oj.uz

Submission #453725

# Submission time Handle Problem Language Result Execution time Memory
453725 2021-08-04T16:08:32 Z blue Constellation 3 (JOI20_constellation3) C++17
35 / 100
 1500 ms 137508 KB 
#include <iostream>
#include <vector>
#include <algorithm>
#include <set>
#include <cassert>
using namespace std;

const int maxN = 200'000;
const int maxM = 200'000;
const int lgM = 18;
const int INF = 1'000'000'000;

int N;
vector<int> A(1+maxN+1);
vector<int> star_list[1+maxN];

int M;
vector<int> X(1+maxM);
vector<int> Y(1+maxM);
vector<long long> C(1+maxM);

long long total_cost = 0;


struct segtree
{
    int l;
    int r;
    int mx;

    segtree* left = NULL;
    segtree* right = NULL;

    segtree()
    {
        ;
    }

    segtree(int L, int R)
    {
        l = L;
        r = R;
        if(l == r)
        {
            mx = A[l];
        }
        else
        {
            int m = (l+r)/2;
            left = new segtree(l, m);
            right = new segtree(m+1, r);
            mx = max(left->mx, right->mx);
        }
    }

    int rangemax(int L, int R)
    {
        if(R < l || r < L) return -INF;
        else if(L <= l && r <= R) return mx;
        else return max(left->rangemax(L, R), right->rangemax(L, R));
    }
};


vector<int> left_high(1+maxM);
vector<int> right_high(1+maxM);


struct rectangle
{
    int L; //[L, R] x [H, N]
    int R;
    int H;
    int I;
};

bool operator < (rectangle A, rectangle B)
{
    if(A.L != B.L)
        return A.L < B.L;
    else if(A.R != B.R)
        return A.R > B.R;
    else if(A.H != B.H)
        return A.H > B.H;
    else
        return A.I < B.I;
}

vector<rectangle> rect(1+maxM);
vector<int> star_bottom(1+maxM);

vector<int> openings[1+maxN];
vector<int> closings[1+maxN];



int anc[1+maxM][lgM];
vector<int> desc[1+maxM][lgM];
vector<int> depth(1+maxM, 0);

long long anc_dp_sum[1+maxM][lgM]; //exclusive
vector<long long> dp(1+maxM, 0LL);
vector<long long> child_dp_sum(1+maxM, 0LL);


bool dbg_flag = 0;




void dfs1(int u)
{
    for(int v: desc[u][0])
    {
        depth[v] = depth[u] + 1;
        dfs1(v);
    }
}

int getAnc(int u, int d)
{
    for(int e = 0; e < lgM; e++)
    {
        if(d & (1 << e))
            u = anc[u][e];
    }
    return u;
}

long long chain_sum(int u, int d)
{
    int u1 = u;
    long long ans = 0;
    for(int e = 0; e < lgM; e++)
    {
        if(d & (1 << e))
        {
            // if(dbg_flag)
            // {
            //     cerr << "jumping from " << u << " to " << anc[u][e] << ", adding " << anc_dp_sum[u][e] << " to answer\n";
            // }
            ans += anc_dp_sum[u][e];
            u = anc[u][e];
        }
    }
    // cerr << "chain sum " << u1 << ' ' << d << " " << ans << '\n';
    return ans;
}




void binary_lift(int u, int e)
{
    // cerr << "binary lift " << u << ' ' << e << '\n';
    anc_dp_sum[u][e] = anc_dp_sum[u][e-1] + anc_dp_sum[ anc[u][e-1] ][e-1];
    // cerr << "anc dp sum " << u << ' ' << e << " = " << anc_dp_sum[u][e] << '\n';

    for(int v: desc[u][e])
        binary_lift(v, e+1);
}

void dfs2(int u)
{
    // cerr << "\n\n\n\n";
    // cerr << "entered dfs2 " << u << "\n";
    for(int v: desc[u][0])
    {
        // cerr << u << " -> " << v << '\n';
        dfs2(v);
        child_dp_sum[u] += dp[v];
    }

