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Submission #366783

# Submission time Handle Problem Language Result Execution time Memory
366783 2021-02-15T09:47:09 Z VEGAnn 3D Histogram (COCI20_histogram) C++14
110 / 110
 523 ms 45676 KB 
#include <bits/stdc++.h>
#define PB push_back
#define sz(x) ((int)x.size())
using namespace std;
typedef long long ll;
const int N = 200100;
const int BIG = int(4e6);
const int oo = 2e9;
const ll OO = 1e18;
ll B[BIG], ans = 0, FRM[BIG];
int n, a[N], b[N], pref[N], suf[N], pref2[N], suf2[N];
int root[4 * N], ptr[4 * N];
int LST, K[BIG], PRV[BIG];

int NEW(int nk, ll nb, ll wh){
    assert(LST < BIG);

    K[LST] = nk;
    B[LST] = nb;
    FRM[LST] = wh;
    PRV[LST] = -1;

    LST++;

    return LST - 1;
}

ll get_cross_point(int FI, int SE){
    if (K[FI] == K[SE])
        return (B[FI] > B[SE] ? -OO : OO);

    ll BB = B[FI] - B[SE];
    ll KK = K[SE] - K[FI];

    if ((BB >= 0 && KK > 0) || (BB <= 0 && KK < 0))
        return BB / KK + bool(BB % KK);
    else return BB / KK;
}

void build(int v, int l, int r){
    {
        int tit = l;

        while (tit < r && pref2[tit + 1] == pref2[l])
            tit++;

        root[v] = NEW(-pref2[tit], ll(pref2[tit]) * ll(tit), -OO);

        ptr[v] = root[v];

        for (int it = tit + 1; it <= r; it++){
            int cur = NEW(-pref2[it], ll(pref2[it]) * ll(it), -OO);

            while (PRV[ptr[v]] > 0){
                ll CR = get_cross_point(cur, ptr[v]);

                if (CR > FRM[ptr[v]]) break;

                ptr[v] = PRV[ptr[v]];
            }

            PRV[cur] = ptr[v];
            FRM[cur] = get_cross_point(cur, ptr[v]);

            ptr[v] = cur;
        }
    }

    if (l == r) return;

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

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

//3166121245150

ll get_best(int v, int tl, int tr, int ql, int qr, int X){
    if (ql > qr) return -OO;

    if (tl == ql && qr == tr){
        while (FRM[ptr[v]] > X)
            ptr[v] = PRV[ptr[v]];

        return ll(K[ptr[v]]) * ll(X) + B[ptr[v]];
    }

    int md = (tl + tr) >> 1;

    return max(get_best(v + v, tl, md, ql, min(qr, md), X),
               get_best(v + v + 1, md + 1, tr, max(md + 1, ql), qr, X));
}

void DO_IT(int l, int r){
    for (int i = l; i <= r; i++)
        swap(a[i], b[i]);

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

    suf[md + 1] = suf2[md + 1] = oo;

    for (int i = md; i >= l; i--) {
        suf[i] = min(suf[i + 1], a[i]);
        suf2[i] = min(suf2[i + 1], b[i]);
    }

    pref[md] = pref2[md] = oo;

    for (int i = md + 1; i <= r; i++) {
        pref[i] = min(pref[i - 1], a[i]);
        pref2[i] = min(pref2[i - 1], b[i]);
    }

    LST = 1;

    build(1, md + 1, r);

    {
        // min_a -- left
        // min_b -- right

        int ptr1 = md, ptr2 = md + 1;

        for (int i = md; i >= l; i--){
            while (ptr1 < r && suf[i] <= pref[ptr1 + 1])
                ptr1++;

            while (ptr2 <= r && suf2[i] < pref2[ptr2])
                ptr2++;

            if (ptr1 >= ptr2)
                ans = max(ans, get_best(1, md + 1, r, ptr2, ptr1, i - 1) * ll(suf[i]));
        }
    }
}

void calc(int l, int r){
    if (l == r) {
        ans = max(ans, ll(a[l]) * ll(b[l]));
        return;
    }

    DO_IT(l, r);
    DO_IT(l, r);

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

    {
        // min_a -- left
        // min_b -- left

        int ptr1 = md, ptr2 = md;

        for (int i = md; i >= l; i--){
            while (ptr1 < r && suf[i] <= pref[ptr1 + 1])
                ptr1++;

            while (ptr2 < r && suf2[i] <= pref2[ptr2 + 1])
                ptr2++;

            ll MN = min(ptr1, ptr2);

            if (MN > md)
                ans = max(ans, ll(suf[i]) * ll(suf2[i]) * (MN - ll(i) + 1ll));
        }
    }

    {
        // min_a -- right
        // min_b -- right

        int ptr1 = md + 1, ptr2 = md + 1;

        for (int i = md + 1; i <= r; i++){
            while (ptr1 > l && pref[i] <= suf[ptr1 - 1])
                ptr1--;

            while (ptr2 > l && pref2[i] <= suf2[ptr2 - 1])
                ptr2--;

            ll MX = max(ptr1, ptr2);

            if (MX <= md)
                ans = max(ans, ll(pref[i]) * ll(pref2[i]) * (ll(i) - ll(MX) + 1ll));
        }
    }

    calc(l, md);
    calc(md + 1, r);
}

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

#ifdef _LOCAL
    freopen("in.txt","r",stdin);
#endif // _LOCAL

    cin >> n;

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

    calc(1, n);

    cout << ans;

    return 0;
}

Subtask #1
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 460 KB Output is correct
2 Correct 2 ms 460 KB Output is correct
3 Correct 3 ms 588 KB Output is correct
4 Correct 2 ms 588 KB Output is correct
5 Correct 4 ms 588 KB Output is correct
6 Correct 3 ms 460 KB Output is correct
7 Correct 2 ms 460 KB Output is correct
8 Correct 3 ms 624 KB Output is correct
9 Correct 3 ms 588 KB Output is correct
10 Correct 5 ms 588 KB Output is correct
11 Correct 1 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 3 ms 460 KB Output is correct
2 Correct 2 ms 460 KB Output is correct
3 Correct 3 ms 588 KB Output is correct
4 Correct 2 ms 588 KB Output is correct
5 Correct 4 ms 588 KB Output is correct
6 Correct 3 ms 460 KB Output is correct
7 Correct 2 ms 460 KB Output is correct
8 Correct 3 ms 624 KB Output is correct
9 Correct 3 ms 588 KB Output is correct
10 Correct 5 ms 588 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 2 ms 460 KB Output is correct
13 Correct 384 ms 19412 KB Output is correct
14 Correct 193 ms 16404 KB Output is correct
15 Correct 523 ms 33440 KB Output is correct
16 Correct 401 ms 33420 KB Output is correct
17 Correct 490 ms 45676 KB Output is correct
18 Correct 447 ms 23376 KB Output is correct
19 Correct 455 ms 18288 KB Output is correct
20 Correct 462 ms 20744 KB Output is correct
21 Correct 393 ms 33512 KB Output is correct
22 Correct 479 ms 45504 KB Output is correct
23 Correct 29 ms 2252 KB Output is correct
24 Correct 324 ms 16536 KB Output is correct