oj.uz

Submission #1107193

# Submission time Handle Problem Language Result Execution time Memory
1107193 2024-11-01T01:10:10 Z lmToT27 3D Histogram (COCI20_histogram) C++17
110 / 110
 462 ms 37668 KB 
#include <bits/stdc++.h>
#define all(dataStructure) dataStructure.begin(),dataStructure.end()

typedef long long ll;

using namespace std;
namespace std {
        template <typename T, int D>
        struct _vector : public vector <_vector <T, D - 1>> {
                static_assert(D >= 1, "Dimension must be positive!");
                template <typename... Args>
                _vector(int n = 0, Args... args) : vector <_vector <T, D - 1>> (n, _vector <T, D - 1> (args...)) {}
        };
        // _vector <int, 3> a(n, m, k);: int a[n][m][k].
        // _vector <int, 3> a(n, m, k, x);: int a[n][m][k] initialized with x.
        template <typename T>
        struct _vector <T, 1> : public vector <T> {
                _vector(int n = 0, const T& val = T()) : vector <T> (n, val) {}
        };
}

const int MAX = 2e5 + 3;
const ll MOD[] = {1000000007, 998244353};

int n;
ll a[MAX], b[MAX];
ll A[MAX], B[MAX];

struct eq_t {
        ll a, b;

        eq_t(ll a = 0, ll b = 0) : a(a), b(b) {}

        bool operator < (const eq_t &other) const {
                return a < other.a;
        }

        ll operator () (ll x) {
                return a * x + b;
        }
};

bool bad(eq_t A, eq_t B, eq_t C) {
        return (A.a - C.a) * (A.b - B.b) <= (A.a - B.a) * (A.b - C.b);
}

vector <eq_t> st[MAX << 2];

void modify(vector <eq_t> &f) {
        sort(all(f));
        vector <eq_t> hull;
        for (auto &x : f) {
                while (hull.size() >= 2 && bad(hull[(int)hull.size() - 2], hull.back(), x)) hull.pop_back();
                hull.push_back(x);
        }
        f = hull;
}

void build(int i, int id, int l, int r) {
        st[id].clear();
        if (l == r) {
                st[id].push_back(eq_t(B[l], B[l] * abs(l - i)));
        } else {
                int mid = (l + r) / 2;
                build(i, id << 1, l, mid);
                build(i, id << 1 | 1, mid + 1, r);
                st[id] = st[id << 1];
                for (auto &x : st[id << 1 | 1]) st[id].push_back(x);
                modify(st[id]);
        }
}

ll getMax(ll x, int u, int v, int id, int l, int r) {
        if (u > v || v < l || r < u) return 0;
        if (u <= l && r <= v) {
                if (st[id].empty()) return 0;
                ll res = st[id][0](x), optL, optR;
                int L = 0, R = (int)st[id].size() - 1, mid;
                while (L < R) {
                        mid = (L + R) / 2;
                        optL = st[id][mid](x);
                        optR = st[id][mid + 1](x);
                        res = max({res, optL, optR});
                        if (optL < optR) L = mid + 1;
                        else R = mid;
                }
                return res;
        }
        int mid = (l + r) / 2;
        return max(getMax(x, u, v, id << 1, l, mid), getMax(x, u, v, id << 1 | 1, mid + 1, r));
}

ll dnc(int L, int R) {
        if (L == R) return a[L] * b[L];
        int mid = (L + R) / 2;
        ll res = max(dnc(L, mid), dnc(mid + 1, R));
        
        A[mid] = a[mid];
        B[mid] = b[mid];
        A[mid + 1] = a[mid + 1];
        B[mid + 1] = b[mid + 1];

        for (int i = mid - 1; i >= L; i--) {
                A[i] = min(A[i + 1], a[i]);
                B[i] = min(B[i + 1], b[i]);
        }

        for (int i = mid + 2; i <= R; i++) {
                A[i] = min(A[i - 1], a[i]);
                B[i] = min(B[i - 1], b[i]);
        }

        if (1) {
                int l = mid, r = mid;
                build(mid, 1, mid + 1, R);
                for (int i = mid; i >= L; i--) {
                        while (r < R && A[r + 1] >= A[i]) r++;
                        while (l < r && B[l + 1] >= B[i]) l++;

