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답안 #453727

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
453727 2021-08-04T16:09:27 Z blue 별자리 3 (JOI20_constellation3) C++17
35 / 100
 1500 ms 137448 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);
    }
    
        assert(N + M <= 10000);
    // 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';
        }
    }

    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:328:17: warning: unused variable 'c' [-Wunused-variable]
  328 |         for(int c: closings[i])
      |                 ^

Subtask #1
14.0 / 14.0

# 결과 실행 시간 메모리 Grader output
1 Correct 62 ms 112364 KB Output is correct
2 Correct 63 ms 112344 KB Output is correct
3 Correct 60 ms 112380 KB Output is correct
4 Correct 60 ms 112356 KB Output is correct
5 Correct 62 ms 112328 KB Output is correct
6 Correct 61 ms 112408 KB Output is correct
7 Correct 59 ms 112364 KB Output is correct
8 Correct 70 ms 112360 KB Output is correct
9 Correct 60 ms 112392 KB Output is correct
10 Correct 61 ms 112396 KB Output is correct
11 Correct 60 ms 112480 KB Output is correct
12 Correct 62 ms 112412 KB Output is correct
13 Correct 61 ms 112452 KB Output is correct
14 Correct 63 ms 112452 KB Output is correct
15 Correct 67 ms 112444 KB Output is correct
16 Correct 61 ms 112468 KB Output is correct
17 Correct 61 ms 112452 KB Output is correct
18 Correct 61 ms 112440 KB Output is correct
19 Correct 61 ms 112348 KB Output is correct
20 Correct 60 ms 112324 KB Output is correct
21 Correct 61 ms 112488 KB Output is correct
22 Correct 61 ms 112408 KB Output is correct

Subtask #2
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 62 ms 112364 KB Output is correct
2 Correct 63 ms 112344 KB Output is correct
3 Correct 60 ms 112380 KB Output is correct
4 Correct 60 ms 112356 KB Output is correct
5 Correct 62 ms 112328 KB Output is correct
6 Correct 61 ms 112408 KB Output is correct
7 Correct 59 ms 112364 KB Output is correct
8 Correct 70 ms 112360 KB Output is correct
9 Correct 60 ms 112392 KB Output is correct
10 Correct 61 ms 112396 KB Output is correct
11 Correct 60 ms 112480 KB Output is correct
12 Correct 62 ms 112412 KB Output is correct
13 Correct 61 ms 112452 KB Output is correct
14 Correct 63 ms 112452 KB Output is correct
15 Correct 67 ms 112444 KB Output is correct
16 Correct 61 ms 112468 KB Output is correct
17 Correct 61 ms 112452 KB Output is correct
18 Correct 61 ms 112440 KB Output is correct
19 Correct 61 ms 112348 KB Output is correct
20 Correct 60 ms 112324 KB Output is correct
21 Correct 61 ms 112488 KB Output is correct
22 Correct 61 ms 112408 KB Output is correct
23 Correct 71 ms 113220 KB Output is correct
24 Correct 70 ms 113220 KB Output is correct
25 Correct 72 ms 113160 KB Output is correct
26 Correct 71 ms 113164 KB Output is correct
27 Correct 69 ms 113268 KB Output is correct
28 Correct 69 ms 113232 KB Output is correct
29 Correct 72 ms 113148 KB Output is correct
30 Correct 73 ms 113220 KB Output is correct
31 Correct 73 ms 113184 KB Output is correct
32 Correct 74 ms 113692 KB Output is correct
33 Correct 72 ms 113724 KB Output is correct
34 Correct 72 ms 113676 KB Output is correct
35 Correct 71 ms 113732 KB Output is correct
36 Correct 73 ms 113804 KB Output is correct
37 Correct 72 ms 113744 KB Output is correct
38 Correct 73 ms 113788 KB Output is correct
39 Correct 71 ms 113472 KB Output is correct
40 Correct 72 ms 113736 KB Output is correct
41 Correct 71 ms 113496 KB Output is correct
42 Correct 70 ms 113348 KB Output is correct
43 Correct 69 ms 113768 KB Output is correct
44 Correct 70 ms 113328 KB Output is correct

Subtask #3
0 / 65.0

# 결과 실행 시간 메모리 Grader output
1 Correct 62 ms 112364 KB Output is correct
2 Correct 63 ms 112344 KB Output is correct
3 Correct 60 ms 112380 KB Output is correct
4 Correct 60 ms 112356 KB Output is correct
5 Correct 62 ms 112328 KB Output is correct
6 Correct 61 ms 112408 KB Output is correct
7 Correct 59 ms 112364 KB Output is correct
8 Correct 70 ms 112360 KB Output is correct
9 Correct 60 ms 112392 KB Output is correct
10 Correct 61 ms 112396 KB Output is correct
11 Correct 60 ms 112480 KB Output is correct
12 Correct 62 ms 112412 KB Output is correct
13 Correct 61 ms 112452 KB Output is correct
14 Correct 63 ms 112452 KB Output is correct
15 Correct 67 ms 112444 KB Output is correct
16 Correct 61 ms 112468 KB Output is correct
17 Correct 61 ms 112452 KB Output is correct
18 Correct 61 ms 112440 KB Output is correct
19 Correct 61 ms 112348 KB Output is correct
20 Correct 60 ms 112324 KB Output is correct
21 Correct 61 ms 112488 KB Output is correct
22 Correct 61 ms 112408 KB Output is correct
23 Correct 71 ms 113220 KB Output is correct
24 Correct 70 ms 113220 KB Output is correct
25 Correct 72 ms 113160 KB Output is correct
26 Correct 71 ms 113164 KB Output is correct
27 Correct 69 ms 113268 KB Output is correct
28 Correct 69 ms 113232 KB Output is correct
29 Correct 72 ms 113148 KB Output is correct
30 Correct 73 ms 113220 KB Output is correct
31 Correct 73 ms 113184 KB Output is correct
32 Correct 74 ms 113692 KB Output is correct
33 Correct 72 ms 113724 KB Output is correct
34 Correct 72 ms 113676 KB Output is correct
35 Correct 71 ms 113732 KB Output is correct
36 Correct 73 ms 113804 KB Output is correct
37 Correct 72 ms 113744 KB Output is correct
38 Correct 73 ms 113788 KB Output is correct
39 Correct 71 ms 113472 KB Output is correct
40 Correct 72 ms 113736 KB Output is correct
41 Correct 71 ms 113496 KB Output is correct
42 Correct 70 ms 113348 KB Output is correct
43 Correct 69 ms 113768 KB Output is correct
44 Correct 70 ms 113328 KB Output is correct
45 Execution timed out 1581 ms 137448 KB Time limit exceeded
46 Halted 0 ms 0 KB -