oj.uz

Submission #758013

# Submission time Handle Problem Language Result Execution time Memory
758013 2023-06-14T04:46:57 Z ProtonDecay314 Towers (NOI22_towers) C++17
23 / 100
 1143 ms 78944 KB 
/*
Time complexity: O(N^2 2^N) general case (which should pass 1-2)

Subtask 3
This is a rectangle (wow)
So what it looks like is this:

T---T
-T-T-
--T--
-----
--T--
-T-T-
T---T

T--T
-TT-
----
----
-TT-
T--T

We just have to construct this, essentially

Subtask 4
For this one, we go through every x-coordinate and get the 
smallest Y and largest Y
Well, we can probably sort the values by Y
and then I can keep a set of encountered Xs
// ! Warning: the set may increase the constant factor
if an X has been encountered, then don't bother with it anymore

Now do the same, but going in reverse order of Y
*/
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

vector<bool> solve16(ll n, const vector<tuple<ll, ll>>& pos) {
    vector<ll> xs;
    vector<ll> ys;
    for(const tuple<ll, ll>& tup : pos) {
        ll x, y;
        tie(x, y) = tup;
        xs.push_back(x);
        ys.push_back(y);
    }

    
    for(ll i = 0; i < (1 << n); i++) {
        vector<bool> third_satisfied(n, false);

        ll has_bad_x_coords = false;
        for(ll targx : xs) {
            /*
            TODO count the number of towers with this x
            mark the ones in the middle as "satisfied"
            */

            ll count_towers = 0ll;
            ll min_tower_y = numeric_limits<ll>::max();
            ll max_tower_y = numeric_limits<ll>::min();
            for(ll j = 0ll; j < n; j++) {
                ll x, y;
                tie(x, y) = pos[j];
                if(x == targx) {
                    if((i >> j) & 1) {
                        count_towers++;
                        third_satisfied[j] = true;
                        min_tower_y = min(min_tower_y, y);
                        max_tower_y = max(max_tower_y, y);
                    }
                }
            }
            if(count_towers > 2ll) {
                has_bad_x_coords = true;
                break;
            }

            for(ll j = 0ll; j < n; j++) {
                ll x, y;
                tie(x, y) = pos[j];
                if(x == targx) {
                    if(min_tower_y <= y && y <= max_tower_y) {
                        third_satisfied[j] = true;
                    }
                }
            }
        }
        if(has_bad_x_coords) continue;

        ll has_bad_y_coords = false;
        for(ll targy : ys) {
            /*
            TODO count the number of towers with this y
            mark the ones in the middle as "satisfied"
            */

            ll count_towers = 0ll;
            ll min_tower_x = numeric_limits<ll>::max();
            ll max_tower_x = numeric_limits<ll>::min();
            for(ll j = 0ll; j < n; j++) {
                ll x, y;
                tie(x, y) = pos[j];
                if(y == targy) {
                    if((i >> j) & 1) {
                        count_towers++;
                        third_satisfied[j] = true;
                        min_tower_x = min(min_tower_x, x);
                        max_tower_x = max(max_tower_x, x);
                    }
                }
            }
            if(count_towers > 2ll) {
                has_bad_y_coords = true;
                break;
            }

            for(ll j = 0ll; j < n; j++) {
                ll x, y;
                tie(x, y) = pos[j];
                if(y == targy) {
                    if(min_tower_x <= x && x <= max_tower_x) {
                        third_satisfied[j] = true;
                    }
                }
            }
        }
        if(has_bad_y_coords) continue;

        if(all_of(third_satisfied.begin(), third_satisfied.end(), [](bool v) {return v;})) {
            vector<bool> ans;
            for(ll j = 0ll; j < n; j++) {
                ans.push_back((i >> j) & 1);
            }
            return ans;
        }
    }

    return *(new vector<bool>());
}

vector<bool> solve_subtask_3(ll b, ll a) {
    vector<bool> ans;

    for(ll i = 0ll; i < b; i++) {
        for(ll j = 0ll; j < a; j++) {
            ll ni = (i >= (b >> 1) ? b - i - 1ll : i);
            ll nj = (j >= (a >> 1) ? a - j - 1ll : j);
            ans.push_back(ni == nj);
        }
    }

    return ans;
}

void print_bool_vec(const vector<bool>& vec) {
    for(bool v : vec) {
        cout << v;
    }
    cout << endl;
}

bool satisfies_subtask_3(ll n, vector<tuple<ll, ll>> pos) {
    ll b, a;
    tie(b, a) = pos[n - 1];

