Submission #709995

#	Time	Username	Problem	Language	Result	Execution time	Memory
709995		alvingogo	Road Construction (JOI21_road_construction)	C++14	100 / 100	3365 ms	14260 KiB

road_construction

#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#define AquA cin.tie(0);ios_base::sync_with_stdio(0);
#define fs first
#define sc second
#define p_q priority_queue
#define int long long
using namespace std;

/*

never did before, write down here

we want to find out the minimum k mahhaton dist
transform the (x, y) into (x+y, x-y)
so that |x-a|+|y-b| = max(|x'-a'|,|y'-b'|)

and binary search the k, find how many pair of points dis <= k

actually, it's like: 
maintain a single-point-modify-range-query-sum DS
scan one axis, the DS is for another axis, when we want to cal all points whose x' = z
just add the Y to the DS, and count the amount of [Y-k, Y+k], 
wow, not that hard, right?  

we need to find the 1st to kth smallest distance

find the k-th smallest distance, let it be x

for all dist<x, the sum is small enough so we can iterate all of it

let's go

*/

struct BIT{
    int n;
    vector<int> bt;
    void init(int x){
        n=x;
        bt.resize(x+1);
    }
    void update(int x,int y){
        x++;
        for(;x<=n;x+=(x&-x)){
            bt[x]+=y;
        }
    }
    int query(int x){
        int ans=0;
        x++;
        for(;x>0;x-=(x&-x)){
            ans+=bt[x];
        }
        return ans;
    }
    int ask(int l,int r){
        return query(r)-query(l-1);
    }
}bt;

signed main(){
    AquA;
    //freopen("01-03.txt","r",stdin);
    //freopen("abc.txt","w",stdout);
    int n,m;
    cin >> n >> m;
    vector<pair<int,int> > v;
    vector<int> g;
    for(int i=0;i<n;i++){
        int a,b;
        cin >> a >> b;
        v.push_back({a+b,a-b});
        g.push_back(a-b);
    }
    sort(v.begin(),v.end());
    sort(g.begin(),g.end());
    g.erase(unique(g.begin(),g.end()),g.end());
    auto lis=[&](int x){
        return lower_bound(g.begin(),g.end(),x)-g.begin();
    };
    bt.init(g.size());
    for(auto &h:v){
        h.sc=lis(h.sc);
    }
    auto cal=[&](int k){
        int z=0;
        int ans=0;
        for(int i=0;i<n;i++){
            while(z<i && v[z].fs+k<v[i].fs){
                bt.update(v[z].sc,-1);
                z++;
            }
            int l=lis(g[v[i].sc]-k),r=upper_bound(g.begin(),g.end(),g[v[i].sc]+k)-g.begin()-1;
            ans+=bt.ask(l,r);
            bt.update(v[i].sc,1);
        }
        while(z<n){
            bt.update(v[z].sc,-1);
            z++;
        }
        return ans;
    };
    int l=0,r=9e10;
    while(r>l){
        int mid=(l+r+1)/2;
        //cout << l << " " << mid << " " << r << "\n";
        //cout << cal(mid) << "\n";
        if(cal(mid)>m){
            r=mid-1;
        }
        else{
            l=mid;
        }
    }
    vector<int> ret;
    set<pair<int,int> > s;
    int z=0;
    for(int i=0;i<n;i++){
        while(z<i && v[z].fs+l<v[i].fs){
            s.erase({g[v[z].sc],v[z].fs});
            z++;
        }
        for(auto h=s.lower_bound({g[v[i].sc]-l,-3e10});h!=s.end() && ((*h).fs-l<=g[v[i].sc]);h=next(h)){
            ret.push_back(max(v[i].fs-(*h).sc,abs(g[v[i].sc]-(*h).fs)));
        }
        s.insert({g[v[i].sc],v[i].fs});
    }
    sort(ret.begin(),ret.end());
    while(ret.size()<m){
        ret.push_back(l+1);
    }
    assert(ret.size()==m);
    for(auto h:ret){
        cout << h << '\n';
    }
    return 0;
}

Compilation message (stderr)

road_construction.cpp: In function 'int main()':
road_construction.cpp:130:21: warning: comparison of integer expressions of different signedness: 'std::vector<long long int>::size_type' {aka 'long unsigned int'} and 'long long int' [-Wsign-compare]
  130 |     while(ret.size()<m){
      |           ~~~~~~~~~~^~
In file included from /usr/include/c++/10/cassert:44,
                 from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:33,
                 from road_construction.cpp:1:
road_construction.cpp:133:22: warning: comparison of integer expressions of different signedness: 'std::vector<long long int>::size_type' {aka 'long unsigned int'} and 'long long int' [-Wsign-compare]
  133 |     assert(ret.size()==m);
      |            ~~~~~~~~~~^~~

• Subtask 1: 5 / 5
• Subtask 2: 6 / 6
• Subtask 3: 7 / 7
• Subtask 4: 20 / 20
• Subtask 5: 27 / 27
• Subtask 6: 35 / 35