    for(int v: desc[u][0])
    {
        anc_dp_sum[v][0] = child_dp_sum[u] - dp[v];
        // cerr << "anc dp sum " << v << ' ' << 0 << " = " << anc_dp_sum[v][0] << '\n';
        for(int v2: desc[v][0])
            binary_lift(v2, 1);
    }
    if(star_bottom[u] == u)
    {
        dp[u] = child_dp_sum[u] + C[u];
        // cerr << "!!! ";
        // cerr << "dp[" << u << "] = " << dp[u] << '\n';
    }
    else
    {
        // cerr << "case 2\n";
        int sb = star_bottom[u];
        long long new_dp = child_dp_sum[sb] + chain_sum(sb, depth[sb] - depth[u]) + C[u];
        // new_dp += child_dp_sum[u] - dp[ getAnc(sb, depth[sb] - depth[u] - 1) ];




        // cerr << sb << ' ' << child_dp_sum[sb] << ' ' << chain_sum(sb, depth[sb] - depth[u]) << ' ' << C[u] << '\n';
        // cerr << child_dp_sum[u] << '\n';
        // cerr << new_dp << '\n';

        dp[u] = max(child_dp_sum[u],   new_dp);

// cerr << "!!! ";
        // cerr << "dp[" << u << "] = " << dp[u] << '\n';
    }
    // cerr << "exited dfs2 " << u << "\n";
    // cerr << "\n\n\n\n";
}







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

    cin >> N;
    A[0] = N+1;
    for(int i = 1; i <= N; i++) cin >> A[i];
    A[N+1] = N+1;

    cin >> M;
    for(int j = 1; j <= M; j++)
    {
        cin >> X[j] >> Y[j] >> C[j];
        star_list[ X[j] ].push_back(j);
        total_cost += C[j];
    }
    // cerr << "total cost = " << total_cost << '\n';

    segtree S(0, N+1);

    // cerr << "check\n";
    // cerr << "\n\n\n";


    for(int j = 1; j <= M; j++)
    {
        // cerr << "j = " << j << '\n';
        int lo, hi, mid;
        //closest building on left
        lo = 0;
        hi = X[j]-1;
        while(lo != hi)
        {
            mid = (lo+hi)/2+1;
            if(S.rangemax(mid, hi) >= Y[j])
                lo = mid;
            else
                hi = mid-1;
        }
        left_high[j] = lo;

        // cerr << "part 1 done\n";


        //closest building on right
        lo = X[j]+1;
        hi = N+1;
        while(lo != hi)
        {
            // cerr << lo << ' ' << hi << '\n';
            mid = (lo+hi)/2;
            if(S.rangemax(lo, mid) >= Y[j])
                hi = mid;
            else
                lo = mid+1;
        }
        right_high[j] = lo;

        // cerr << j << ' ' << left_high[j] << ' ' << right_high[j] << '\n';

        rect[j] = rectangle{left_high[j] + 1, right_high[j] - 1, Y[j], j};
        openings[rect[j].L].push_back(j);
        closings[rect[j].R].push_back(j);
    }
    // cerr << "\n\n\n\n";


    for(int i = 1; i <= N; i++)
    {
        // cerr << "i = " << i << '\n';
        sort(openings[i].begin(), openings[i].end(), [] (int o1, int o2)
        {
            return rect[o1] < rect[o2];
        });

        // for(int o: openings[i]) cerr << o << ' ';
        // cerr << '\n';

        sort(closings[i].begin(), closings[i].end(), [] (int c1, int c2)
        {
            return rect[c2] < rect[c1]; //  REVERSED!!!!!!
        });

