oj.uz

Submission #575475

# Submission time Handle Problem Language Result Execution time Memory
575475 2022-06-10T18:15:29 Z rainliofficial Road Construction (JOI21_road_construction) C++17
100 / 100
 2013 ms 14364 KB 
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
#define sz(x) (int)x.size()
#define f first
#define s second

/* 
Date: 2022/06/10
Problem Link: https://oj.uz/problem/view/JOI21_road_construction
Topic(s): Binary search, sorting
Time Spent: 1 hr impl
Solution Outline:
- The distance between two points can be written as max(abs((xi + yi) - (xj + yj)), abs((xi - yi) - (xj - yj)))
Binary search on v, which is the kth largest value. We have to check whether there more or less than k roads with
cost <= v. 
- Maintain a sliding window of size v. 
- Sort the points by xi + yi. For a point i, remove all points j that has xj + yj further than v units away.
- Put xi - yi into the set. 
- We know all js that came before i must have xi + yi - (xj + yj) <= v. So we can simply call lower_bound on the set
with xi - yi - v and vi - vi + v. The range that it gives us will be the amount of points within v distance of i. 
*/

/* 
AC at 2022/06/10 14:14
*/

const int MAXN = 2e5+5;
int n, k;
vector<pll> arr;
vector<ll> res;

ll sum(const pll& a){
    return a.f + a.s;
}
ll dif(const pll& a){
    return a.f - a.s;
}

bool check(ll v, bool upd){
    int l = 0;
    auto cmp = [](const pll& a, const pll& b){
        if (dif(a) == dif(b)){
            return a < b;
        }else{
            return a.f - a.s < b.f - b.s;
        }
    };
    set<pll, decltype(cmp)> set(cmp);
    ll ans = 0;
    for (int i=0; i<n; i++){
        while (l < n && sum(arr[i]) - sum(arr[l]) > v){
            set.erase(arr[l++]);
        }
        auto inc = set.lower_bound(arr[i]);
        auto dec = inc;
        while (inc != set.end() && dif(*inc) - dif(arr[i]) <= v){
            // If we are updating the answer, than we have to find all the roads that can be built, bc we only take the k minimum. 
            if (upd) res.push_back(abs(arr[i].f - (*inc).f) + abs(arr[i].s - (*inc).s));
            inc++;
            ans++;
            // If we are not trying to get the final answer, we just need to know whether there is more than k roads with cost <= v or not. 
            // We don't care which roads they are. 
            if (!upd && ans >=k){
                return true;
            }
        }
        while (dec != set.begin() && dif(arr[i]) - dif(*prev(dec)) <= v){
            dec--;
            if (upd) res.push_back(abs(arr[i].f - (*dec).f) + abs(arr[i].s - (*dec).s));
            ans++;
            if (!upd && ans >=k){
                return true; 
            }
        }
        set.insert(arr[i]);
    }
    return ans >= k;
}
int main(){
    cin.tie(0); ios_base::sync_with_stdio(0);
    // freopen("file.in", "r", stdin);
    // freopen("file.out", "w", stdout);
    cin >> n >> k;
    arr.resize(n);
    for (int i=0; i<n; i++){
        int x, y;
        cin >> x >> y;
        arr[i] = {x, y};
    }
    sort(arr.begin(), arr.end(), [](const pll& a, const pll& b){
        return a.f + a.s < b.f + b.s;
    });
    ll low = 0, high = 4e9;
    while (low < high){
        ll mid = (low + high)/2;
        if (check(mid, false)){
            high = mid;
        }else{
            low = mid+1;
        }
    }
    check(low, true);
    assert((int)res.size() >= k);
    sort(res.begin(), res.end());
    for (int i=0; i<k; i++){
        cout << res[i] << "\n";
    }
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 128 ms 4920 KB Output is correct
2 Correct 135 ms 5084 KB Output is correct
3 Correct 123 ms 5072 KB Output is correct
4 Correct 109 ms 5084 KB Output is correct
5 Correct 120 ms 3896 KB Output is correct
6 Correct 6 ms 340 KB Output is correct