    // Check if subtask 3
    if(a * b != n) return false;

    for(ll j = 0ll; j < a; j++) {
        for(ll i = 0ll; i < b; i++) {
            ll curx, cury;
            tie(curx, cury) = pos[i * a + j];
            if(curx != i + 1 || cury != j + 1) return false;
        }
    }

    return true;
}

vector<bool> solve_subtask_4(ll n, const vector<tuple<ll, ll>>& pos) {
    /*
    For this one, we go through every x-coordinate and get the 
    smallest Y and largest Y
    Well, we can probably sort the values by Y
    and then I can keep a set of encountered Xs
    // ! Warning: the set may increase the constant factor
    if an X has been encountered, then don't bother with it anymore

    Now do the same, but going in reverse order of Y
    */
    vector<tuple<ll, ll, ll>> spos;
    vector<bool> ans(n, false);
    spos.reserve(n);
    for(ll i = 0ll; i < n; i++) {
        ll x, y;
        tie(x, y) = pos[i];

        spos.push_back({x, y, i});
    }

    // Phase 1: increasing Y
    unordered_set<ll> xs;
    sort(spos.begin(), spos.end(), [](tuple<ll, ll, ll> a, tuple<ll, ll, ll> b) {return get<1>(a) < get<1>(b);});
    for(const tuple<ll, ll, ll> cpos : spos) {
        if(xs.count(get<0>(cpos)) == 0) {
            ans[get<2>(cpos)] = true;
        }
        xs.insert(get<0>(cpos));
    }

    // Phase 2: decreasing Y
    xs.clear();
    sort(spos.begin(), spos.end(), [](tuple<ll, ll, ll> a, tuple<ll, ll, ll> b) {return get<1>(a) > get<1>(b);});
    for(const tuple<ll, ll, ll> cpos : spos) {
        if(xs.count(get<0>(cpos)) == 0) {
            ans[get<2>(cpos)] = true;
        }
        xs.insert(get<0>(cpos));
    }

    return ans;
}

int main() {
    ll n;
    cin >> n;

    vector<tuple<ll, ll>> pos;
    for(ll i = 0ll; i < n; i++) {
        ll x, y;
        cin >> x >> y;
        pos.push_back({x, y});
    }

    bool subtask3 = satisfies_subtask_3(n, pos);

    if(subtask3) {
        ll b, a;
        tie(b, a) = pos[n - 1];

        vector<bool> ans = solve_subtask_3(b, a);
        print_bool_vec(ans);
    } else if(n <= 16) {
        vector<bool> ans = solve16(n, pos);
        print_bool_vec(ans);
    } else {
        // Assume subtask 4
        vector<bool> ans = solve_subtask_4(n, pos);
        print_bool_vec(ans);
    }
    
    return 0;
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 300 KB Output is correct

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 300 KB Output is correct
11 Correct 57 ms 276 KB Output is correct
12 Correct 16 ms 212 KB Output is correct
13 Correct 67 ms 272 KB Output is correct
14 Correct 43 ms 272 KB Output is correct
15 Correct 41 ms 276 KB Output is correct
16 Correct 13 ms 212 KB Output is correct
17 Correct 31 ms 212 KB Output is correct
18 Correct 37 ms 212 KB Output is correct
19 Correct 13 ms 212 KB Output is correct
20 Correct 30 ms 212 KB Output is correct
21 Correct 11 ms 212 KB Output is correct
22 Correct 13 ms 292 KB Output is correct
23 Correct 12 ms 296 KB Output is correct
24 Correct 9 ms 212 KB Output is correct
25 Correct 33 ms 280 KB Output is correct

Subtask #3
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 38 ms 3256 KB Output is correct
2 Correct 50 ms 3836 KB Output is correct
3 Correct 159 ms 10968 KB Output is correct
4 Correct 286 ms 21304 KB Output is correct
5 Correct 52 ms 4176 KB Output is correct
6 Correct 11 ms 1080 KB Output is correct
7 Correct 277 ms 19996 KB Output is correct
8 Correct 202 ms 13556 KB Output is correct
9 Correct 434 ms 29608 KB Output is correct
10 Correct 359 ms 25044 KB Output is correct
11 Correct 490 ms 31644 KB Output is correct
12 Correct 487 ms 31720 KB Output is correct