        // for(int c: closings[i]) cerr << c << ' ';
        // cerr << '\n';
    }

    vector<int> ST(1, 0);
    anc[0][0] = 0;
    for(int i = 1; i <= N; i++)
    {
        // cerr << "i = " << i << '\n';
        for(int o: openings[i])
        {
            // cerr << "   o = " << o << '\n';
            // cerr << "parent " << o << " = " << ST.back() << '\n';
            anc[o][0] = ST.back();
            desc[ anc[o][0] ][0].push_back(o);
            ST.push_back(o);
        }

        for(int j: star_list[i])
        {
            star_bottom[j] = ST.back();
            // cerr << "star bottom of " << j << " = " << star_bottom[j] << '\n';
        }

        for(int c: closings[i])
        {
            ST.pop_back();
            // cerr << "   c = " << c << '\n';
        }
    }
    assert(N + M <= 10000);

    for(int e = 1; e < lgM; e++)
        for(int j = 0; j <= M; j++)
        {
            anc[j][e] = anc[ anc[j][e-1] ][e-1];
            desc[ anc[j][e] ][e].push_back(j);
        }

    for(int j = 1; j <= M; j++)
        if(anc[j][0] == 0)
        {
            depth[j] = 1;
            dfs1(j);
        }

    long long max_kept = 0;


    for(int j = 1; j <= M; j++)
    {
        // cerr << "anc " << j << " = " << anc[j][0] << '\n';
        if(anc[j][0] == 0)
        {
            // cerr << "calling " << j << '\n';
            dfs2(j);
            max_kept += dp[j];
        }
    }

    cout << total_cost - max_kept << '\n';
}

Compilation message

constellation3.cpp: In function 'long long int chain_sum(int, int)':
constellation3.cpp:132:9: warning: unused variable 'u1' [-Wunused-variable]
  132 |     int u1 = u;
      |         ^~
constellation3.cpp: In function 'int main()':
constellation3.cpp:324:17: warning: unused variable 'c' [-Wunused-variable]
  324 |         for(int c: closings[i])
      |                 ^

Subtask #1
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 60 ms 112324 KB Output is correct
2 Correct 60 ms 112324 KB Output is correct
3 Correct 64 ms 112324 KB Output is correct
4 Correct 62 ms 112424 KB Output is correct
5 Correct 61 ms 112324 KB Output is correct
6 Correct 59 ms 112416 KB Output is correct
7 Correct 61 ms 112328 KB Output is correct
8 Correct 60 ms 112432 KB Output is correct
9 Correct 59 ms 112308 KB Output is correct
10 Correct 62 ms 112436 KB Output is correct
11 Correct 61 ms 112360 KB Output is correct
12 Correct 61 ms 112416 KB Output is correct
13 Correct 60 ms 112384 KB Output is correct
14 Correct 60 ms 112368 KB Output is correct
15 Correct 60 ms 112452 KB Output is correct
16 Correct 61 ms 112472 KB Output is correct
17 Correct 60 ms 112444 KB Output is correct
18 Correct 63 ms 112448 KB Output is correct
19 Correct 62 ms 112412 KB Output is correct
20 Correct 60 ms 112432 KB Output is correct
21 Correct 59 ms 112452 KB Output is correct
22 Correct 62 ms 112436 KB Output is correct

