Submission #335742

#	Time	Username	Problem	Language	Result	Execution time	Memory
335742		12tqian	Tug of War (BOI15_tug)	C++17	100 / 100	1538 ms	13568 KiB

tug

#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <iostream>
#include <iomanip>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>

using namespace std;
using namespace __gnu_pbds;
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;

typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str;

typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<db, db> pd;

typedef vector<int> vi;
typedef vector<bool> vb;
typedef vector<ll> vl;
typedef vector<db> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<pd> vpd;

#define mp make_pair
#define f first
#define s second
#define sz(x) (int) (x).size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define sor(x) sort(all(x))
#define rsz resize
#define resz resize
#define ins insert
#define ft front()
#define bk back()
#define pf push_front
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound

#define f1r(i, a, b) for(int i = (a); i < (b); ++i)
#define f0r(i, a) f1r(i, 0, a)
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define F0R(i, a) FOR(i,0,a)
#define ROF(i, a, b) for (int i = (b) - 1; i >= (a); --i)
#define R0F(i, a) ROF(i, 0, a)
#define trav(a, x) for (auto& a : x)

mt19937 rng((uint32_t) chrono::steady_clock::now().time_since_epoch().count());

template<class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
template<class T> using V = vector<T>;

#ifdef LOCAL
#define dbg(...) debug(#__VA_ARGS__, __VA_ARGS__);
#else
#define dbg(...) 17;
#endif

template<typename T, typename S> ostream& operator << (ostream &os, const pair<T, S> &p) { return os << "(" << p.first << ", " << p.second << ")"; }
template<typename C, typename T = decay<decltype(*begin(declval<C>()))>, typename enable_if<!is_same<C, string>::value>::type* = nullptr>
ostream& operator << (ostream &os, const C &c) { bool f = true; os << "{"; for (const auto &x : c) { if (!f) os << ", "; f = false; os << x; } return os << "}"; }
template<typename T> void debug(string s, T x) { cerr << s << " = " << x << "\n"; }
template<typename T, typename... Args> void debug(string s, T x, Args... args) { cerr << s.substr(0, s.find(',')) << " = " << x << " | "; debug(s.substr(s.find(',') + 2), args...); }

constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int bits(int x) { return 31 - __builtin_clz(x); } // floor(log2(x))

namespace input {
    template<class T> void re(complex<T>& x);
    template<class T1, class T2> void re(pair<T1, T2>& p);
    template<class T> void re(vector<T>& a);
    template<class T, int SZ> void re(array<T, SZ>& a);
    template<class T> void re(T& x) { cin >> x; }
    void re(double& x) { string t; re(t); x = stod(t); }
    void re(ld& x) { string t; re(t); x = stold(t); }
    template<class T, class... Ts> void re(T& t, Ts&... ts) {
        re(t); re(ts...); }
    template<class T> void re(complex<T>& x) { T a, b; re(a, b); x = cd(a, b); }
    template<class T1, class T2> void re(pair<T1, T2>& p) { re(p.f, p.s); }
    template<class T> void re(vector<T>& a) { F0R(i, sz(a)) re(a[i]); }
    template<class T, int SZ> void re(array<T, SZ>& a) { F0R(i, SZ) re(a[i]); }
}

using namespace input;

