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Submission #1051090

# Submission time Handle Problem Language Result Execution time Memory
1051090 2024-08-09T19:34:37 Z sofijavelkovska Stranded Far From Home (BOI22_island) C++17
100 / 100
 428 ms 76504 KB 
#include <bits/stdc++.h>
using namespace std;

const int MAXN=2e5, INF=2e9;

int n, m;
int a[MAXN];
vector<int> adj[MAXN];
int link[MAXN], csize[MAXN], cindex[MAXN];
long long sum[MAXN];
set<pair<int, int> > neighbours[MAXN];

bool compare(int x, int y)
{
    return a[x]<a[y];
}

int find(int x)
{
    if (x==link[x])
        return x;

    return link[x]=find(link[x]);
}

void unite(int x, int y, int maxvalue)
{
    x=find(x);
    y=find(y);
    if (neighbours[cindex[x]].size()<neighbours[cindex[y]].size())
        swap(x, y);
    for (auto t : neighbours[cindex[y]])
        if (t.first>maxvalue)
            neighbours[cindex[x]].insert(t);
    neighbours[cindex[y]].clear();
    cindex[y]=cindex[x];
    if (csize[x]<csize[y])
        swap(x, y);
    csize[x]=csize[x]+csize[y];
    sum[x]=sum[x]+sum[y];
    link[y]=x;

    return;
}

vector<bool> brute()
{
    vector<bool> possible(n, 0);
    for (int i=0; i<n; i++)
    {
        priority_queue<pair<int, int> > pq;
        pq.push({-a[i], i});
        long long sum=0;
        bool visited[n]={false};
        while (!pq.empty())
        {
            int x=pq.top().second;
            pq.pop();
            if (x!=i && sum<a[x])
                continue;
            if (visited[x])
                continue;
            visited[x]=true;
            sum=sum+a[x];
            for (auto y : adj[x])
                if (!visited[y])
                    pq.push({-a[y], y});
        }
        if (*min_element(visited, visited+n)==1)
            possible[i]=true;
    }

    return possible;
}

int main()
{
    //ios_base::sync_with_stdio(0);
    //cin.tie(0);

    srand(time(0));
    int tc=0;
    int K=10;
    //cin >> tc;
    //while (true)
    {
        /*n=rand()%K+1;
        m=n-1+rand()%K;
        if (m>n*(n-1)/2)
            continue;
        tc=tc+1;
        cout << "tc " << tc << '\n';
        for (int i=0; i<n; i++)
        {
            adj[i].clear();
            neighbours[i].clear();
        }
        for (int i=0; i<n; i++)
            a[i]=rand()%K+1;
        set<pair<int, int> > used;
        for (int x=1; x<n; x++)
        {
            int y=rand()%x;
            adj[x].push_back(y);
            adj[y].push_back(x);
            used.insert({x, y});
        }
        while (used.size()<m)
        {
            int x=rand()%n;
            int y=rand()%n;
            if (x==y)
                continue;
            if (used.count({x, y}) || used.count({y, x}))
                continue;
            adj[x].push_back(y);
            adj[y].push_back(x);
            used.insert({x, y});
        }*/
        /*cin >> n >> m;
        for (int i=0; i<n; i++)
            cin >> a[i];
        for (int i=0; i<m; i++)
        {
            int x, y;
            cin >> x >> y;
            adj[x].push_back(y);
            adj[y].push_back(x);
        }*/


