Submission #742036

#	Time	Username	Problem	Language	Result	Execution time	Memory
742036		marvinthang	Aliens (IOI16_aliens)	C++17	100 / 100	216 ms	14520 KiB

aliens

/*************************************
*    author: marvinthang             *
*    created: 15.05.2023 18:35:26    *
*************************************/

#include "aliens.h"
#include <bits/stdc++.h>

using namespace std;

#define                  fi  first
#define                  se  second
#define                left  ___left
#define               right  ___right
#define                TIME  (1.0 * clock() / CLOCKS_PER_SEC)
#define             MASK(i)  (1LL << (i))
#define           BIT(x, i)  ((x) >> (i) & 1)
#define  __builtin_popcount  __builtin_popcountll
#define              ALL(v)  (v).begin(), (v).end()
#define           REP(i, n)  for (int i = 0, _n = (n); i < _n; ++i)
#define          REPD(i, n)  for (int i = (n); i--; )
#define        FOR(i, a, b)  for (int i = (a), _b = (b); i < _b; ++i) 
#define       FORD(i, b, a)  for (int i = (b), _a = (a); --i >= _a; ) 
#define       FORE(i, a, b)  for (int i = (a), _b = (b); i <= _b; ++i) 
#define      FORDE(i, b, a)  for (int i = (b), _a = (a); i >= _a; --i) 
#define        scan_op(...)  istream & operator >> (istream &in, __VA_ARGS__ &u)
#define       print_op(...)  ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#ifdef LOCAL
    #include "debug.h"
#else
    #define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
    #define DB(...) 23
    #define db(...) 23
    #define debug(...) 23
#endif

template <class U, class V> scan_op(pair <U, V>)  { return in >> u.first >> u.second; }
template <class T> scan_op(vector <T>)  { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class U, class V> print_op(pair <U, V>)  { return out << '(' << u.first << ", " << u.second << ')'; }
template <size_t i, class T> ostream & print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")";  else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); }
template <class ...U> print_op(tuple<U...>) { return print_tuple_utils<0, tuple<U...>>(out, u); }
template <class Con, class = decltype(begin(declval<Con>()))> typename enable_if <!is_same<Con, string>::value, ostream&>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; }
template <class A, class B> bool minimize(A &a, B b)  { if (a > b) { a = b; return true; } return false; }
template <class A, class B> bool maximize(A &a, B b)  { if (a < b) { a = b; return true; } return false; }

// end of template

const long long INF = 1e18;

long long sqr(int a) {
    return 1LL * a * a;
}

struct Line {
    long long a, b;
    int cnt;
    Line(long long a = 0, long long b = INF, int c = 0): a(a), b(b), cnt(c) {}
    long long eval(long long x) { return a * x + b; }
};

struct ConvexHullTrick {
    vector <Line> lines;
    int ptr;
    ConvexHullTrick(): ptr(0) {}
    bool bad(Line a, Line b, Line c) {
        return (long double) (c.b - a.b) / (a.a - c.a) < (long double) (b.b - a.b) / (a.a - b.a);
    }
    void addLine(long long a, long long b, int c) {
        Line l(a, b, c);
        while (lines.size() >= 2 && bad(lines.end()[-2], lines.back(), l)) lines.pop_back();
        lines.push_back(l);
    }
    Line getMin(long long x) {
        if (ptr >= (int) lines.size()) ptr = (int) lines.size() - 1;
        while (ptr < (int) lines.size() - 1 && lines[ptr].eval(x) > lines[ptr + 1].eval(x)) ++ptr;
        return lines[ptr];
    }
};

long long take_photos(int n, int m, int k, vector <int> X, vector <int> Y) {
    vector <pair <int, int>> squares;
    vector <int> ma(m + 1);
    REP(i, n) {
        ++X[i]; ++Y[i];
        if (X[i] > Y[i]) swap(X[i], Y[i]);
        maximize(ma[X[i]], Y[i]);
    }
    int cur = 0;
    squares.push_back(make_pair(0, 0));
    FORE(i, 1, m) {
        if (ma[i] > cur) squares.push_back(make_pair(i, ma[i]));
        cur = max(cur, ma[i]);
    }
    n = (int) squares.size() - 1;
    k = min(n, k);
    vector <long long> dp(n + 1);
    vector <int> minc(n + 1);
    auto calc = [&] (long long cost) {
        dp[0] = 0;
        ConvexHullTrick cht;
        REP(i, n + 1) {
            if (!i) dp[i] = minc[i] = 0;
            else {
                Line l = cht.getMin(squares[i].se + 1);
                dp[i] = sqr(squares[i].se + 1) + l.eval(squares[i].se + 1) + cost;
                minc[i] = l.cnt + 1;
            }
            if (i == n) return;
            cht.addLine(-2 * squares[i + 1].fi, dp[i] + sqr(squares[i + 1].fi) - sqr(max(0, squares[i].se - squares[i + 1].fi + 1)), minc[i]);
        }
    };
    long long l = 0, r = INF;
    while (l <= r) {
        long long m = l + r >> 1;
        calc(m);
        if (minc[n] <= k) r = m - 1;
        else l = m + 1;
    }
    calc(l);
    return dp[n] - k * l;
}

#ifdef LOCAL
#include "aliens.h"

#include <cstdio>
#include <cassert>

int main() {
    file("aliens");
    int n, m, k;
    assert(3 == scanf("%d %d %d", &n, &m, &k));
    std::vector<int> r(n), c(n);
    for (int i = 0; i < n; i++) {
        assert(2 == scanf("%d %d", &r[i], &c[i]));
    }
    long long ans = take_photos(n, m, k, r, c);
    
    
    printf("%lld\n", ans);
    return 0;
}
#endif

Compilation message (stderr)

aliens.cpp: In function 'long long int take_photos(int, int, int, std::vector<int>, std::vector<int>)':
aliens.cpp:114:25: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  114 |         long long m = l + r >> 1;
      |                       ~~^~~

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