oj.uz

Submission #709995

# Submission time Handle Problem Language Result Execution time Memory
709995 2023-03-15T02:35:12 Z alvingogo Road Construction (JOI21_road_construction) C++14
100 / 100
 3365 ms 14260 KB 
#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

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
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 45 ms 4924 KB Output is correct
2 Correct 48 ms 4920 KB Output is correct
3 Correct 41 ms 5036 KB Output is correct
4 Correct 57 ms 5064 KB Output is correct
5 Correct 46 ms 3848 KB Output is correct
6 Correct 2 ms 340 KB Output is correct

Subtask #2
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 1558 ms 13312 KB Output is correct
2 Correct 1485 ms 13364 KB Output is correct
3 Correct 38 ms 4932 KB Output is correct
4 Correct 1583 ms 13200 KB Output is correct
5 Correct 1623 ms 13356 KB Output is correct
6 Correct 1454 ms 13364 KB Output is correct
7 Correct 1329 ms 12592 KB Output is correct

Subtask #3
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2855 ms 8124 KB Output is correct
2 Correct 2876 ms 8120 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1336 ms 8208 KB Output is correct
5 Correct 955 ms 8188 KB Output is correct

Subtask #4
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2855 ms 8124 KB Output is correct
2 Correct 2876 ms 8120 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1336 ms 8208 KB Output is correct
5 Correct 955 ms 8188 KB Output is correct
6 Correct 3100 ms 8228 KB Output is correct
7 Correct 3320 ms 8164 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 2952 ms 8208 KB Output is correct
11 Correct 1382 ms 8128 KB Output is correct
12 Correct 902 ms 8240 KB Output is correct

Subtask #5
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 45 ms 4924 KB Output is correct
2 Correct 48 ms 4920 KB Output is correct
3 Correct 41 ms 5036 KB Output is correct
4 Correct 57 ms 5064 KB Output is correct
5 Correct 46 ms 3848 KB Output is correct
6 Correct 2 ms 340 KB Output is correct
7 Correct 1130 ms 9584 KB Output is correct
8 Correct 1137 ms 9580 KB Output is correct
9 Correct 40 ms 5120 KB Output is correct
10 Correct 1079 ms 8684 KB Output is correct
11 Correct 1010 ms 8556 KB Output is correct
12 Correct 288 ms 9148 KB Output is correct
13 Correct 370 ms 7656 KB Output is correct

Subtask #6
35.0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 45 ms 4924 KB Output is correct
2 Correct 48 ms 4920 KB Output is correct
3 Correct 41 ms 5036 KB Output is correct
4 Correct 57 ms 5064 KB Output is correct
5 Correct 46 ms 3848 KB Output is correct
6 Correct 2 ms 340 KB Output is correct
7 Correct 1558 ms 13312 KB Output is correct
8 Correct 1485 ms 13364 KB Output is correct
9 Correct 38 ms 4932 KB Output is correct
10 Correct 1583 ms 13200 KB Output is correct
11 Correct 1623 ms 13356 KB Output is correct
12 Correct 1454 ms 13364 KB Output is correct
13 Correct 1329 ms 12592 KB Output is correct
14 Correct 2855 ms 8124 KB Output is correct
15 Correct 2876 ms 8120 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1336 ms 8208 KB Output is correct
18 Correct 955 ms 8188 KB Output is correct
19 Correct 3100 ms 8228 KB Output is correct
20 Correct 3320 ms 8164 KB Output is correct
21 Correct 0 ms 212 KB Output is correct
22 Correct 0 ms 212 KB Output is correct
23 Correct 2952 ms 8208 KB Output is correct
24 Correct 1382 ms 8128 KB Output is correct
25 Correct 902 ms 8240 KB Output is correct
26 Correct 1130 ms 9584 KB Output is correct
27 Correct 1137 ms 9580 KB Output is correct
28 Correct 40 ms 5120 KB Output is correct
29 Correct 1079 ms 8684 KB Output is correct
30 Correct 1010 ms 8556 KB Output is correct
31 Correct 288 ms 9148 KB Output is correct
32 Correct 370 ms 7656 KB Output is correct
33 Correct 3365 ms 14260 KB Output is correct
34 Correct 3319 ms 14124 KB Output is correct
35 Correct 2915 ms 12972 KB Output is correct
36 Correct 791 ms 12968 KB Output is correct
37 Correct 809 ms 13236 KB Output is correct
38 Correct 1049 ms 11652 KB Output is correct