제출 #632835

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
632835		rainliofficial	Aliens (IOI16_aliens)	C++14	4 / 100	1 ms	300 KiB

aliens

#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pii;
template<class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
#define sz(x) (int)x.size()

const int MAXN = 2e5+5;
const ll INF = 1e18;

void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}

template<typename T, typename V>
void __print(const pair<T, V> &x);
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? ", " : ""), __print(i); cerr << "}";}
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ", "; __print(x.second); cerr << '}';}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifdef DEBUG
#define dbg(x...) cerr << "\e[91m"<<__func__<<":"<<__LINE__<<" [" << #x << "] = ["; _print(x); cerr << "\e[39m" << endl;
#else
#define dbg(x...)
#endif

struct Point{
    ll r, c, id, cnt;
    bool operator<(const Point& o) const{
        if (r != o.r){
            return r < o.r;
        }
        return c < o.c;
    }
};

bool byr(const Point& a, const Point& b){
    return a.r != b.r ? a.r < b.r : a.c > b.c;  // sort by smaller row, then by greater col
}

bool byc(const Point& a, const Point& b){
    return a.c != b.c ? a.c < b.c : a.r > b.r; // smaller col, smaller row
}

ll sq(ll x){
    return x*x;
}
ll get(pii a, int c){
    return a.first * c + a.second;
}
double intersectX(pii a, pii b){
    return (double)(b.second - a.second)/(a.first - b.first); // (b2 - b1)/(m1 - m2)
}

/*
ll subtask5(int n, int k, vector<Point>& arr){
    vector<vector<ll>> dp(n+1, vector<ll>(k+1, INF)); // dp[i][j] = max cover up to ith point after taking j pictures
    for (int i=0; i<=k; i++) dp[0][i] = 0;

    vector<deque<pii>> lines(k+1);
    vector<int> pj(k+1, 1);
    for (int i=1; i<=n; i++){
        for (int j=1; j<=k; j++){
            ll overlap = i > 1 && arr[i-2].c >= arr[i-1].r ? sq(arr[i-2].c - arr[i-1].r + 1) : 0;
            pii cur = {-2*(arr[i-1].r - 1), sq(arr[i-1].r - 1) + dp[i-1][j-1] - overlap};
            while (sz(lines[j]) > 1 && intersectX(cur, lines[j][sz(lines[j])-2]) < intersectX(lines[j].back(), lines[j][sz(lines[j])-2])){
                lines[j].pop_back();
            }
            lines[j].push_back(cur);

            if (j > 1 && !lines[j].empty()){
                while (sz(lines[j]) > 1 && get(lines[j].front(), arr[i-1].c) >= get(lines[j][1], arr[i-1].c)){
                    lines[j].pop_front();
                }
                dp[i][j] = sq(arr[i-1].c) + get(lines[j].front(), arr[i-1].c);
            }else{
                // take all points before in 1 single picture
                dp[i][j] = sq(arr[i-1].c - arr[0].r + 1);
            }
            // for (int ip=1; ip<=i; ip++){
            //     ll area = sq(arr[i-1].c - arr[ip-1].r + 1);
            //     overlap = ip > 1 && arr[ip-2].c >= arr[ip-1].r ? sq(arr[ip-2].c - arr[ip-1].r + 1) : 0;
            //     if (dp[i][j] > dp[ip-1][j-1] + area - overlap){
            //         dbg(dp[i][j]);
            //     }
            // }
        }
    }
    // for (int i=0; i<=n; i++){
    //     for (int j=0; j<=k; j++){
    //         cout << dp[i][j] << " ";
    //     }
    //     cout << "\n";
    // }
}
*/


pii solve(ll penalty, vector<Point>& arr, int n, int k){
    vector<pii> dp(n+1); // dp[i] = min area needed with penalty to cover the first i pictures
    deque<pair<pii, ll>> lines;
    for (int i=1; i<=n; i++){
        ll overlap = i > 1 && arr[i-2].c >= arr[i-1].r ? sq(arr[i-2].c - arr[i-1].r + 1) : 0;
        pii cur = {-2*(arr[i-1].r - 1), sq(arr[i-1].r - 1) + dp[i-1].first - overlap + penalty};
        while (sz(lines) > 1 && intersectX(cur, lines[sz(lines)-2].first) < intersectX(lines.back().first, lines[sz(lines)-2].first)){
            lines.pop_back();
        }
        lines.push_back({cur, dp[i-1].second + 1});

        while (sz(lines) > 1 && get(lines.front().first, arr[i-1].c) >= get(lines[1].first, arr[i-1].c)){
            lines.pop_front();
        }
        dp[i] = {sq(arr[i-1].c) + get(lines.front().first, arr[i-1].c), lines.front().second};
    }
    return dp[n];
}

long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
    // reflect the points under the diag
    vector<Point> arr;
    int tot = 0;
    set<Point> allPoints;
    for (int i=0; i<n; i++){
        if (r[i] > c[i]){
            swap(r[i], c[i]);
        }
        Point cur = {r[i], c[i], tot, 1};
        auto it = allPoints.find(cur);
        if (it != allPoints.end()){
            arr[(*it).id].cnt++;
        }else{
            arr.push_back(cur);
            allPoints.insert(cur);
            tot++;
        }
    }
    n = tot;
    sort(arr.begin(), arr.end(), byr);
    set<Point, decltype(&byc)> seen(&byc);
    for (int i=0; i<n; i++){
        auto it = seen.lower_bound(arr[i]);
        if (it == seen.end()){
            seen.insert(arr[i]);
        }else{
            // Point upd = *it;
            // upd.cnt++;
            // seen.erase(it);
            // seen.insert(upd);
        }
    }

    arr.clear();
    for (Point x : seen){
        // cout << x.r << " " << x.c << " " << x.id << " " << x.cnt << "\n";
        arr.push_back(x);
    }

    n = sz(arr);

    ll low = 0, high = 1e12;
    while (low < high){
        ll mid = (low + high)/2;
        if (solve(mid, arr, n, k).second <= k){
            // we can lower the price/penalty per photo
            high = mid;
        }else{
            low = high + 1;
        }
    }

    // run dp
    pii ans = solve(high, arr, n, k);
    return ans.first - ans.second * high;
}


/**
 * Debugging checklist:
 * - Reset everything after each TC
 * - Integer overflow, index overflow
 * - Special cases?
 */

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