Subtask #2
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 60 ms 112324 KB Output is correct
2 Correct 60 ms 112324 KB Output is correct
3 Correct 64 ms 112324 KB Output is correct
4 Correct 62 ms 112424 KB Output is correct
5 Correct 61 ms 112324 KB Output is correct
6 Correct 59 ms 112416 KB Output is correct
7 Correct 61 ms 112328 KB Output is correct
8 Correct 60 ms 112432 KB Output is correct
9 Correct 59 ms 112308 KB Output is correct
10 Correct 62 ms 112436 KB Output is correct
11 Correct 61 ms 112360 KB Output is correct
12 Correct 61 ms 112416 KB Output is correct
13 Correct 60 ms 112384 KB Output is correct
14 Correct 60 ms 112368 KB Output is correct
15 Correct 60 ms 112452 KB Output is correct
16 Correct 61 ms 112472 KB Output is correct
17 Correct 60 ms 112444 KB Output is correct
18 Correct 63 ms 112448 KB Output is correct
19 Correct 62 ms 112412 KB Output is correct
20 Correct 60 ms 112432 KB Output is correct
21 Correct 59 ms 112452 KB Output is correct
22 Correct 62 ms 112436 KB Output is correct
23 Correct 68 ms 113236 KB Output is correct
24 Correct 68 ms 113252 KB Output is correct
25 Correct 71 ms 113180 KB Output is correct
26 Correct 74 ms 113172 KB Output is correct
27 Correct 71 ms 113228 KB Output is correct
28 Correct 70 ms 113172 KB Output is correct
29 Correct 80 ms 113176 KB Output is correct
30 Correct 72 ms 113188 KB Output is correct
31 Correct 70 ms 113220 KB Output is correct
32 Correct 72 ms 113828 KB Output is correct
33 Correct 74 ms 113828 KB Output is correct
34 Correct 83 ms 113808 KB Output is correct
35 Correct 74 ms 113816 KB Output is correct
36 Correct 72 ms 113772 KB Output is correct
37 Correct 73 ms 113732 KB Output is correct
38 Correct 67 ms 113812 KB Output is correct
39 Correct 72 ms 113396 KB Output is correct
40 Correct 74 ms 113812 KB Output is correct
41 Correct 70 ms 113476 KB Output is correct
42 Correct 78 ms 113424 KB Output is correct
43 Correct 71 ms 113732 KB Output is correct
44 Correct 69 ms 113356 KB Output is correct

Subtask #3
0 / 65.0

# Verdict Execution time Memory Grader output
1 Correct 60 ms 112324 KB Output is correct
2 Correct 60 ms 112324 KB Output is correct
3 Correct 64 ms 112324 KB Output is correct
4 Correct 62 ms 112424 KB Output is correct
5 Correct 61 ms 112324 KB Output is correct
6 Correct 59 ms 112416 KB Output is correct
7 Correct 61 ms 112328 KB Output is correct
8 Correct 60 ms 112432 KB Output is correct
9 Correct 59 ms 112308 KB Output is correct
10 Correct 62 ms 112436 KB Output is correct
11 Correct 61 ms 112360 KB Output is correct
12 Correct 61 ms 112416 KB Output is correct
13 Correct 60 ms 112384 KB Output is correct
14 Correct 60 ms 112368 KB Output is correct
15 Correct 60 ms 112452 KB Output is correct
16 Correct 61 ms 112472 KB Output is correct
17 Correct 60 ms 112444 KB Output is correct
18 Correct 63 ms 112448 KB Output is correct
19 Correct 62 ms 112412 KB Output is correct
20 Correct 60 ms 112432 KB Output is correct
21 Correct 59 ms 112452 KB Output is correct
22 Correct 62 ms 112436 KB Output is correct
23 Correct 68 ms 113236 KB Output is correct
24 Correct 68 ms 113252 KB Output is correct
25 Correct 71 ms 113180 KB Output is correct
26 Correct 74 ms 113172 KB Output is correct
27 Correct 71 ms 113228 KB Output is correct
28 Correct 70 ms 113172 KB Output is correct
29 Correct 80 ms 113176 KB Output is correct
30 Correct 72 ms 113188 KB Output is correct
31 Correct 70 ms 113220 KB Output is correct
32 Correct 72 ms 113828 KB Output is correct
33 Correct 74 ms 113828 KB Output is correct
34 Correct 83 ms 113808 KB Output is correct
35 Correct 74 ms 113816 KB Output is correct
36 Correct 72 ms 113772 KB Output is correct
37 Correct 73 ms 113732 KB Output is correct
38 Correct 67 ms 113812 KB Output is correct
39 Correct 72 ms 113396 KB Output is correct
40 Correct 74 ms 113812 KB Output is correct
41 Correct 70 ms 113476 KB Output is correct
42 Correct 78 ms 113424 KB Output is correct
43 Correct 71 ms 113732 KB Output is correct
44 Correct 69 ms 113356 KB Output is correct
45 Execution timed out 1588 ms 137508 KB Time limit exceeded
46 Halted 0 ms 0 KB -