namespace output {
    void pr(int x) { cout << x; }
    void pr(long x) { cout << x; }
    void pr(ll x) { cout << x; }
    void pr(unsigned x) { cout << x; }
    void pr(unsigned long x) { cout << x; }
    void pr(unsigned long long x) { cout << x; }
    void pr(float x) { cout << x; }
    void pr(double x) { cout << x; }
    void pr(ld x) { cout << x; }
    void pr(char x) { cout << x; }
    void pr(const char* x) { cout << x; }
    void pr(const string& x) { cout << x; }
    void pr(bool x) { pr(x ? "true" : "false"); }
    template<class T> void pr(const complex<T>& x) { cout << x; }
    template<class T1, class T2> void pr(const pair<T1, T2>& x);
    template<class T> void pr(const T& x);
    template<class T, class... Ts> void pr(const T& t, const Ts&... ts) {
        pr(t); pr(ts...); }
    template<class T1, class T2> void pr(const pair<T1,T2>& x) {
        pr("{", x.f, ", ", x.s, "}"); }
    template<class T> void pr(const T& x) {
        pr("{"); // const iterator needed for vector<bool>
        bool fst = 1; for (const auto& a: x) pr(!fst ? ", " : "", a), fst = 0;
        pr("}"); }
    void ps() { pr("\n"); } // print w/ spaces
    template<class T, class... Ts> void ps(const T& t, const Ts&... ts) {
        pr(t); if (sizeof...(ts)) pr(" "); ps(ts...); }
    void pc() { pr("]\n"); } // debug w/ commas
    template<class T, class... Ts> void pc(const T& t, const Ts&... ts) {
        pr(t); if (sizeof...(ts)) pr(", "); pc(ts...); }
}

using namespace output;

namespace io {
    void setIn(string s) { freopen(s.c_str(), "r", stdin); }
    void setOut(string s) { freopen(s.c_str(), "w", stdout); }
    void setIO(string s = "") {
        cin.sync_with_stdio(0); cin.tie(0);
        if (sz(s)) { setIn(s + ".in"), setOut(s + ".out"); }
    }
}

using namespace io;

const int MOD = 1e9 + 7; // 998244353;
const ld PI = acos((ld) -1);

typedef std::decay <decltype(MOD)>::type mod_t;
struct mi {
    mod_t val;
    explicit operator mod_t() const { return val; }
    mi() { val = 0; }
    mi(const long long& v) {
        val = (-MOD <= v && v <= MOD) ? v : v % MOD;
        if (val < 0) val += MOD; }
    friend std::istream& operator >> (std::istream& in, mi& a) {
        long long x; std::cin >> x; a = mi(x); return in; }
    friend std::ostream& operator << (std::ostream& os, const mi& a) { return os << a.val; }
    friend bool operator == (const mi& a, const mi& b) { return a.val == b.val; }
    friend bool operator != (const mi& a, const mi& b) { return !(a == b); }
    friend bool operator < (const mi& a, const mi& b) { return a.val < b.val; }
    friend bool operator > (const mi& a, const mi& b) { return a.val > b.val; }
    friend bool operator <= (const mi& a, const mi& b) { return a.val <= b.val; }
    friend bool operator >= (const mi& a, const mi& b) { return a.val >= b.val; }
    mi operator - () const { return mi(-val); }
    mi& operator += (const mi& m) {
        if ((val += m.val) >= MOD) val -= MOD;
        return *this; }
    mi& operator -= (const mi& m) {
        if ((val -= m.val) < 0) val += MOD;
        return *this; }
    mi& operator *= (const mi& m) { val = (long long) val * m.val % MOD;
        return *this; }
    friend mi pow(mi a, long long p) {
        mi ans = 1; assert(p >= 0);
        for (; p; p /= 2, a *= a) if (p & 1) ans *= a;
        return ans; }
    friend mi inv(const mi& a) { assert(a != 0); return pow(a, MOD - 2); }
    mi& operator /= (const mi& m) { return (*this) *= inv(m); }
    friend mi operator + (mi a, const mi& b) { return a += b; }
    friend mi operator - (mi a, const mi& b) { return a -= b; }
    friend mi operator * (mi a, const mi& b) { return a *= b; }
    friend mi operator / (mi a, const mi& b) { return a /= b; }
};
typedef pair<mi, mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;

int main() {
    const int INF = 1e9;
    setIO("");

    int n, k; re(n, k);
    // right minus left
    auto no = []() {
        ps("NO");
        exit(0);
    };
    auto yes = []() {
        ps("YES");
        exit(0);
    };

    vector<multiset<pi>> adj(2 * n);
    f0r(i, 2 * n) {
        int u, v, w; re(u, v, w);
        u--, v--; v += n;
        adj[u].emplace(v, w);
        adj[v].emplace(u, -w);
    }