    cin >> n >> m;
    for (int i=0; i<n; i++)
        cin >> a[i];
    for (int i=0; i<m; i++)
    {
        int x, y;
        cin >> x >> y;
        adj[x-1].push_back(y-1);
        adj[y-1].push_back(x-1);
    }
    int sorted[n];
    for (int i=0; i<n; i++)
        sorted[i]=i;
    sort(sorted, sorted+n, compare);
    for (int i=0; i<n; i++)
    {
        link[i]=i;
        csize[i]=1;
        sum[i]=a[i];
        cindex[i]=i;
        for (auto x : adj[i])
            neighbours[i].insert({a[x], x});
    }
    map<int, vector<int> > byvalue;
    for (int i=0; i<n; i++)
        byvalue[a[i]].push_back(i);
    bool possible[n];
    for (int i=0; i<n; i++)
        possible[i]=true;
    queue<int> q;
    vector<int> todelete[n];
    for (auto k : byvalue)
    {
        for (auto x : k.second)
        {
        for (auto y : adj[x])
            if (a[y]<=a[x] && find(x)!=find(y))
                unite(x, y, a[x]);
        }
        for (auto x : k.second)
        {
        int leader=find(x);
        while (!neighbours[cindex[leader]].empty() && (*neighbours[cindex[leader]].begin()).first<=a[x])
            neighbours[cindex[leader]].erase(neighbours[cindex[leader]].begin());
        if (neighbours[cindex[leader]].empty())
            continue;
        auto it=neighbours[cindex[leader]].begin();
        //cout << "x sum min " << x << ' ' << sum[leader] << ' ' << (*it).first << '\n';
        if (sum[leader]>=(*it).first)
        {
            todelete[(*it).second].push_back(x);
            continue;
        }
        possible[x]=false;
        q.push(x);
        while (!q.empty())
        {
            int y=q.front();
            q.pop();
            for (auto t : todelete[y])
                if (a[t]<=a[x] && possible[t])
                {
                    possible[t]=false;
                    q.push(t);
                }
        }
        }
    }
    for (int i=0; i<n; i++)
        cout << possible[i];

        /*auto br=brute();
        bool flop=false;
        for (int i=0; i<n; i++)
            if (possible[i]!=br[i])
                flop=true;
        if (flop)
        {
            cout << "FLOP\n";
            cout << n << ' ' << m << '\n';
            for (int i=0; i<n; i++)
                cout << a[i] << ' ';
            cout << '\n';
            for (auto edge : used)
                cout << edge.first << ' ' << edge.second << '\n';
            for (int i=0; i<n; i++)
                cout << possible[i];
            cout << '\n';
            for (int i=0; i<n; i++)
                cout << br[i];
            cout << '\n';
            //break;
        }*/
    }

    return 0;
}


/*#include <bits/stdc++.h>
using namespace std;

const int MAXN=2e5, INF=2e9;

int n, m;
int a[MAXN];
vector<int> adj[MAXN];

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    cin >> n >> m;
    for (int i=0; i<n; i++)
        cin >> a[i];
    for (int i=0; i<m; i++)
    {
        int x, y;
        cin >> x >> y;
        adj[x-1].push_back(y-1);
        adj[y-1].push_back(x-1);
    }
    set<int> values;
    for (int i=0; i<n; i++)
        values.insert(-a[i]);
    bool possible[n]={false};
    queue<int> q;
    for (auto kt : values)
    {
        int k=-kt;
        bool visited[n]={false};
        for (int i=0; i<n; i++)
        {
            if (a[i]!=k || visited[i])
                continue;
            visited[i]=true;
            long long sum=a[i];
            q.push(i);
            vector<int> nodes;
            nodes.push_back(i);
            int minsum=INF;
            while (!q.empty())
            {
                int x=q.front();
                q.pop();
                for (auto y : adj[x])
                {
                    if (a[y]<=k && !visited[y])
                    {
                        visited[y]=true;
                        sum=sum+a[y];
                        q.push(y);
                        if (a[y]==k)
                            nodes.push_back(y);
                    }
                    if (a[y]>k && possible[y])
                        minsum=min(minsum, a[y]);
                }
            }
            if (minsum>sum && k!=-(*values.begin()))
                continue;
            for (auto x : nodes)
                possible[x]=true;
        }
    }
    for (int i=0; i<n; i++)
        cout << possible[i];

    return 0;
}*/


/*#include <bits/stdc++.h>
using namespace std;

const int MAXN=300000;

int n, m;
int a[MAXN];
vector<int> adj[MAXN];
long long prefix[MAXN];

