Submission #969338

#	Time	Username	Problem	Language	Result	Execution time	Memory
969338		VinhLuu	Aliens (IOI16_aliens)	C++17	60 / 100	2043 ms	16616 KiB

aliens

//#pragma GCC optimize("O3,unroll-loops")
//#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include <bits/stdc++.h>
//#define int long long
#define ll long long
#define fi first
#define se second
#define pb push_back
#define all(lmao) lmao.begin(), lmao.end()

using namespace std;

typedef pair<ll,ll> pii;
typedef tuple<int,int,int> tp;
const int N = 1e6 + 5;
//const int mod = 1e9 + 7;
const ll oo = 5e18;

ll n, m, k, val[N], f[5][N], pre, nx, p[N];

struct line{
    ll x, y;
    int id;
};

vector<line> hull;
int ptr = 0;

bool kt(line a, line b, line c){
    return (double)(c.y - b.y) / (double)(b.x - c.x) < (double)(b.y - a.y) / (double)(a.x - b.x);
}

ll cal(int w, ll a){
    return 1ll * hull[w].x * a + hull[w].y;
}

pii get(ll x){
//    ll ans = cal(0, x), pos = 0;
//    for(int i = 0; i < hull.size(); i ++){
//        cerr << cal(i, x) << " " << hull[i].x <<" " << hull[i].y << " o\n";
//        if(cal(i, x) < ans){
//            ans = cal(i, x);
//            pos = i;
//        }
//    }
//    cerr << " h\n";

    if(ptr > hull.size() - 1) ptr = hull.size() - 1;
    while(ptr < hull.size() - 1 && cal(ptr + 1, x) <= cal(ptr, x)) ptr++;
//    cerr << hull.size() << " " << pos << " " << ptr << " " << cal(ptr + 1, x) << " " << cal(ptr, x) << " y\n";
    return {cal(ptr, x), hull[ptr].id};
}

void add(line x){
    while(hull.size() >= 2 && kt(hull[hull.size() - 2], hull.back(), x)) hull.pop_back();
    hull.push_back(x);
}

ll take_photos(int _n,int _m,int _k,vector<int> R,vector<int> C){
    n = _n, m = _m, k = _k;
    deque<int> sk;
    for(int i = 0; i < n; i ++){
        ll r = ++R[i], c = ++C[i];
        if(r <= c) val[c] = max(val[c], c - r + 1);
        else val[r] = max(val[r], r - c + 1);
    }
    for(int i = 1; i <= m; i ++){
        if(!val[i]) continue;
//        cout << i << " " << val[i] << " u\n";
        while(!sk.empty() && i - val[i] + 1 <= sk.front() - val[sk.front()] + 1) sk.pop_front();
        sk.push_front(i);
    }
    vector<pii> vr;
    int t = 0;
    while(!sk.empty()){
        p[++t] = sk.back();
        sk.pop_back();
    }
    n = t;
    if(n <= k){
        ll ans = 1ll * val[p[1]] * val[p[1]];
        for(int i = 2; i <= n; i ++){
            ans += 1ll * val[p[i]] * val[p[i]] - 1ll * max(0ll, val[p[i]] - p[i] + p[i - 1]) * max(0ll, val[p[i]] - p[i] + p[i - 1]);
        }
        return ans;
    }
    nx = 1, pre = 0;
//    for(int i = 1; i <= n; i ++){
//        cout << p[i] << " " << val[p[i]] << " t\n";
//    }
    for(int i = 1; i <= n; i ++) f[0][i] = 1ll * (p[i] - p[1] + val[p[1]]) * (p[i] - p[1] + val[p[1]]);
//    for(int i = 1; i <= n; i ++) cout << f[0][i] << " ";
//    cout << "\n";

    for(int j = 2; j <= k; j ++){
        hull.clear();
        ptr = 0;
        for(int i = j; i <= n; i ++){
            ll X = val[p[i]] - p[i];
            ll w = 1ll * X * X - 1ll * max(0ll, val[p[i]] - p[i] + p[i - 1])
                                    * max(0ll, val[p[i]] - p[i] + p[i - 1]);
            line tmp = {2 * X, f[pre][i - 1] + w, i - 1};
            add(tmp);
            f[nx][i] = get(p[i]).first + p[i] * p[i];
        }
        swap(pre, nx);
    }
//    cerr << f[pre][n] << "\n";
    return f[pre][n];
}

//#define lpv
#ifdef lpv

signed main(){
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);

    #define task "v"
    if(fopen(task ".inp","r")){
        freopen(task ".inp","r",stdin);
        freopen(task ".out","w",stdout);
    }

    int n, m, k; cin >> n >> m >> k;
    vector<int> r(n), c(n);
    for (int i = 0; i < n; ++i) cin >> r[i] >> c[i];

    cout << take_photos(n, m, k, r, c) << "\n";
}

#endif // lpv

Compilation message (stderr)

aliens.cpp: In function 'pii get(long long int)':
aliens.cpp:48:12: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   48 |     if(ptr > hull.size() - 1) ptr = hull.size() - 1;
      |        ~~~~^~~~~~~~~~~~~~~~~
aliens.cpp:49:15: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   49 |     while(ptr < hull.size() - 1 && cal(ptr + 1, x) <= cal(ptr, x)) ptr++;
      |           ~~~~^~~~~~~~~~~~~~~~~

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