Subtask #4
0 / 6.0

# Verdict Execution time Memory Grader output
1 Incorrect 1143 ms 78944 KB Output isn't correct
2 Halted 0 ms 0 KB -

Subtask #5
0 / 31.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 300 KB Output is correct
11 Correct 57 ms 276 KB Output is correct
12 Correct 16 ms 212 KB Output is correct
13 Correct 67 ms 272 KB Output is correct
14 Correct 43 ms 272 KB Output is correct
15 Correct 41 ms 276 KB Output is correct
16 Correct 13 ms 212 KB Output is correct
17 Correct 31 ms 212 KB Output is correct
18 Correct 37 ms 212 KB Output is correct
19 Correct 13 ms 212 KB Output is correct
20 Correct 30 ms 212 KB Output is correct
21 Correct 11 ms 212 KB Output is correct
22 Correct 13 ms 292 KB Output is correct
23 Correct 12 ms 296 KB Output is correct
24 Correct 9 ms 212 KB Output is correct
25 Correct 33 ms 280 KB Output is correct
26 Correct 5 ms 596 KB Output is correct
27 Correct 5 ms 724 KB Output is correct
28 Incorrect 7 ms 520 KB Output isn't correct
29 Halted 0 ms 0 KB -

Subtask #6
0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 300 KB Output is correct
11 Correct 57 ms 276 KB Output is correct
12 Correct 16 ms 212 KB Output is correct
13 Correct 67 ms 272 KB Output is correct
14 Correct 43 ms 272 KB Output is correct
15 Correct 41 ms 276 KB Output is correct
16 Correct 13 ms 212 KB Output is correct
17 Correct 31 ms 212 KB Output is correct
18 Correct 37 ms 212 KB Output is correct
19 Correct 13 ms 212 KB Output is correct
20 Correct 30 ms 212 KB Output is correct
21 Correct 11 ms 212 KB Output is correct
22 Correct 13 ms 292 KB Output is correct
23 Correct 12 ms 296 KB Output is correct
24 Correct 9 ms 212 KB Output is correct
25 Correct 33 ms 280 KB Output is correct
26 Correct 5 ms 596 KB Output is correct
27 Correct 5 ms 724 KB Output is correct
28 Incorrect 7 ms 520 KB Output isn't correct
29 Halted 0 ms 0 KB -

Subtask #7
0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 300 KB Output is correct
11 Correct 57 ms 276 KB Output is correct
12 Correct 16 ms 212 KB Output is correct
13 Correct 67 ms 272 KB Output is correct
14 Correct 43 ms 272 KB Output is correct
15 Correct 41 ms 276 KB Output is correct
16 Correct 13 ms 212 KB Output is correct
17 Correct 31 ms 212 KB Output is correct
18 Correct 37 ms 212 KB Output is correct
19 Correct 13 ms 212 KB Output is correct
20 Correct 30 ms 212 KB Output is correct
21 Correct 11 ms 212 KB Output is correct
22 Correct 13 ms 292 KB Output is correct
23 Correct 12 ms 296 KB Output is correct
24 Correct 9 ms 212 KB Output is correct
25 Correct 33 ms 280 KB Output is correct
26 Correct 38 ms 3256 KB Output is correct
27 Correct 50 ms 3836 KB Output is correct
28 Correct 159 ms 10968 KB Output is correct
29 Correct 286 ms 21304 KB Output is correct
30 Correct 52 ms 4176 KB Output is correct
31 Correct 11 ms 1080 KB Output is correct
32 Correct 277 ms 19996 KB Output is correct
33 Correct 202 ms 13556 KB Output is correct
34 Correct 434 ms 29608 KB Output is correct
35 Correct 359 ms 25044 KB Output is correct
36 Correct 490 ms 31644 KB Output is correct
37 Correct 487 ms 31720 KB Output is correct
38 Incorrect 1143 ms 78944 KB Output isn't correct
39 Halted 0 ms 0 KB -