bool compare(int x, int y)
{
    return a[x]>a[y];
}

long long sum(int l, int r)
{
    if (l==0)
        return prefix[r];

    return prefix[r]-prefix[l-1];
}

vector<bool> brute()
{
    vector<bool> possible(n, 0);
    for (int i=0; i<n; i++)
    {
        priority_queue<pair<int, int> > pq;
        pq.push({-a[i], i});
        long long sum=0;
        bool visited[n]={false};
        while (!pq.empty())
        {
            int x=pq.top().second;
            pq.pop();
            if (x!=i && sum<a[x])
                continue;
            if (visited[x])
                continue;
            visited[x]=true;
            sum=sum+a[x];
            for (auto y : adj[x])
                if (!visited[y])
                    pq.push({-a[y], y});
        }
        if (*min_element(visited, visited+n)==1)
            possible[i]=true;
    }

    return possible;
}

int main()
{
    //ios_base::sync_with_stdio(0);
    //cin.tie(0);

    srand(time(0));
    int tc=0;
    //cin >> tc;
    //while (true)
    {
        tc=tc+1;
        cout << "tc " << tc << '\n';
        n=rand()%100+1, m=0;
        for (int i=0; i<n; i++)
            a[i]=rand()%100000+1;
        //for (int i=0; i<n; i++)
          //  cout << a[i] << ' ';
        //cout << '\n';

    cin >> n >> m;
    for (int i=0; i<n; i++)
        cin >> a[i];
    for (int i=0; i<n; i++)
        adj[i].clear();
    for (int i=0; i<m; i++)
    {
        int x, y;
        cin >> x >> y;
        adj[x-1].push_back(y-1);
        adj[y-1].push_back(x-1);
    }
    int sorted[n];
    for (int i=0; i<n; i++)
        sorted[i]=i;
    sort(sorted, sorted+n, compare);
    int possible[n]={false};
    possible[sorted[0]]=true;
    set<int> larger;
    larger.insert(sorted[0]);
    prefix[0]=a[0];
    for (int i=1; i<=n; i++)
        prefix[i]=prefix[i-1]+a[i];
    for (int i=1; i<n; i++)
    {
        int x=sorted[i];
        int l=-1, r=n;
        auto it=larger.lower_bound(x);
        if (it!=larger.end())
            r=*it;
        if (it!=larger.begin())
        {
            it--;
            l=*it;
        }
        if (l!=-1 && possible[l] && sum(l+1, r-1)>=a[l])
            possible[x]=true;
        if (r!=n && possible[r] && sum(l+1, r-1)>=a[r])
            possible[x]=true;
        larger.insert(x);
    }
    for (int i=0; i<n; i++)
        cout << possible[i];

        auto br=brute();
        bool flop=false;
        for (int i=0; i<n; i++)
            if (possible[i]!=br[i])
                flop=true;
        if (flop)
        {
            cout << "FLOP\n";
            cout << n << '\n';
            for (int i=0; i<n; i++)
                cout << a[i] << ' ';
            cout << '\n';
            for (int i=0; i<n; i++)
                cout << possible[i];
            cout << '\n';
            for (int i=0; i<n; i++)
                cout << br[i];
            cout << '\n';
            break;
        }
    }

    return 0;
}*/

Compilation message

island.cpp: In function 'int main()':
island.cpp:82:9: warning: unused variable 'tc' [-Wunused-variable]
   82 |     int tc=0;
      |         ^~
island.cpp:83:9: warning: unused variable 'K' [-Wunused-variable]
   83 |     int K=10;
      |         ^

