Submission #969368

#	Time	Username	Problem	Language	Result	Execution time	Memory
969368		VinhLuu	Aliens (IOI16_aliens)	C++17	100 / 100	179 ms	19588 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], d[N], g[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){
    if(ptr > hull.size() - 1) ptr = hull.size() - 1;
    while(ptr < hull.size() - 1 && cal(ptr + 1, x) < cal(ptr, x)) ptr++;
    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);
}

pii pc(ll C){
    hull.clear();
    ptr = 0;
    d[1] = 1ll * val[p[1]] * val[p[1]] + C;
    g[1] = 1;
    for(int i = 2; 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, d[i - 1] + w, i - 1};
        add(tmp);
        auto kq = get(p[i]);
        d[i] = kq.fi + p[i] * p[i] + C;
        g[i] = g[kq.se] + 1;
//        cerr << i << " " << d[i] << " " << g[i] << " u\n";
        if(1ll * (p[i] - p[1] + val[p[1]]) * (p[i] - p[1] + val[p[1]]) + C <= d[i]){
            d[i] = 1ll * (p[i] - p[1] + val[p[1]]) * (p[i] - p[1] + val[p[1]]) + C;
            g[i] = 1;
        }
    }
    return {d[n], g[n]};
}

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;
        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;
    }
    if(n * k <= 1e7){
        nx = 1, pre = 0;

        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 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);
        }
        return f[pre][n];
    }
//    for(int i = 1; i <= n; i ++) cout << p[i] << " " << val[p[i]] << " o\n";
    ll l = 0, r = 1e18, mid, ans = 1e18;
    while(l <= r){
        mid = (l + r) / 2;
        pii kq = pc(mid);
//        cerr << mid << " " << kq.fi << " " << kq.se << " i\n";
        if(kq.se <= k){
            r = mid - 1;
            ans = kq.fi - 1ll * k * mid;
//            if(kq.fi - 1ll * k * mid == 1660355) cerr << kq.fi << " " << mid << " " << kq.se << " dcm\n";
        }else l = mid + 1;
    }
    return ans;
}

//#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:38:12: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   38 |     if(ptr > hull.size() - 1) ptr = hull.size() - 1;
      |        ~~~~^~~~~~~~~~~~~~~~~
aliens.cpp:39:15: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   39 |     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: 40 / 40