oj.uz

Submission #369316

# Submission time Handle Problem Language Result Execution time Memory
369316 2021-02-21T09:50:50 Z kartel 3D Histogram (COCI20_histogram) C++14
110 / 110
 392 ms 30576 KB 
#include <bits/stdc++.h>
#define in(x) freopen(x, "r", stdin)
#define out(x) freopen(x, "w", stdout)
//#include <time.h>
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC optimize("-O3")
#define F first
#define S second
#define pb push_back
#define M ll(1e9 + 7)
#define sz(x) (int)x.size()
#define re return
#define oo ll(1e18)
#define el '\n'
#define pii pair <ll, ll>
#define all(x) (x).begin(), (x).end()
#define arr_all(x, n) (x + 1), (x + 1 + n)
#define vi vector<int>
using namespace std;
typedef long long ll;
//using namespace __gnu_pbds;
//typedef tree <ll, null_type, less_equal <ll> , rb_tree_tag, tree_order_statistics_node_update> ordered_set;
typedef long double ld;
typedef unsigned long long ull;
typedef short int si;

const int N = 2e5 + 500;
const int MS = 1e6;

ll sfa[N], sfb[N], pra[N], prb[N], a[N], b[N];
ll ans;
int n;

int root[4 * N];
ll lst[MS], cr[MS];
pair <ll, ll> ln[MS];
int siz;

int add(ll k, ll b) {
    int v = siz++;
    ln[v] = {k, b};

    return siz - 1;
}

ll cross(ll k, ll b, ll k1, ll b1) {
    return ((b - b1) / (k1 - k) + !!((b - b1) % (k1 - k)));
}

void build(int v, int l, int r) {
    int i = l;
    while (i <= r && prb[l] == prb[i])
        i++;

    root[v] = add(-prb[i - 1], prb[i - 1] * i);
    lst[root[v]] = root[v];
    cr[root[v]] = -1e18;

    int last = root[v];

    for (; i <= r;) {
        int j = i;
        while (i <= r && prb[i] == prb[j])
            i++;

        ll k = -prb[i - 1], b = prb[i - 1] * i;
        ll crp;

        while (1) {
            crp = cross(k, b, ln[last].F, ln[last].S);

            if (crp > cr[last])
                break;

            last = lst[last];
        }

        root[v] = add(k, b);
        lst[root[v]] = last;
        cr[root[v]] = crp;
        last = root[v];
    }

    if (l == r)
        return;

    int md = (l + r) >> 1;

    build(v * 2, l, md);
    build(v * 2 + 1, md + 1, r);
}

void upd_a(ll vl) {
    ans = max(ans, vl);
}

ll get(int v, int l, int r, int tl, int tr, int X) {
    if (l > r || tl > tr || tl > r || l > tr)
        return -1e18;

    if (l == tl && r == tr) {
        while (cr[root[v]] > X)
            root[v] = lst[root[v]];

        return ln[root[v]].F * X + ln[root[v]].S;
    }

    int md = (l + r) >> 1;

    return max(get(v * 2, l, md, tl, min(md, tr), X),
               get(v * 2 + 1, md + 1, r, max(md + 1, tl), tr, X));
}

void solve(int le, int ri) {
    if (le > ri)
        return;

    if (le == ri) {
        upd_a(a[le] * b[le]);
        return;
    }

    int md = (le + ri) >> 1;

    /// f -> [le, md], g -> [le, md]
    pra[md] = prb[md] = 1e9;
    for (int i = md + 1; i <= ri; i++) {
        pra[i] = min(pra[i - 1], a[i]);
        prb[i] = min(prb[i - 1], b[i]);
    }

    ll r = md + 1, f = 1e9, g = 1e9;

    for (int l = md; l >= le; l--) {
        f = min(f, a[l]);
        g = min(g, b[l]);
        while (r <= ri && pra[r] >= f && prb[r] >= g)
            r++;

        upd_a((r - l) * 1ll * f * g);
    }

    ///f -> [md, ri], g -> [md; ri]

    sfa[md] = sfb[md] = 1e9;
    for (int l = md - 1; l >= le; l--) {
        sfa[l] = min(sfa[l + 1], a[l]);
        sfb[l] = min(sfb[l + 1], b[l]);
    }