                        res = max(res, A[i] * B[i] * (l - i + 1));
                        res = max(res, A[i] * getMax(mid  - i + 1, l + 1, r, 1, mid + 1, R));             
                }
        }

        if (1) {
                int l = mid + 1, r = mid + 1;
                build(mid + 1, 1, L, mid);
                for (int i = mid + 1; i <= R; i++) {
                        while (l > L && A[l - 1] >= A[i]) l--;
                        while (r > l && B[r - 1] >= B[i]) r--;

                        res = max(res, A[i] * B[i] * (i - r + 1));
                        res = max(res, A[i] * getMax(i - mid, l, r - 1, 1, L, mid));
                }
        }

        return res;
}

void Solve() {
        cin >> n;
        for (int i = 1; i <= n; i++) {
                cin >> a[i] >> b[i];
        }
        cout << dnc(1, n);
}

int32_t main() {
        std::ios_base::sync_with_stdio(0);
        std::cin.tie(0); std::cout.tie(0);

        #define TASK ""
        if (fopen(TASK".INP", "r")) {
                freopen(TASK".INP", "r", stdin);
                freopen(TASK".OUT", "w", stdout);
        }
        
        if (fopen("TASK.INP", "r")) {
                freopen("TASK.INP", "r", stdin);
                freopen("TASK.OUT", "w", stdout);
        }
        
        /* int TEST = 1; cin >> TEST; while (TEST--) */ Solve();

        cerr << "\nTime elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << "s\n";
        return 0;
}

Compilation message

histogram.cpp: In function 'int32_t main()':
histogram.cpp:154:24: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  154 |                 freopen(TASK".INP", "r", stdin);
      |                 ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
histogram.cpp:155:24: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  155 |                 freopen(TASK".OUT", "w", stdout);
      |                 ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
histogram.cpp:159:24: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  159 |                 freopen("TASK.INP", "r", stdin);
      |                 ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
histogram.cpp:160:24: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  160 |                 freopen("TASK.OUT", "w", stdout);
      |                 ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 25168 KB Output is correct
2 Correct 6 ms 25168 KB Output is correct
3 Correct 6 ms 25168 KB Output is correct
4 Correct 6 ms 25168 KB Output is correct
5 Correct 6 ms 25168 KB Output is correct
6 Correct 6 ms 25168 KB Output is correct
7 Correct 6 ms 25180 KB Output is correct
8 Correct 6 ms 25168 KB Output is correct
9 Correct 6 ms 25168 KB Output is correct
10 Correct 7 ms 25168 KB Output is correct
11 Correct 4 ms 25168 KB Output is correct
12 Correct 6 ms 25168 KB Output is correct

Subtask #2
90.0 / 90.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 25168 KB Output is correct
2 Correct 6 ms 25168 KB Output is correct
3 Correct 6 ms 25168 KB Output is correct
4 Correct 6 ms 25168 KB Output is correct
5 Correct 6 ms 25168 KB Output is correct
6 Correct 6 ms 25168 KB Output is correct
7 Correct 6 ms 25180 KB Output is correct
8 Correct 6 ms 25168 KB Output is correct
9 Correct 6 ms 25168 KB Output is correct
10 Correct 7 ms 25168 KB Output is correct
11 Correct 4 ms 25168 KB Output is correct
12 Correct 6 ms 25168 KB Output is correct
13 Correct 423 ms 35568 KB Output is correct
14 Correct 342 ms 36856 KB Output is correct
15 Correct 347 ms 35496 KB Output is correct
16 Correct 431 ms 35400 KB Output is correct
17 Correct 450 ms 37540 KB Output is correct
18 Correct 380 ms 37164 KB Output is correct
19 Correct 349 ms 36424 KB Output is correct
20 Correct 377 ms 37092 KB Output is correct
21 Correct 362 ms 35400 KB Output is correct
22 Correct 462 ms 37668 KB Output is correct
23 Correct 33 ms 26012 KB Output is correct
24 Correct 265 ms 35156 KB Output is correct