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 19032 KB Output is correct
2 Correct 2 ms 19036 KB Output is correct
3 Correct 2 ms 19032 KB Output is correct
4 Correct 4 ms 19560 KB Output is correct
5 Correct 4 ms 19548 KB Output is correct
6 Correct 3 ms 19292 KB Output is correct
7 Correct 4 ms 19524 KB Output is correct
8 Correct 4 ms 19292 KB Output is correct
9 Correct 3 ms 19304 KB Output is correct
10 Correct 5 ms 19804 KB Output is correct
11 Correct 4 ms 19644 KB Output is correct
12 Correct 4 ms 19800 KB Output is correct
13 Correct 3 ms 19292 KB Output is correct
14 Correct 4 ms 19292 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 19036 KB Output is correct
2 Correct 2 ms 19036 KB Output is correct
3 Correct 221 ms 71868 KB Output is correct
4 Correct 152 ms 51464 KB Output is correct
5 Correct 281 ms 70228 KB Output is correct
6 Correct 235 ms 66896 KB Output is correct
7 Correct 268 ms 72016 KB Output is correct
8 Correct 207 ms 51656 KB Output is correct
9 Correct 238 ms 66676 KB Output is correct
10 Correct 249 ms 67544 KB Output is correct
11 Correct 222 ms 52324 KB Output is correct
12 Correct 218 ms 51724 KB Output is correct
13 Correct 136 ms 51396 KB Output is correct
14 Correct 140 ms 51400 KB Output is correct
15 Correct 210 ms 72016 KB Output is correct
16 Correct 167 ms 71248 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 19032 KB Output is correct
2 Correct 381 ms 71760 KB Output is correct
3 Correct 360 ms 71324 KB Output is correct
4 Correct 169 ms 56008 KB Output is correct
5 Correct 148 ms 54468 KB Output is correct
6 Correct 428 ms 76368 KB Output is correct
7 Correct 247 ms 76368 KB Output is correct
8 Correct 229 ms 76480 KB Output is correct
9 Correct 172 ms 75176 KB Output is correct
10 Correct 209 ms 65276 KB Output is correct
11 Correct 213 ms 54868 KB Output is correct

Subtask #4
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 19036 KB Output is correct
2 Correct 274 ms 51072 KB Output is correct
3 Correct 269 ms 51056 KB Output is correct
4 Correct 301 ms 55908 KB Output is correct
5 Correct 234 ms 56020 KB Output is correct
6 Correct 200 ms 54768 KB Output is correct
7 Correct 218 ms 56596 KB Output is correct
8 Correct 139 ms 54476 KB Output is correct
9 Correct 169 ms 48184 KB Output is correct
10 Correct 207 ms 54496 KB Output is correct
11 Correct 202 ms 54072 KB Output is correct

