Submission #504198

#	Time	Username	Problem	Language	Result	Execution time	Memory
504198		maximumSHOT	Aliens (IOI16_aliens)	C++17	100 / 100	246 ms	9728 KiB

aliens

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using ui = unsigned int;
using ull = unsigned long long;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<long long, long long>;

const int inf = 1e9;
const ll inf64 = 1e18;

struct output {
    ll res;

    void print() {
        cout << res << "\n";
    }

    bool operator == (const output& o) const {
        return res == o.res;
    }
};

struct input {
    int n, m, k;
    vector<pii> a;

    input() = default;

    void read() {
        cin >> n >> m >> k;
        a.resize(n);
        for (auto& [x, y] : a)
            cin >> x >> y;
    }

    void print() {
        cout << n << " " << m << " " << k << "\n";
        for (auto [x, y] : a)
            cout << x << " " << y << "\n";
    }

    void gen() {
        static mt19937 rnd(42);
        const int MAXN = 100;
        n = rnd() % MAXN + 1;
        m = rnd() % MAXN + 1;
        k = rnd() % n + 1;
        a.resize(n);
        for (auto& [x, y] : a) {
            x = rnd() % m;
            y = rnd() % m;
        }
    }

    void gen_max_test() {

    }

    void prepare() {
        for (auto& [x, y] : a) {
            if (y > x)
                swap(x, y);
        }
        vector<pii> st;
        sort(a.begin(), a.end());
        for (int i = 0; i < n; i++) {
            if (i > 0 && a[i].first == a[i - 1].first)
                continue;
            while (!st.empty() && st.back().second >= a[i].second)
                st.pop_back();
            st.push_back(a[i]);
        }
        a = st;
        n = (int) a.size();
    }

    ll f(int len) {
        return 1ll * len * len;
    }

    struct Line {
        ll k = 0;
        ll b = 0;
        int c = 0;

        ld intersect(const Line& o) const {
            return ld(o.b - b) / ld(k - o.k);
        }

        ll f(ll x) const {
            return k * x + b;
        }
    };

    output fast() {
        prepare();
        vector<ll> rem(n);
        for (int j = 0; j < n; j++)
            rem[j] = f(max(0, (j > 0 ? a[j - 1].first : -1) - a[j].second + 1));
        vector<pair<ll, int>> dp(n);

        vector<Line> lines(n);
        for (int j = 0; j < n; j++) {
            lines[j] = {
                -2ll * a[j].second,
                (j > 0 ? dp[j - 1].first : 0ll) + 1ll * a[j].second * a[j].second - rem[j]
            };
        }

        auto calc = [&](ll lambda) -> pair<ll, int> {
            deque<Line> st;
            for (int i = 0; i < n; i++) {
                dp[i] = {inf64, inf};
                ll CONST = lambda + 1ll * (a[i].first + 1) * (a[i].first + 1);
                ll x0 = a[i].first + 1;
                lines[i] = {
                    -2ll * a[i].second,
                    (i > 0 ? dp[i - 1].first : 0ll) + 1ll * a[i].second * a[i].second - rem[i],
                    (i > 0 ? dp[i - 1].second : 0)
                };
                while ((int) st.size() >= 2) {
                    Line L1 = st[(int) st.size() - 2];
                    Line L2 = st[(int) st.size() - 1];
                    if (L1.intersect(L2) < L2.intersect(lines[i]))
                        break;
                    st.pop_back();
                }
                st.push_back(lines[i]);
                while ((int) st.size() >= 2 && st[0].intersect(st[1]) < x0)
                    st.pop_front();
                dp[i] = {
                    CONST + st[0].f(x0),
                    st[0].c - 1
                };
                if ((int) st.size() > 1) {
                    dp[i] = min(dp[i], make_pair(CONST + st[1].f(x0), st[1].c - 1));
                }
//                for (Line line : st) {
//                    dp[i] = min(dp[i], make_pair(
//                            CONST + line.f(x0),
//                            line.c - 1
//                    ));
//                }
//                for (int j = i; j >= 0; j--) {
//                    dp[i] = min(dp[i], make_pair(
//                        CONST + lines[j].k * x0 + lines[j].b,
//                        lines[j].c - 1
//                    ));
//                }
            }
            return dp[n - 1];
        };
        ll bl = 0, br = 1ll * m * m + 10, bm;
        while (br - bl > 1) {
            bm = bl + (br - bl) / 2;
            auto tmp = calc(bm);
            if (-tmp.second >= k) bl = bm;
            else br = bm;
        }
        ll lambda = bl;
        auto tmp = calc(lambda);
        ll res = tmp.first - lambda * k;
        return output{res};
    }

    output slow() {
#ifndef DEBUG
        throw;
#endif
        prepare();
        vector<vector<ll>> dp(n, vector<ll>(k + 1, inf64));
        for (int i = 0; i < n; i++) {
            for (int j = i; j >= 0; j--) {
                ll cost =
                        f(a[i].first - a[j].second + 1) -
                        f(max(0, (j > 0 ? a[j - 1].first : -1) - a[j].second + 1));
                for (int c = 1; c <= k; c++)
                    dp[i][c] = min(dp[i][c], (j > 0 ? dp[j - 1][c - 1] : 0) + cost);
            }
        }
        ll res = inf64;
        for (int c = 1; c <= k; c++)
            res = min(res, dp[n - 1][c]);
        return output{res};
    }
};

void test_case() {
    input in;
    in.read();
    output res = in.fast();
    res.print();
}

void work() {
    int t = 1;
    while (t--)
        test_case();
}

void test() {
    for (int t = 1;;t++) {
        input in;
        in.gen();
        input in_fs = in;
        input in_sl = in;
        output fs = in_fs.fast();
        output sl = in_sl.slow();
        if (fs == sl) {
            cout << "OK" << endl;
            fs.print();
            cout << "\n=========" << endl;
        } else {
            cout << "WA " << t << "\n";
            cout << "exp\n";
            sl.print();
            cout << "\n=========\n";
            cout << "fnd\n";
            fs.print();
            cout << "\n=========\n";
            in.print();
            break;
        }
    }
}

void max_test() {
    input in;
    in.gen_max_test();
    input in_fs = in;
    output fs = in_fs.fast();
    fs.print();
}

#ifdef DEBUG

int main() {

#ifdef DEBUG
    freopen("input.txt", "r", stdin);
#endif

    ios_base::sync_with_stdio(0);
    cin.tie(0);

    work();
//    test();
//    max_test();

    return 0;
}
#else

ll take_photos(int n, int m, int k, vector<int> r, vector<int> c) {
    input in;
    in.n = n;
    in.m = m;
    in.k = k;
    in.a.resize(n);
    for (int i = 0; i < n; i++)
        in.a[i] = {r[i], c[i]};
    output fs = in.fast();
    return fs.res;
}

#endif

Compilation message (stderr)

aliens.cpp: In function 'void max_test()':
aliens.cpp:27:8: warning: 'in.input::k' is used uninitialized in this function [-Wuninitialized]
   27 | struct input {
      |        ^~~~~
aliens.cpp:27:8: warning: 'in' is used uninitialized in this function [-Wuninitialized]

• Subtask 1: 4 / 4
• Subtask 2: 12 / 12
• Subtask 3: 9 / 9
• Subtask 4: 16 / 16
• Subtask 5: 19 / 19
• Subtask 6: 40 / 40