Subtask #2
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 366 ms 7540 KB Output is correct
2 Correct 366 ms 7476 KB Output is correct
3 Correct 108 ms 4980 KB Output is correct
4 Correct 292 ms 8388 KB Output is correct
5 Correct 309 ms 9624 KB Output is correct
6 Correct 299 ms 9532 KB Output is correct
7 Correct 269 ms 8512 KB Output is correct

Subtask #3
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 216 ms 4180 KB Output is correct
2 Correct 307 ms 4180 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 139 ms 6344 KB Output is correct
5 Correct 693 ms 8492 KB Output is correct

Subtask #4
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 216 ms 4180 KB Output is correct
2 Correct 307 ms 4180 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 139 ms 6344 KB Output is correct
5 Correct 693 ms 8492 KB Output is correct
6 Correct 448 ms 4180 KB Output is correct
7 Correct 416 ms 4180 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 303 ms 4180 KB Output is correct
11 Correct 108 ms 6396 KB Output is correct
12 Correct 680 ms 4248 KB Output is correct

Subtask #5
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 128 ms 4920 KB Output is correct
2 Correct 135 ms 5084 KB Output is correct
3 Correct 123 ms 5072 KB Output is correct
4 Correct 109 ms 5084 KB Output is correct
5 Correct 120 ms 3896 KB Output is correct
6 Correct 6 ms 340 KB Output is correct
7 Correct 959 ms 6020 KB Output is correct
8 Correct 960 ms 6080 KB Output is correct
9 Correct 110 ms 5052 KB Output is correct
10 Correct 510 ms 5380 KB Output is correct
11 Correct 306 ms 5180 KB Output is correct
12 Correct 651 ms 7284 KB Output is correct
13 Correct 605 ms 6184 KB Output is correct

Subtask #6
35.0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 128 ms 4920 KB Output is correct
2 Correct 135 ms 5084 KB Output is correct
3 Correct 123 ms 5072 KB Output is correct
4 Correct 109 ms 5084 KB Output is correct
5 Correct 120 ms 3896 KB Output is correct
6 Correct 6 ms 340 KB Output is correct
7 Correct 366 ms 7540 KB Output is correct
8 Correct 366 ms 7476 KB Output is correct
9 Correct 108 ms 4980 KB Output is correct
10 Correct 292 ms 8388 KB Output is correct
11 Correct 309 ms 9624 KB Output is correct
12 Correct 299 ms 9532 KB Output is correct
13 Correct 269 ms 8512 KB Output is correct
14 Correct 216 ms 4180 KB Output is correct
15 Correct 307 ms 4180 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 139 ms 6344 KB Output is correct
18 Correct 693 ms 8492 KB Output is correct
19 Correct 448 ms 4180 KB Output is correct
20 Correct 416 ms 4180 KB Output is correct
21 Correct 0 ms 212 KB Output is correct
22 Correct 1 ms 212 KB Output is correct
23 Correct 303 ms 4180 KB Output is correct
24 Correct 108 ms 6396 KB Output is correct
25 Correct 680 ms 4248 KB Output is correct
26 Correct 959 ms 6020 KB Output is correct
27 Correct 960 ms 6080 KB Output is correct
28 Correct 110 ms 5052 KB Output is correct
29 Correct 510 ms 5380 KB Output is correct
30 Correct 306 ms 5180 KB Output is correct
31 Correct 651 ms 7284 KB Output is correct
32 Correct 605 ms 6184 KB Output is correct
33 Correct 2013 ms 8312 KB Output is correct
34 Correct 1974 ms 8272 KB Output is correct
35 Correct 1262 ms 7648 KB Output is correct
36 Correct 1158 ms 14128 KB Output is correct
37 Correct 1186 ms 14364 KB Output is correct
38 Correct 1018 ms 8576 KB Output is correct