Submission #316366

#	Time	Username	Problem	Language	Result	Execution time	Memory
316366		georgerapeanu	3D Histogram (COCI20_histogram)	C++11	0 / 110	16 ms	2148 KiB

histogram

#include <bits/stdc++.h>

using namespace std;

const int NMAX = 2e5;

long long det(pair<int,int> a,pair<int,int> b,pair<int,int> c) {
    return 1LL * a.first * (b.second - c.second) + 1LL * b.first * (c.second - a.second) + 1LL * c.first * (a.second - b.second);
}

bool cmp(pair<int,int> a,pair<int,int> b) {
    return det(make_pair(0,0),a,b) > 0;
}

struct node_t {

    int lst_ind;
    vector<pair<long long,long long> > points;

    node_t operator + (const node_t &other)const {
        node_t ans;
        
        merge(points.begin(),points.end(),other.points.begin(),other.points.end(),back_inserter(ans.points),cmp);
        
        vector<pair<long long,long long> > tmp;
 
        for(auto it:ans.points) {
            while((int)tmp.size() >= 2 && det(tmp[(int)tmp.size() - 2],tmp[(int)tmp.size() - 1],it) < 0) {
                tmp.pop_back();
            }
            tmp.push_back(it);
        }
        ans.points.swap(tmp);
        ans.lst_ind = (int)ans.points.size() - 1;

        return ans;
    }

    long long query(pair<long long,long long> v) {
        while(lst_ind - 1 >= 0 && points[lst_ind].first * v.first + points[lst_ind].second * v.second <= points[lst_ind - 1].first * v.first + points[lst_ind - 1].second * v.second) {
            lst_ind--;
        }
        return points[lst_ind].first * v.first + points[lst_ind].second * v.second;
    }

    node_t() {
        lst_ind = 0;
        points = vector<pair<long long,long long> >();
    }

};

class SegmentTree {
    int n;
    vector<node_t> aint;

public:

    SegmentTree(int n,vector<pair<long long,long long> > v) {
        this->n = n;
        this->aint = vector<node_t>(2 * n + 5,node_t());
        for(int i = 1;i <= n;i++){
            aint[n + i].points = {v[i]};
        }
        for(int i = n;i;i--){
            aint[i] = aint[(i << 1)] + aint[(i << 1) | 1];
        }
    }

    long long query(int l,int r,pair<long long,long long> v) {
        long long ans = 0;
        l += n;
        r += n + 1;

        for(;l < r;l <<= 1,r <<= 1){
            if(l & 1){
                ans = max(ans,aint[l++].query(v));
            }
            if(r & 1){
                ans = max(ans,aint[--r].query(v));
            }
        }

        return ans;
    }

};

int n;
int a[NMAX + 5];
int b[NMAX + 5];

long long solve(int st,int dr) {
    if(st == dr) {
        return 1LL * a[st] * b[st];
    }

    int mid = (st + dr) / 2;

    long long ans = max(solve(st,mid),solve(mid + 1,dr));

    int mi_a = 1e9;
    int mi_b = 1e9;

    int i_a = mid;
    int i_b = mid;
    int i2_b = mid;

    vector<pair<long long,long long> > points = {};

    int mip_b = 1e9;

    for(int i = mid; i >= st; i--) {
        mip_b = min(mip_b,b[i]);
        points.push_back({1LL * mip_b,1LL * mip_b * (1 - i)});
    }
    points.push_back({0LL,0LL});
    reverse(points.begin(),points.end());

    SegmentTree aint(mid - st + 1,points);

    for(int i = mid + 1; i <= dr; i++) {
        mi_a = min(mi_a,a[i]);
        mi_b = min(mi_b,b[i]);
        while(i_a >= st && a[i_a] >= mi_a) {
            i_a--;
        }
        while(i_b >= st && b[i_b] > mi_b) {
            i_b--;
        }
        while(i2_b >= st && b[i2_b] >= mi_b) {
            i2_b--;
        }
        ans = max(ans,1LL * mi_a * mi_b * (i - max(i_a,i2_b)));
        if(i_a + 1 <= i_b) {
            ans = max(ans,aint.query(i_a + 1 - (st - 1),i_b - (st - 1),make_pair(1LL * mi_a * i,1LL * mi_a)));
        }
        ///[i_a + 1,i_b]
    }
    return ans;
}

int main() {

    scanf("%d",&n);

    for(int i = 1; i <= n; i++) {
        scanf("%d %d",&a[i],&b[i]);
    }

    long long ans = 0;

    ans = max(ans,solve(1,n));
    ans = max(ans,solve(1,n));
    swap(a,b);
    ans = max(ans,solve(1,n));
    reverse(a + 1,a + 1 + n);
    reverse(b + 1,b + 1 + n);
    ans = max(ans,solve(1,n));
    swap(a,b);

    printf("%lld\n",ans);

    return 0;
}

Compilation message (stderr)

histogram.cpp: In function 'int main()':
histogram.cpp:145:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  145 |     scanf("%d",&n);
      |     ~~~~~^~~~~~~~~
histogram.cpp:148:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  148 |         scanf("%d %d",&a[i],&b[i]);
      |         ~~~~~^~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 0 / 20
• Subtask 2: 0 / 90