Subtask #5
35.0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 19032 KB Output is correct
2 Correct 2 ms 19036 KB Output is correct
3 Correct 2 ms 19032 KB Output is correct
4 Correct 4 ms 19560 KB Output is correct
5 Correct 4 ms 19548 KB Output is correct
6 Correct 3 ms 19292 KB Output is correct
7 Correct 4 ms 19524 KB Output is correct
8 Correct 4 ms 19292 KB Output is correct
9 Correct 3 ms 19304 KB Output is correct
10 Correct 5 ms 19804 KB Output is correct
11 Correct 4 ms 19644 KB Output is correct
12 Correct 4 ms 19800 KB Output is correct
13 Correct 3 ms 19292 KB Output is correct
14 Correct 4 ms 19292 KB Output is correct
15 Correct 2 ms 19036 KB Output is correct
16 Correct 2 ms 19036 KB Output is correct
17 Correct 221 ms 71868 KB Output is correct
18 Correct 152 ms 51464 KB Output is correct
19 Correct 281 ms 70228 KB Output is correct
20 Correct 235 ms 66896 KB Output is correct
21 Correct 268 ms 72016 KB Output is correct
22 Correct 207 ms 51656 KB Output is correct
23 Correct 238 ms 66676 KB Output is correct
24 Correct 249 ms 67544 KB Output is correct
25 Correct 222 ms 52324 KB Output is correct
26 Correct 218 ms 51724 KB Output is correct
27 Correct 136 ms 51396 KB Output is correct
28 Correct 140 ms 51400 KB Output is correct
29 Correct 210 ms 72016 KB Output is correct
30 Correct 167 ms 71248 KB Output is correct
31 Correct 2 ms 19032 KB Output is correct
32 Correct 381 ms 71760 KB Output is correct
33 Correct 360 ms 71324 KB Output is correct
34 Correct 169 ms 56008 KB Output is correct
35 Correct 148 ms 54468 KB Output is correct
36 Correct 428 ms 76368 KB Output is correct
37 Correct 247 ms 76368 KB Output is correct
38 Correct 229 ms 76480 KB Output is correct
39 Correct 172 ms 75176 KB Output is correct
40 Correct 209 ms 65276 KB Output is correct
41 Correct 213 ms 54868 KB Output is correct
42 Correct 2 ms 19036 KB Output is correct
43 Correct 274 ms 51072 KB Output is correct
44 Correct 269 ms 51056 KB Output is correct
45 Correct 301 ms 55908 KB Output is correct
46 Correct 234 ms 56020 KB Output is correct
47 Correct 200 ms 54768 KB Output is correct
48 Correct 218 ms 56596 KB Output is correct
49 Correct 139 ms 54476 KB Output is correct
50 Correct 169 ms 48184 KB Output is correct
51 Correct 207 ms 54496 KB Output is correct
52 Correct 202 ms 54072 KB Output is correct
53 Correct 2 ms 19032 KB Output is correct
54 Correct 2 ms 19040 KB Output is correct
55 Correct 2 ms 19036 KB Output is correct
56 Correct 4 ms 19548 KB Output is correct
57 Correct 5 ms 19548 KB Output is correct
58 Correct 4 ms 19292 KB Output is correct
59 Correct 5 ms 19548 KB Output is correct
60 Correct 4 ms 19340 KB Output is correct
61 Correct 3 ms 19292 KB Output is correct
62 Correct 4 ms 19616 KB Output is correct
63 Correct 4 ms 19548 KB Output is correct
64 Correct 3 ms 19588 KB Output is correct
65 Correct 3 ms 19292 KB Output is correct
66 Correct 3 ms 19292 KB Output is correct
67 Correct 233 ms 76392 KB Output is correct
68 Correct 157 ms 54540 KB Output is correct
69 Correct 259 ms 74576 KB Output is correct
70 Correct 240 ms 71492 KB Output is correct
71 Correct 258 ms 76368 KB Output is correct
72 Correct 225 ms 56012 KB Output is correct
73 Correct 249 ms 71256 KB Output is correct
74 Correct 248 ms 71216 KB Output is correct
75 Correct 224 ms 55624 KB Output is correct
76 Correct 193 ms 54628 KB Output is correct
77 Correct 136 ms 54500 KB Output is correct
78 Correct 137 ms 54520 KB Output is correct
79 Correct 212 ms 76368 KB Output is correct
80 Correct 169 ms 75088 KB Output is correct
81 Correct 384 ms 76112 KB Output is correct
82 Correct 378 ms 71504 KB Output is correct
83 Correct 171 ms 56004 KB Output is correct
84 Correct 141 ms 54544 KB Output is correct
85 Correct 372 ms 76368 KB Output is correct
86 Correct 237 ms 76500 KB Output is correct
87 Correct 244 ms 76504 KB Output is correct
88 Correct 186 ms 65228 KB Output is correct
89 Correct 220 ms 54980 KB Output is correct
90 Correct 287 ms 55564 KB Output is correct
91 Correct 259 ms 55400 KB Output is correct
92 Correct 264 ms 55772 KB Output is correct
93 Correct 213 ms 55792 KB Output is correct
94 Correct 207 ms 54876 KB Output is correct
95 Correct 229 ms 56664 KB Output is correct
96 Correct 133 ms 54464 KB Output is correct
97 Correct 208 ms 48464 KB Output is correct
98 Correct 201 ms 54472 KB Output is correct
99 Correct 183 ms 53944 KB Output is correct
100 Correct 130 ms 42372 KB Output is correct
101 Correct 374 ms 71504 KB Output is correct
102 Correct 181 ms 52440 KB Output is correct
103 Correct 356 ms 66392 KB Output is correct
104 Correct 398 ms 75604 KB Output is correct