Submission #588218

#	Time	Username	Problem	Language	Result	Execution time	Memory
588218		georgievskiy	Aliens (IOI16_aliens)	C++17	100 / 100	351 ms	16328 KiB

aliens

#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ll long long
#define sqr(x) ((x)*(x))
#define ld long double
using pii = pair<int, int>;
const int inf = 3e18;

struct line {
    int k, b;
    line() {
        k = 0, b = inf;
    }
    line(int k, int b) : k(k), b(b) {}
    int get(int x) {return k * x + b;}
};

ld inter(line a, line b) {
    return 1.0 * (a.b - b.b) / (b.k - a.k);
}

vector<line> cht;
vector<ld> xs;
vector<int> ks;

void push(line t, int k) {
    while (cht.size() && inter(cht.back(), t) < xs.back()) {
        cht.pop_back();
        xs.pop_back();
        ks.pop_back();
    }
    if (cht.size())
        xs.push_back(inter(cht.back(), t));
    else
        xs.push_back(-inf);
    cht.push_back(t);
    ks.push_back(k);
}

pii get(int x) {
    int ind = upper_bound(xs.begin(), xs.end(), (ld)x) - xs.begin() - 1;
    return {cht[ind].get(x), ks[ind]};
}

int calc(int n, vector<int>& x, vector<int>& y, vector<int>& t, vector<int>& d, int lambda) {
    cht.clear(), xs.clear(), ks.clear();
    d[0] = 0;
    vector<int> c(n + 1, 0);
    for (int i = 0; i < n; i++) {
        int k = -2 * y[i];
        int b = sqr(y[i]) - t[i] + d[i];
        push(line(k, b), i);

        auto p = get(x[i] + 1);
        int f = p.second;

        c[i + 1] = c[f] + 1;
        d[i + 1] = p.first + sqr(x[i] + 1) + lambda;
    }
    return c.back();
}

long long take_photos(signed n, signed m, signed k, std::vector<signed> r, std::vector<signed> c) {
    vector<pii> a(n);
    for (int i = 0; i < n; i++) a[i] = {max(r[i], c[i]), min(r[i], c[i])};
    sort(a.begin(), a.end(), [](pii a, pii b) {return a.first < b.first || a.first == b.first && a.second > b.second;});
    vector<pii> st;
    for (pii p : a) {
        while (st.size() && st.back().second >= p.second)
            st.pop_back();
        st.push_back(p);
    }
    n = st.size();
    k = min(k, n);
    vector<int> x(n), y(n);
    for (int i = 0; i < n; i++)
        x[i] = st[i].first, y[i] = st[i].second;

    vector<int> t(n, 0);
    for (int i = 1; i < n; i++)
        t[i] = sqr(max(0ll, x[i - 1] - y[i] + 1));

    vector<int> d(n + 1);
    int lo = -1, hi = inf+1;
    while (hi - lo > 1) {
        int c = (hi + lo) / 2;
        if (calc(n, x, y, t, d, c) > k)
            lo = c;
        else
            hi = c;
    }
    int x1 = calc(n, x, y, t, d, lo);
    int y1 = d.back() - lo * x1;
    int x2 = calc(n, x, y, t, d, hi);
    int y2 = d.back() - hi * x2;
    if (y1 == y2)
        return y1;
    int cf = (y2 - y1) / (x2 - x1);
    int ans = y1 + (k - x1) * cf;

    return ans;
}

Compilation message (stderr)

aliens.cpp: In lambda function:
aliens.cpp:68:95: warning: suggest parentheses around '&&' within '||' [-Wparentheses]
   68 |     sort(a.begin(), a.end(), [](pii a, pii b) {return a.first < b.first || a.first == b.first && a.second > b.second;});
      |                                                                            ~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~

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