Submission #309789

#	Time	Username	Problem	Language	Result	Execution time	Memory
309789		phathnv	Aliens (IOI16_aliens)	C++11	60 / 100	2085 ms	9180 KiB

aliens

#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

struct segment{
    int l, r;
    segment(int _l, int _r){
        l = _l;
        r = _r;
    }
};

struct line{
    ll a, b;
    line(ll _a = 0, ll _b = 0){
        a = _a;
        b = _b;
    }
};

struct convexHull{
    vector <line> d;
    int ptr;
    void reset(){
        d.clear();
        ptr = 0;
    }
    ll calcY(const line &l, ll x){
        return l.a * x + l.b;
    }
    bool bad(const line &l1, const line &l2, const line &l3){
        return (l2.a - l3.a) * (l2.b - l1.b) >= (l1.a - l2.a) * (l3.b - l2.b);
    }
    void add(const line &newLine){
        while (d.size() > 1){
            if (bad(d[d.size() - 2], d[d.size() - 1], newLine))
                d.pop_back();
            else
                break;
        }
        d.push_back(newLine);
    }
    ll getMin(ll x){
        assert(!d.empty());
        ptr = min(ptr, (int) d.size() - 1);
        while (ptr < (int) d.size() - 1)
            if (calcY(d[ptr], x) >= calcY(d[ptr + 1], x))
                ptr++;
            else
                break;
        return calcY(d[ptr], x);
    }
} cvh;

int n, m, k;
vector <segment> segs;
vector <vector <ll> > dp;

void prepare(){
    sort(segs.begin(), segs.end(), [](const segment &a, const segment &b){
        if (a.l != b.l)
            return a.l < b.l;
        return a.r > b.r;
    });

    vector <segment> tmp;
    int maxR = -1;
    for(segment s : segs){
        if (s.r > maxR)
            tmp.push_back(s);
        maxR = max(maxR, s.r);
    }
    segs = tmp;
    n = segs.size();
}

ll cost(int l, int r){
    assert(l <= r || l > 0);
    int w = segs[r].r - segs[l].l + 1;
    int intersect = max(0, segs[l - 1].r - segs[l].l + 1);
    return (ll) w * w - (ll) intersect * intersect;
}

ll solve(){
    segs.insert(segs.begin(), segment(-1, -1));
    dp.resize(2, vector<ll>(n + 1));

    dp[0][0] = dp[1][0] = 0;
    for(int i = 1; i <= n; i++)
        dp[1][i] = cost(1, i);

    for(int i = 2; i <= k; i++){
        int id = i & 1;
        cvh.reset();
        cvh.add(line(-2 * segs[1].l, (ll) segs[1].l * segs[1].l));
        for(int j = 1; j <= n; j++){
            dp[id][j] = cvh.getMin(segs[j].r + 1) + (ll) (segs[j].r + 1) * (segs[j].r + 1);
            cvh.add(line(-2 * segs[j + 1].l, (ll) segs[j + 1].l * segs[j + 1].l + dp[id ^ 1][j]
                         - (ll) max(0, segs[j].r - segs[j + 1].l + 1) * max(0, segs[j].r - segs[j + 1].l + 1)));
        }
    }

    return dp[k & 1][n];
}

ll take_photos(int _n, int _m, int _k, vector<int> r, vector<int> c){
    n = _n;
    m = _m;
    k = _k;
    for(int i = 0; i < n; i++)
        segs.push_back(segment(min(r[i], c[i]), max(r[i], c[i])));

    prepare();
    return solve();
}

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