    multiset<pi> use;
    f0r(i, 2 * n) {
        if (sz(adj[i]) == 0) continue;
        use.emplace(sz(adj[i]), i);
    }

    auto one_rem = [&](int u, int v, int w) {
        assert(use.find({sz(adj[u]), u}) != use.end());
        use.erase(use.find({sz(adj[u]), u}));

        assert(adj[u].find({v, w}) != adj[u].end());
        adj[u].erase(adj[u].find({v, w}));
        if (sz(adj[u]) == 0) return;

        use.emplace(sz(adj[u]), u);
    };
    auto rem = [&](int u, int v, int w) {
        assert(u != v);
        one_rem(u, v, w);
        one_rem(v, u, -w);
    };

    int diff = 0;
    vector<int> vis(2 * n);
    // these are forced
    while (!use.empty()) {
        auto beg = *use.begin();
        if (beg.f > 1) break;

        int u = beg.s;
        int v = (*adj[u].begin()).f;
        int w = (*adj[u].begin()).s;

        // you delete the reverse edge also
        rem(u, v, w);

        vis[u] = 1;
        diff += -w;
    }

    vi can;

    f0r(i, 2 * n) {
        if (vis[i]) continue;
        if (sz(adj[i]) == 0) continue;
        int val = 0;
        int u = i;
        int v, w;

        for (auto nxt : adj[u]) {
            if (vis[nxt.f] == 0) {
                v = nxt.f;
                w = nxt.s;
                break;
            }
        }
        assert(adj[u].find({v, w}) != adj[u].end());
        assert(adj[v].find({u, -w}) != adj[v].end());
        adj[u].erase(adj[u].find({v, w}));
        adj[v].erase(adj[v].find({u, -w}));
        // u to v weight w

        val += w;

        function<void(int)> dfs = [&](int src) {
            vis[src] = 1;

            for (auto nxt : adj[src]) {
                int go = nxt.f;
                int we = nxt.s;

                if (vis[go]) {
                    continue;
                } else { 
                    val += we;
                    dfs(go);
                }

            }
        };

        dfs(v);

        val = abs(val);
        can.eb(val);
    }
    int res = 0;
    f0r(i, 2 * n) res += vis[i];
    if (res != 2 * n) no();

    // sum stuff in can, add to diff, abs between -k, k
    // you want to make a sum in the range of left, right
    const int MX = 1e6 + 5;
    const int ADD = MX / 2;

    bitset<MX> B;

    f0r(i, sz(can)) {
        int x = can[i];

        if (i == 0) { 
            B[x + ADD] = 1;
            B[-x + ADD] = 1;
            continue;
        }
        B <<= x;
        B |= (B >> (2 * x));
    }

    f1r(i, -k - diff, k - diff + 1) {
        int x = i+ADD;
        if (B[x]) {
            yes();
        }
    }

    no();    
    return 0;
}

Compilation message (stderr)

tug.cpp: In function 'int main()':
tug.cpp:208:15: warning: unused variable 'INF' [-Wunused-variable]
  208 |     const int INF = 1e9;
      |               ^~~
tug.cpp: In function 'void io::setIn(std::string)':
tug.cpp:153:35: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
  153 |     void setIn(string s) { freopen(s.c_str(), "r", stdin); }
      |                            ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~
tug.cpp: In function 'void io::setOut(std::string)':
tug.cpp:154:36: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
  154 |     void setOut(string s) { freopen(s.c_str(), "w", stdout); }
      |                             ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
tug.cpp: In function 'int main()':
tug.cpp:287:32: warning: 'w' may be used uninitialized in this function [-Wmaybe-uninitialized]
  287 |         assert(adj[v].find({u, -w}) != adj[v].end());
      |                                ^

• Subtask 1: 18 / 18
• Subtask 2: 30 / 30
• Subtask 3: 23 / 23
• Subtask 4: 29 / 29