maxrss / 1024.0;
    cerr << "Memory usage: " << memoryMB << " MB" << "\n";
}

#define startClock clock_t tStart = clock();
#define endClock std::cout << std::fixed << std::setprecision(10) << "\nTime Taken: " << (double)(clock() - tStart) / CLOCKS_PER_SEC << " seconds" << std::endl;
#else
#define debug(...)
#define startClock
#define endClock

#endif
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());

#define eps 1e-9
#define M_PI 3.14159265358979323846
const static string pi = "3141592653589793238462643383279";
const static ll INF = 1LL << 62;
const static int inf = 1e9 + 100;
const static int MK = 20;
const static int MX = 1e5 + 5;
ll gcd(ll a, ll b) { while (b != 0) { ll temp = b; b = a % b; a = temp; } return a; }
ll lcm(ll a, ll b) { return (a / gcd(a, b)) * b; }
ll floor(ll a, ll b) { if(b < 0) a = -a, b = -b; if (a >= 0) return a / b; return a / b - (a % b ? 1 : 0); }
ll ceil(ll a, ll b) { if (b < 0) a = -a, b = -b; if (a >= 0) return (a + b - 1) / b; return a / b; }
int pct(ll x) { return __builtin_popcountll(x); }
ll have_bit(ll x, int b) { return x & (1LL << b); }
int min_bit(ll x) { return __builtin_ctzll(x); }
int max_bit(ll x) { return 63 - __builtin_clzll(x); } 
const vvi dirs = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}, {1, 1}, {-1, -1}, {1, -1}, {-1, 1}}; // UP, DOWN, LEFT, RIGHT
const vvi knight_dirs = {{-2, -1}, {-2,  1}, {-1, -2}, {-1,  2}, {1, -2}, {1,  2}, {2, -1}, {2,  1}}; // knight dirs
const vc dirChar = {'U', 'D', 'L', 'R'};
int modExpo(ll base, ll exp, ll mod) { ll res = 1; base %= mod; while(exp) { if(exp & 1) res = (res * base) % mod; base = (base * base) % mod; exp >>= 1; } return res; }
ll extended_gcd(ll a, ll b, ll &x, ll &y) { if (b == 0) { x = 1; y = 0; return a; } ll d = extended_gcd(b, a % b, y, x); y -= (a / b) * x; return d; }
ll modInv(ll a, ll m) { ll x, y; ll g = extended_gcd(a, m, x, y); if (g != 1) { return -1; } x %= m; if (x < 0) x += m; return x; }
int modExpo_on_string(ll a, string exp, int mod) { ll b = 0; for(auto& ch : exp) b = (b * 10 + (ch - '0')) % (mod - 1); return modExpo(a, b, mod); }
ll sum_even_series(ll n) { return (n / 2) * (n / 2 + 1);} 
ll sum_odd_series(ll n) {return n - sum_even_series(n);} // sum of first n odd number is n ^ 2
ll sum_of_square(ll n) { return n * (n + 1) * (2 * n + 1) / 6; } // sum of 1 + 2 * 2 + 3 * 3 + 4 * 4 + ... + n * n
string make_lower(const string& t) { string s = t; transform(all(s), s.begin(), [](unsigned char c) { return tolower(c); }); return s; }
string make_upper(const string&t) { string s = t; transform(all(s), s.begin(), [](unsigned char c) { return toupper(c); }); return s; }
ll sqrt(ll n) { ll t = sqrtl(n); while(t * t < n) t++; while(t * t > n) t--; return t;}
bool is_perm(ll sm, ll square_sum, ll len) {return sm == len * (len + 1) / 2 && square_sum == len * (len + 1) * (2 * len + 1) / 6;} // determine if an array is a permutation base on sum and square_sum
bool is_vowel(char c) {return c == 'a' || c == 'e' || c == 'u' || c == 'o' || c == 'i';}

struct sos_dp {
    int B, N;
    vi f;
    vi a, subset, superset;
    sos_dp(const vi& a) : a(a) {
        B = 0;
        int m = MAX(a);
        while((1LL << B) <= m) B++;
        N = 1LL << B;
        f.rsz(N);
    }
    sos_dp(const vi& a, int B) : a(a), B(B), N(1LL << B), f(1LL << B) {}

    int low;
    sos_dp(int _B, int low) : low(low), B(_B), N(1LL << _B) { } // meet in the middle, https://www.codechef.com/problems/MONSTER?tab=statement

    void load() {
        f = a;
    }
    // how many element have a[i] as a super set
    void subsetSOS() {
        load();
        assert(subset.empty());
        for(int bit = 0; bit < B; bit++){
            for(int mask = 0; mask < N; mask++){
                if(have_bit(mask, bit)){
                    f[mask] += f[mask ^ (1 << bit)];
                }
            }
        }
        subset = f;
    }

