Submission #1075950

#	Time	Username	Problem	Language	Result	Execution time	Memory
1075950		steveonalex	Aliens (IOI16_aliens)	C++17	100 / 100	189 ms	10108 KiB

aliens

#include "aliens.h"
#include <bits/stdc++.h>
 
using namespace std;
 
typedef long long ll;
typedef unsigned long long ull;
 
#define MASK(i) (1LL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
#define block_of_code if(true)
 
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(a, b);}
ll lcm(ll a, ll b){return a / gcd(a, b) * b;}
 
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ll mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
 
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll rngesus(ll l, ll r){return l + (ull) rng() % (r - l + 1);}
double rngesus_d(double l, double r){
    double cur = rngesus(0, MASK(60) - 1);
    cur /= MASK(60) - 1;
    return l + cur * (r - l);
}
 
template <class T1, class T2>
    bool maximize(T1 &a, T2 b){
        if (a < b) {a = b; return true;}
        return false;
    }
 
template <class T1, class T2>
    bool minimize(T1 &a, T2 b){
        if (a > b) {a = b; return true;}
        return false;
    }
 
template <class T>
    void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
        for(auto item: container) out << item << separator;
        out << finish;
    }
 
template <class T>
    void remove_dup(vector<T> &a){
        sort(ALL(a));
        a.resize(unique(ALL(a)) - a.begin());
    }

const ll INF = 1e18 + 69;

ll sqr(ll x){return x * x;}

vector<pair<int, int>> compress(vector<pair<int, int>> a){
    vector<pair<int, int>> tmp = a;
    a.clear();
    for(pair<int, int> i: tmp){
        if (a.empty() || a.back().second != i.second) a.push_back(i);
        else minimize(a.back().first, i.first);
    }
    return a;
}

 
struct CHT{
    #define Node pair<ll, ll>
    vector<Node> a;
    vector<int> cnt;
    vector<double> bubble;
    bool flag;

    // if flag = 0: if inserted in decreasing order, return min, otherwise return max
    // flag = 1: the opposite
 
    CHT(bool _flag){
        flag = _flag;
    }
 
    double getInter(Node a, Node b){
        double x = (double) (b.second - a.second) / (a.first - b.first);
        return x;
    }
 
    void add(Node x, int c, bool isMin = 1){
        if (a.empty()) {a.push_back(x); cnt.push_back(c); return;}
        if (a.back().first == x.first){
            if (isMin) {
                if (minimize(a.back().second, x.second)) cnt.back() = c;
            }
            else {
                if (maximize(a[a.size() - 1].second, x.second)) cnt.back() = c;
            }
            if (a.back().second == x.second )
                minimize(cnt.back(), c);
            return;
        }
        while(a.size() >= 2){
            double x1 = getInter(a.back(), x), x2 = bubble.back();
            if (flag){
                if (x1 >= x2) break;
            }
            else{
                if (x1 <= x2) break;
            }
            a.pop_back(); bubble.pop_back(); cnt.pop_back();
        }
        bubble.push_back(getInter(a.back(), x));
        a.push_back(x);
        cnt.push_back(c);
    }
 
    pair<ll, int> get(ll x){
        if (a.empty()) return make_pair(INF, 0);
        long idx;
        if (flag) idx = lower_bound(ALL(bubble),x) - bubble.begin();
        else idx = lower_bound(ALL(bubble), x, greater<double>()) - bubble.begin();
        return make_pair(a[idx].first * x + a[idx].second, cnt[idx]);
    }
};

int n;
vector<pair<int, int>> point;
vector<int> suff_min, nxt;

pair<ll, ll> go(ll x){
    vector<ll> dp(n+1, INF);
    vector<int> cnt(n+1);
    dp[0] = 0;
    CHT hull_min(1);
    int j = 1;
    for(int i = 1; i<=n; ++i) {
        while(j <= nxt[i+1]){
            if (dp[j-1] != INF) 
                hull_min.add({-2 * suff_min[j], sqr(suff_min[j]) + dp[j-1]}, cnt[j-1]);
            j++;
        }
        int L = suff_min[i+1];
        ll lmao = 0;
        if (L <= point[i].second) lmao = sqr(point[i].second - L + 1);
        tie(dp[i], cnt[i]) = hull_min.get(point[i].second + 1);
        cnt[i]++;
        if (dp[i] != INF){
            dp[i] += sqr(point[i].second + 1) - lmao + x;
        }
    }

    // cout << "Mid = " << x << "\n";
    // printArr(dp); printArr(cnt);

    return make_pair(dp.back(), cnt.back());
}

ll take_photos(int _n, int m, int k, vector<int> R, vector<int> C) {
    n = _n;
    for(int i = 0; i<n; ++i) {
        R[i]++; C[i]++;
        if (R[i] > C[i]) swap(R[i], C[i]);
        point.push_back({R[i], C[i]});
    }
    point.push_back({0, 0});

    sort(ALL(point), [](pair<int, int> x, pair<int, int> y){return x.second < y.second;});

    point = compress(point);
    n = point.size() - 1;
    suff_min = vector<int>(n+2, m+1);
    for(int i = n; i>=0; --i)
        suff_min[i] = min(point[i].first, suff_min[i+1]);
    nxt = vector<int>(n+2);
    for(int i = 1; i<=n+1; ++i){
        if (suff_min[i] != suff_min[i-1]) nxt[i] = i-1;
        else nxt[i] = nxt[i-1];
    }

    ll l = 0, r = 1e14;
    while(l < r){
        ll mid = (l + r) >> 1;
        if (go(mid).second <= k) r = mid;
        else l = mid + 1;
    }

    return go(l).first - k * l;
}


 
// int main(void){
//     ios::sync_with_stdio(0);cin.tie(0); cout.tie(0);
//     clock_t start = clock();
 
//     int n, m, k; cin >> n >> m >> k;
//     vector<int> r(m), c(m);
//     for(int i = 0; i<n; ++i) cin >> r[i] >> c[i];

//     cout << take_photos(n, m, k, r, c) << "\n";
 
//     cerr << "Time elapsed: " << clock() - start << " ms\n";
//     return 0;
// }

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