Submission #1175738

#	Time	Username	Problem	Language	Result	Execution time	Memory
1175738		totoro	Aliens (IOI16_aliens)	C++17	60 / 100	2136 ms	953092 KiB

aliens

// SOLVED SUBTASK 1   (04 pts)
// SOLVED SUBTASK 2   (12 pts)
// SOLVED SUBTASK 3   (09 pts)
// UNSOLVED SUBTASK 4 (16 pts)
// UNSOLVED SUBTASK 5 (19 pts)
// UNSOLVED SUBTASK 6 (40 pts)
// [+-+]----------------------
// TOTAL     25/100 pts

#include "aliens.h"

#include <algorithm>
#include <climits>
#include <cmath>
#include <iostream>
#include <vector>

struct Coordinate {
    long long row, col;
    Coordinate(long long row, long long col) : row(std::min(row, col)), col(std::max(row, col)) {}
    bool operator<(const Coordinate& other) const {
        if (row == other.row) {
            return col > other.col;
        }
        return row < other.row;
    }
};

struct Range {
    long long start, end;
    Range(long long start, long long end) : start(start), end(end) {};
    long long merge(const Range& other) const {
        return 2 * (other.start - start) * (other.end - end) - (other.start > end ? (other.start - end - 1) * (other.start - end - 1) : 0);
    }
};

struct Parabola {
    double h, v;

    double evaluate(double x) {
        return (x - h) * (x - h) + v;
    }
};

double intersect(Parabola a, Parabola b) {
    return (b.h * b.h + b.v - a.h * a.h - a.v) / (2.0 * (b.h - a.h));
}

struct ConvexHull {
    std::vector<Parabola> parabolas;
    std::vector<double> left, right;

    void insert(Parabola p) {
        while (!parabolas.empty() && intersect(p, parabolas.back()) <= left.back()) {
            parabolas.pop_back();
            left.pop_back();
            right.pop_back();
        }
        if (parabolas.empty()) {
            parabolas.push_back(p);
            left.push_back(-1e18);  // neg infty
            right.push_back(1e18);  // infty
        } else {
            double x = intersect(p, parabolas.back());
            right.back() = x;
            parabolas.push_back(p);
            left.push_back(x);
            right.push_back(1e18);  // infty
        }
        // std::cout << "inserted (x-" << p.h << ")^2 + " << p.v << '\n';
    }

    double min(double x) {
        int index = std::lower_bound(left.begin(), left.end(), x) - left.begin() - 1;
        return parabolas[index].evaluate(x);
    }
};

long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
    std::vector<Coordinate> points;
    for (size_t i = 0; i < n; ++i) {
        points.push_back(Coordinate(r[i], c[i]));
    }
    std::sort(points.begin(), points.end());

    std::vector<Range> ranges;
    long long furthestStart = -1;
    long long furthestEnd = -1;
    for (size_t i = 0; i < points.size(); ++i) {
        Coordinate point = points[i];
        if (point.row > furthestStart && point.col > furthestEnd) {
            ranges.emplace_back(point.row, point.col);
            furthestStart = point.row;
            furthestEnd = point.col;
        }
    }

    std::vector<std::vector<long long>> dp;
    std::vector<ConvexHull> hulls(k + 1);
    ranges.push_back({(long long)1e15, (long long)1e15});
    for (size_t range = 0; range < ranges.size() - 1; ++range) {
        dp.emplace_back();
        for (size_t coverCount = 1; coverCount <= k; ++coverCount) {
            if (coverCount == 1 || range == 0) {
                dp[range].push_back((ranges[range].end - ranges[0].start + 1) * (ranges[range].end - ranges[0].start + 1));
                hulls[coverCount].insert(Parabola{(double)ranges[range + 1].start, (ranges[range].end - ranges[0].start + 1) * (ranges[range].end - ranges[0].start + 1) - std::pow(std::max(0ll, ranges[range].end - ranges[range + 1].start + 1), 2)});
                continue;
            }

            long long best = hulls[coverCount - 1].min(ranges[range].end + 1);
            hulls[coverCount].insert(Parabola{(double)ranges[range + 1].start, (double)best - std::pow(std::max(0ll, ranges[range].end - ranges[range + 1].start + 1), 2)});
            dp[range].push_back(best);
        }
    }

    return dp[ranges.size() - 2][k - 1];
}

Compilation message (stderr)

aliens.h:1:9: warning: #pragma once in main file
    1 | #pragma once
      |         ^~~~
aliens_c.h:1:9: warning: #pragma once in main file
    1 | #pragma once
      |         ^~~~

• Subtask 1: 4 / 4
• Subtask 2: 12 / 12
• Subtask 3: 9 / 9
• Subtask 4: 16 / 16
• Subtask 5: 19 / 19
• Subtask 6: 0 / 40