    // how many element is a[i] a subset of
    // how many element AND together have the freq of it is
    // freq[nxt] - freq[mask] where have_bit(mask, bit) and nxt = (mask ^ (1LL << bit))
    // see max_prefix_sum_and function for reference
    void supersetSOS() {
        load();
        assert(superset.empty());
        for(int bit = 0; bit < B; bit++){
            for(int mask = 0; mask < N; mask++){
                if(!have_bit(mask, bit)){
                    f[mask] += f[mask | (1 << bit)];
                }
            }
        }
        superset = f;
    }

    template<typename T>
    T subset_equal_to(int target) { // how many OR subset equal to target
        // https://www.hackerrank.com/contests/w16/challenges/vim-war/problem
        subsetSOS();
        T res = 0;
        for(int mask = target; ; mask = (mask - 1) & target) {
            if(pct(mask ^ target) & 1) res -= T(2).pow(f[mask]) - 1; // contribution of mask to target is (mask ^ target)
            else res += T(2).pow(f[mask]) - 1;
            if(mask == 0) break;
        }
        return res;
    }

    vll A;
    void update_subset(int mask, ll delta = 1) { // tc : 1 << (K - low)
        if(A.empty()) A.rsz(N);
        int lo = ((1LL << low) - 1) & mask;
        mask = (mask >> low) << low;
        for(int sub = mask; ; sub = (sub - 1) & mask) {
            int now = sub | lo;
            if(now < A.size()) A[now] += delta;
            if(sub == 0) break;
        }
    }

    ll query_subset(int mask) { 
        if(A.empty()) return 0;
        const int LOW = (1LL << low) - 1;
        ll res = 0;
        int hi = (mask >> low) << low;
        int orig_low = mask & LOW;
        mask = ~mask & LOW;
        for(int sub = mask;; sub = (sub - 1) & mask) {
            int now = hi | orig_low | sub;
            if(now < A.size()) res += A[now];
            if(sub == 0) break;
        }
        return res;
    }

    void update_superset(int mask, ll delta = 1) {
        if(A.empty()) A.rsz(N);
        int lo = ((1LL << low) - 1) & mask;
        const int LOW = (((~mask & (N - 1)) >> low) << low);
        for(int sub = LOW; ; sub = (sub - 1) & LOW) {
            int now = sub | mask;
            if(now < A.size()) A[now] += delta;
            if(sub == 0) break;
        }
    }

    ll query_superset(int mask) {
        if(A.empty()) return 0;
        const int LOW = ((1LL << low) - 1) & mask;
        mask = (mask >> low) << low;
        ll res = 0;
        for(int sub = LOW; ; sub = (sub - 1) & LOW) {
            int now = sub | mask;
            if(now < A.size()) res += A[now];
            if(sub == 0) break;
        }
        return res;
    }

    ll max_prefix_sum_and() { // max sum of every prefix and over all permutation
        supersetSOS();
        vll dp(N, -INF);
        dp[N - 1] = (ll)count(all(a), N - 1) * (N - 1);
        for(int mask = N - 1; mask >= 0; mask--) {
            if(dp[mask] == -INF) continue;
            for(int b = 0; b < B; b++) {
                if(have_bit(mask, b)) {
                    ll nxt = mask ^ (1 << b);
                    ll cnt = f[nxt] - f[mask];
                    dp[nxt] = max(dp[nxt], dp[mask] + cnt * nxt);
                }
            }
        }
        return dp[0];
    }

    ll calc_submask(int one, int zero, int question) {
        if(subset.empty()) subsetSOS();
        if(superset.empty()) supersetSOS();
        const int lim = (B + 2) / 3;
        ll ans = 0;
        if(pct(question) <= lim) {
            for(int sub = question; ; sub = (sub - 1) & question) {
                ans += a[sub | one];
                if(sub == 0) break;
            }
        } else if(pct(zero) <= lim) {
            for(int sub = zero; ; sub = (sub - 1) & zero) {
                ll coeff = (pct(sub) & 1) ? -1 : 1;
                ans += coeff * superset[sub | one];
                if(sub == 0) break;
            }
        } else {
            for(int sub = one; ; sub = (sub - 1) & one) {
                ll coeff = (pct(sub) & 1) ? -1 : 1;
                ans += coeff * subset[sub | question];
                if(sub == 0) break;
            }
        }
        return ans;
    }
};

void solve() {
    int n, q; cin >> n >> q;
    const int N = 1LL << n;
    vi base(N), sub, sup;
    for(int i = 0; i < N; i++) {
        char x; cin >> x;
        base[i] = x - '0';
    }
    sos_dp root(base, n);
    while(q--) {
        string s; cin >> s;
        rev(s);
        int N = s.size();
        int one = 0, zero = 0, ques = 0;
        for(int i = 0; i < N; i++) {
            if(s[i] == '1') one |= 1LL << i;
            else if(s[i] == '0') zero |= 1LL << i;
            else ques |= 1LL << i;
        }
        cout << root.calc_submask(one, zero, ques) << '\n';
    }
}

signed main() {
    // careful for overflow, check for long long, use unsigned long long for random generator
    // when mle, look if problem require read in file, typically old problems
    IOS;
    startClock
    //generatePrime();

    int t = 1;
    //cin >> t;
    for(int i = 1; i <= t; i++) {   
        //cout << "Case #" << i << ": ";  
        solve();
    }

    endClock
    #ifdef LOCAL
      printMemoryUsage();
    #endif

    return 0;
}

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• Subtask 1: 5 / 5
• Subtask 2: 7 / 7
• Subtask 3: 0 / 10
• Subtask 4: 0 / 53
• Subtask 5: 0 / 25