    int l = md - 1;
    f = 1e9, g = 1e9;

    for (int r = md; r <= ri; r++) {
        f = min(f, a[r]);
        g = min(g, b[r]);
        while (l >= le && sfa[l] >= f && sfb[l] >= g)
            l--;

        upd_a((r - l) * 1ll * f * g);
    }

    /// f -> [le, md], g -> [md + 1, ri]

    siz = 0;

    build(1, md + 1, ri);

    f = 1e9, g = 1e9;
    r = md + 1;
    int r1 = md + 1;

    for (int l = md; l >= le; l--) {
        f = min(f, a[l]);
        g = min(g, b[l]);

        while (r <= ri && g < prb[r])
            r++;

        while (r1 <= ri && f <= pra[r1])
            r1++;

        if (r <= r1 - 1) {
            ll cur = get(1, md + 1, ri, r, r1 - 1, l);

//            cerr << f * cur << el;

            if (cur != -1e18) {
                upd_a(f * 1ll * cur);
            }
        }
    }

    /// g -> [le, md], f -> [md + 1, ri]

    siz = 0;

    for (int i = md + 1; i <= ri; i++) {
        swap(pra[i], prb[i]);
    }

    build(1, md + 1, ri);

    f = 1e9, g = 1e9;
    r = md + 1;
    r1 = md + 1;

    for (int l = md; l >= le; l--) {
        f = min(f, a[l]);
        g = min(g, b[l]);

        while (r <= ri && g <= pra[r])
            r++;

        while (r1 <= ri && f < prb[r1])
            r1++;

        if (r1 <= r - 1) {
            ll cur = get(1, md + 1, ri, r1, r - 1, l);

            if (cur != -1e18) {
                upd_a(g * 1ll * cur);
            }
        }
    }

    //806801766313992
    //1675888823757

    solve(le, md - 1);
    solve(md + 1, ri);
}

int main()
{
//    mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());;
	ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
//	in("game.in");
//	out("game.out");
//    in("input.txt");
//    out("output.txt");

//    clock_t tStart = clock();

    cin >> n;

    for (int i = 1; i <= n; i++) {
        cin >> a[i] >> b[i];
    }

    solve(1, n);

    cout << ans;
}


/*

7
4 6 7 2 3 1 5
*/

Subtask #1
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 460 KB Output is correct
2 Correct 3 ms 460 KB Output is correct
3 Correct 2 ms 460 KB Output is correct
4 Correct 2 ms 460 KB Output is correct
5 Correct 2 ms 588 KB Output is correct
6 Correct 2 ms 460 KB Output is correct
7 Correct 1 ms 460 KB Output is correct
8 Correct 2 ms 460 KB Output is correct
9 Correct 2 ms 556 KB Output is correct
10 Correct 2 ms 588 KB Output is correct
11 Correct 0 ms 332 KB Output is correct
12 Correct 2 ms 460 KB Output is correct

Subtask #2
90.0 / 90.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 460 KB Output is correct
2 Correct 3 ms 460 KB Output is correct
3 Correct 2 ms 460 KB Output is correct
4 Correct 2 ms 460 KB Output is correct
5 Correct 2 ms 588 KB Output is correct
6 Correct 2 ms 460 KB Output is correct
7 Correct 1 ms 460 KB Output is correct
8 Correct 2 ms 460 KB Output is correct
9 Correct 2 ms 556 KB Output is correct
10 Correct 2 ms 588 KB Output is correct
11 Correct 0 ms 332 KB Output is correct
12 Correct 2 ms 460 KB Output is correct
13 Correct 278 ms 16920 KB Output is correct
14 Correct 144 ms 17240 KB Output is correct
15 Correct 392 ms 17332 KB Output is correct
16 Correct 269 ms 17332 KB Output is correct
17 Correct 362 ms 30576 KB Output is correct
18 Correct 368 ms 25772 KB Output is correct
19 Correct 328 ms 19096 KB Output is correct
20 Correct 359 ms 23876 KB Output is correct
21 Correct 300 ms 17372 KB Output is correct
22 Correct 333 ms 30528 KB Output is correct
23 Correct 22 ms 1996 KB Output is correct
24 Correct 297 ms 17020 KB Output is correct