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답안 #758249

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
758249 2023-06-14T10:17:04 Z ProtonDecay314 Towers (NOI22_towers) C++17
29 / 100
 1447 ms 64944 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 X
    unordered_set<ll> ys;
    sort(spos.begin(), spos.end(), [](tuple<ll, ll, ll> a, tuple<ll, ll, ll> b) {return get<0>(a) < get<0>(b);});
    for(const tuple<ll, ll, ll> cpos : spos) {
        if(ys.count(get<1>(cpos)) == 0) {
            ans[get<2>(cpos)] = true;
        }
        ys.insert(get<1>(cpos));
    }

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

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 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 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct

Subtask #2
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 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 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 53 ms 212 KB Output is correct
12 Correct 15 ms 296 KB Output is correct
13 Correct 63 ms 276 KB Output is correct
14 Correct 39 ms 212 KB Output is correct
15 Correct 42 ms 212 KB Output is correct
16 Correct 13 ms 212 KB Output is correct
17 Correct 29 ms 212 KB Output is correct
18 Correct 40 ms 212 KB Output is correct
19 Correct 14 ms 292 KB Output is correct
20 Correct 31 ms 212 KB Output is correct
21 Correct 8 ms 212 KB Output is correct
22 Correct 11 ms 212 KB Output is correct
23 Correct 10 ms 300 KB Output is correct
24 Correct 8 ms 296 KB Output is correct
25 Correct 30 ms 212 KB Output is correct

Subtask #3
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 44 ms 3252 KB Output is correct
2 Correct 52 ms 3876 KB Output is correct
3 Correct 164 ms 11228 KB Output is correct
4 Correct 319 ms 22920 KB Output is correct
5 Correct 56 ms 4412 KB Output is correct
6 Correct 11 ms 1228 KB Output is correct
7 Correct 277 ms 20756 KB Output is correct
8 Correct 200 ms 13912 KB Output is correct
9 Correct 434 ms 31844 KB Output is correct
10 Correct 393 ms 26044 KB Output is correct
11 Correct 465 ms 32936 KB Output is correct
12 Correct 462 ms 32876 KB Output is correct

Subtask #4
6.0 / 6.0

# 결과 실행 시간 메모리 Grader output
1 Correct 817 ms 41932 KB Output is correct
2 Correct 858 ms 41988 KB Output is correct
3 Correct 823 ms 41876 KB Output is correct
4 Correct 801 ms 42044 KB Output is correct
5 Correct 799 ms 41956 KB Output is correct
6 Correct 1447 ms 64932 KB Output is correct
7 Correct 1327 ms 64836 KB Output is correct
8 Correct 1400 ms 64944 KB Output is correct
9 Correct 1275 ms 64932 KB Output is correct
10 Correct 1363 ms 64932 KB Output is correct

Subtask #5
0 / 31.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 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 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 53 ms 212 KB Output is correct
12 Correct 15 ms 296 KB Output is correct
13 Correct 63 ms 276 KB Output is correct
14 Correct 39 ms 212 KB Output is correct
15 Correct 42 ms 212 KB Output is correct
16 Correct 13 ms 212 KB Output is correct
17 Correct 29 ms 212 KB Output is correct
18 Correct 40 ms 212 KB Output is correct
19 Correct 14 ms 292 KB Output is correct
20 Correct 31 ms 212 KB Output is correct
21 Correct 8 ms 212 KB Output is correct
22 Correct 11 ms 212 KB Output is correct
23 Correct 10 ms 300 KB Output is correct
24 Correct 8 ms 296 KB Output is correct
25 Correct 30 ms 212 KB Output is correct
26 Correct 5 ms 596 KB Output is correct
27 Correct 5 ms 724 KB Output is correct
28 Incorrect 5 ms 552 KB Output isn't correct
29 Halted 0 ms 0 KB -

Subtask #6
0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 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 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 53 ms 212 KB Output is correct
12 Correct 15 ms 296 KB Output is correct
13 Correct 63 ms 276 KB Output is correct
14 Correct 39 ms 212 KB Output is correct
15 Correct 42 ms 212 KB Output is correct
16 Correct 13 ms 212 KB Output is correct
17 Correct 29 ms 212 KB Output is correct
18 Correct 40 ms 212 KB Output is correct
19 Correct 14 ms 292 KB Output is correct
20 Correct 31 ms 212 KB Output is correct
21 Correct 8 ms 212 KB Output is correct
22 Correct 11 ms 212 KB Output is correct
23 Correct 10 ms 300 KB Output is correct
24 Correct 8 ms 296 KB Output is correct
25 Correct 30 ms 212 KB Output is correct
26 Correct 5 ms 596 KB Output is correct
27 Correct 5 ms 724 KB Output is correct
28 Incorrect 5 ms 552 KB Output isn't correct
29 Halted 0 ms 0 KB -

Subtask #7
0 / 19.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 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 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 53 ms 212 KB Output is correct
12 Correct 15 ms 296 KB Output is correct
13 Correct 63 ms 276 KB Output is correct
14 Correct 39 ms 212 KB Output is correct
15 Correct 42 ms 212 KB Output is correct
16 Correct 13 ms 212 KB Output is correct
17 Correct 29 ms 212 KB Output is correct
18 Correct 40 ms 212 KB Output is correct
19 Correct 14 ms 292 KB Output is correct
20 Correct 31 ms 212 KB Output is correct
21 Correct 8 ms 212 KB Output is correct
22 Correct 11 ms 212 KB Output is correct
23 Correct 10 ms 300 KB Output is correct
24 Correct 8 ms 296 KB Output is correct
25 Correct 30 ms 212 KB Output is correct
26 Correct 44 ms 3252 KB Output is correct
27 Correct 52 ms 3876 KB Output is correct
28 Correct 164 ms 11228 KB Output is correct
29 Correct 319 ms 22920 KB Output is correct
30 Correct 56 ms 4412 KB Output is correct
31 Correct 11 ms 1228 KB Output is correct
32 Correct 277 ms 20756 KB Output is correct
33 Correct 200 ms 13912 KB Output is correct
34 Correct 434 ms 31844 KB Output is correct
35 Correct 393 ms 26044 KB Output is correct
36 Correct 465 ms 32936 KB Output is correct
37 Correct 462 ms 32876 KB Output is correct
38 Correct 817 ms 41932 KB Output is correct
39 Correct 858 ms 41988 KB Output is correct
40 Correct 823 ms 41876 KB Output is correct
41 Correct 801 ms 42044 KB Output is correct
42 Correct 799 ms 41956 KB Output is correct
43 Correct 1447 ms 64932 KB Output is correct
44 Correct 1327 ms 64836 KB Output is correct
45 Correct 1400 ms 64944 KB Output is correct
46 Correct 1275 ms 64932 KB Output is correct
47 Correct 1363 ms 64932 KB Output is correct
48 Correct 5 ms 596 KB Output is correct
49 Correct 5 ms 724 KB Output is correct
50 Incorrect 5 ms 552 KB Output isn't correct
51 Halted 0 ms 0 KB -