Submission #539139

#	Time	Username	Problem	Language	Result	Execution time	Memory
539139		huB1erTi2	Tug of War (BOI15_tug)	C++17	100 / 100	1063 ms	5620 KiB

tug

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#include <iostream>
#include <cassert>
#include <vector>
#include <algorithm>

using namespace std;

// #define DEBUG
#ifdef DEBUG
#define dassert(x) assert(x);
#define df(...) printf(__VA_ARGS__)
#else
#define dassert(x)
#define df(...)
#endif

#define x first
#define y second
#define mp make_pair
#define pb push_back
#define ir(x, a, b) ((a) <= (x) && (x) <= (b))
#define vec vector
#define sz(x) (ll)x.size()
#define foru(i, n) for (int i = 0; (i) < (n); ++(i))
#define all(x) (x).begin(), (x).end()

typedef int64_t ll;

int read() {
    int n = 0; bool b = 0; char c = getchar();
    for (; !ir(c, '0', '9'); c = getchar()) b = (c == '-');
    for (; ir(c, '0', '9'); c = getchar()) n = 10*n + (c-'0');
    if (b) return -n;
    return n;
}

vec<vec<pair<int, int>>> g;
vec<int> ct;
vec<char> used;

// edges, vertices
pair<int, int> count(int v) {
    used[v] = 1;
    int se = ct[v], sv = 1;
    for (auto [c, _] : g[v]) {
        if (used[c]) continue;
        auto [ce, cv] = count(c);
        se += ce, sv += cv;
    }
    return {se, sv};
}

int cycle(int v, int p) {
    // df("visiting %d\n", v);
    used[v] = 1;
    int ret = -1;
    for (auto [c, _] : g[v]) {
        if (c == p) continue;
        if (used[c]) { ret = v; continue; }
        int res = cycle(c, v);
        if (res != -1) ret = res;
    }
    return ret;
}

pair<int, int> dfs(int v, int p, int val, int costdown) {
    used[v] = 1;
    int sum = 0, cycle = 1e9;
    bool covered = 0;
    // df("costdown: %d\n", costdown);
    for (auto [c, cost] : g[v]) {
        if (c == p && cost == -costdown && !covered) {
            covered = 1;
            continue;
        }
        if (used[c]) {
            if (v == p) continue;
            // cout << "set cycle " << v <<  " " << c << " " << cost << endl;
            cycle = val + cost;
            sum += cost;
        } else {
            auto [ss, cyc] = dfs(c, v, val + cost, cost);
            if (cyc != 1e9) cycle = cyc;
            sum += ss + cost;
        }
    }
    return {sum, cycle};
}

void fail() {
    cout << "NO\n";
    exit(0);
}

void succeed() {
    cout << "YES\n";
    exit(0);
}

int main() {
    df("debug mode\n");
#ifndef DEBUG
    ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#endif
    int n, k;
    cin >> n >> k;
    g.resize(2*n);
    ct.resize(2*n);
    used.resize(2*n);
    foru (i, 2*n) {
        int v, u, s;
        cin >> v >> u >> s;
        u += n;
        --v, --u;
        df("%d--%d\n", v, u);
        g[v].pb({u, s});
        g[u].pb({v, -s});
        ++ct[u], ++ct[v];
    }
    foru (v, 2*n) {
        if (used[v]) continue;
        auto [ce, cv] = count(v);
        ce /= 2; // in and out counted twice
        if (ce != cv) fail();
    }
    
    used.assign(2*n, 0);
    vec<int> roots;
    foru (v, 2*n) {
        if (used[v]) continue;
        roots.pb(cycle(v, v));
        df("added root %d\n", roots.back());
        dassert(roots.back() != -1);
    }
    
    used.assign(2*n, 0);
    int zero = 0;
    vec<int> ns;
    for (auto root : roots) {
        auto [sum, cycle] = dfs(root, root, 0, 0);
        
        int a = sum, b = sum - 2*cycle;
        if (b < a) swap(a, b);
        
        zero -= a, b -= a, a -= a; // moving everything by -a
        if (b) ns.pb(b);
    }
    df("zero: %d\n", zero);
    // we want a number between zero - k, zero + k
    if (zero - k <= 0 && zero + k >= 0) succeed();
    if (zero < 0) fail();
    vec<char> dp(zero + k + 1);
    dp[0] = 1;
    int hi = 0;
    sort(all(ns));
    vec<pair<int, int>> ps = {{ns.front(), 0}};
    for (auto x : ns) {
        if (ps.back().x == x) ++ps.back().y;
        else ps.push_back({x, 1});
    }
    for (auto [x, c] : ps) {
        if (x > zero+k) continue;
        for (int i = zero+k; i >= 0; --i) { 
            for (int t = 1; t <= c && i + t*x <= zero + k; ++t) {
                if (!dp[i] || dp[i + t*x]) break;
                dp[i+t*x] = 1;
            }
        }
    }
    for (int i = zero - k; i <= zero + k; ++i) {
        if (dp[i]) succeed();
    }
    fail();
    return 0;
}

Compilation message (stderr)

tug.cpp: In function 'int main()':
tug.cpp:161:9: warning: unused variable 'hi' [-Wunused-variable]
  161 |     int hi = 0;
      |         ^~

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