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Submission #940499

# Submission time Handle Problem Language Result Execution time Memory
940499 2024-03-07T10:01:42 Z LucaIlie The short shank; Redemption (BOI21_prison) C++17
35 / 100
 2000 ms 115660 KB 
#include <bits/stdc++.h>

using namespace std;

const int MAX_N = 2e6;
const long double INF = 1e15;
const long double eps = 1e-3;

int groups[MAX_N + 1], firstLower[MAX_N + 1];
long long t[MAX_N + 1];
long double minPrisoners[MAX_N + 1];

struct info {
    long double minn;
    int pos;

    bool operator < ( const info &x ) const {
        return minn < x.minn;
    }
};

struct SegTree {
    int n, ls, rs;
    vector<info> segTree;
    vector<long double> lazy;

    void init( int v, int l, int r ) {
        lazy[v] = 0;
        if ( l == r ) {
            segTree[v] = { 0, l };
            return;
        }
        int mid = (l + r) / 2;
        init( v * 2 + 1, l, mid );
        init( v * 2 + 2, mid + 1, r );
        segTree[v] = min( segTree[v * 2 + 1], segTree[v * 2 + 2] );
    }

    void init( int _ls, int _rs ) {
        ls = _ls;
        rs = _rs;
        n = rs - ls + 1;
        segTree.resize( 4 * n );
        lazy.resize( 4 * n );
        init( 0, ls, rs );
    }

    void propag( int v, int l, int r ) {
        segTree[v].minn += lazy[v];
        if ( l != r ) {
            lazy[v * 2 + 1] += lazy[v];
            lazy[v * 2 + 2] += lazy[v];
        }
        lazy[v] = 0;
    }

    void update( int v, int l, int r, int lu, int ru, long double x ) {
        propag( v, l, r );

        if ( l > ru || r < lu )
            return;

        if ( lu <= l && r <= ru ) {
            lazy[v] += x;
            propag( v, l, r );
            return;
        }

        int mid = (l + r) / 2;
        update( v * 2 + 1, l, mid, lu, ru, x );
        update( v * 2 + 2, mid + 1, r, lu, ru, x );
        segTree[v] = min( segTree[v * 2 + 1], segTree[v * 2 + 2] );
    }

    void update( int l, int r, long double x ) {
        update( 0, ls, rs, l, r, x );
    }

    info query( int v, int l, int r, int lq, int rq ) {
        propag( v, l, r );

        if ( l > rq || r < lq )
            return { INF, 0 };

        if ( lq <= l && r <= rq )
            return segTree[v];

        int mid = (l + r) / 2;
        return min( query( v * 2 + 1, l, mid, lq, rq ), query( v * 2 + 2, mid + 1, r, lq, rq ) );
    }
} prisoners;

int main() {
    cin.tie( NULL );
    cout.tie( NULL );
    ios_base::sync_with_stdio( false );
    int n, d, s;

    cin >> n >> d >> s;
    d++;
    for ( int i = 1; i <= n; i++ ) {
        cin >> t[i];
        t[i] -= i;
    }
    t[0] = -INF;

    vector<int> stack;
    stack.push_back( 0 );
    for ( int i = 1; i <= n; i++ ) {
        while ( t[i] <= t[stack.back()] )
            stack.pop_back();
        stack.push_back( i );

        int l = 0, r = stack.size();
        while ( r - l > 1 ) {
            int mid = (l + r) / 2;

            if ( t[stack[mid]] <= s - i )
                l = mid;
            else
                r = mid;
        }
        firstLower[i] = stack[l];
    }


    cout << fixed << setprecision( 15 );
    long double lc = 0, rc = 1e8;
    while ( rc - lc > eps ) {
        long double cost = (rc + lc) / 2;

        prisoners.init( 1, n );
        for ( int i = 1; i <= n; i++ ) {
            prisoners.update( i, i, minPrisoners[i - 1] + cost );
            prisoners.update( 1, firstLower[i], 1 );

            auto x = prisoners.query( 0, 1, n, 1, i );
            minPrisoners[i] = x.minn;
            groups[i] = groups[x.pos - 1] + 1;
        }

        if ( groups[n] > d )
            lc = cost;
        else
            rc = cost;
    }
    long double cost = rc;
    prisoners.init( 1, n );
    for ( int i = 1; i <= n; i++ ) {
        prisoners.update( i, i, minPrisoners[i - 1] + cost );
        prisoners.update( 1, firstLower[i], 1 );

        auto x = prisoners.query( 0, 1, n, 1, i );
        minPrisoners[i] = x.minn;
        groups[i] = groups[x.pos] + 1;
    }

    long double ans = minPrisoners[n] - d * cost;
    if ( ceil( ans ) - ans < ans - floor( ans ) )
        cout << (int)ceil( ans );
    else
        cout << (int)floor( ans );

    return 0;
}

Subtask #1
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4440 KB Output is correct
2 Correct 20 ms 4652 KB Output is correct
3 Correct 17 ms 4440 KB Output is correct
4 Correct 22 ms 4440 KB Output is correct
5 Correct 22 ms 4440 KB Output is correct
6 Correct 21 ms 4444 KB Output is correct
7 Correct 20 ms 4444 KB Output is correct
8 Correct 20 ms 4676 KB Output is correct
9 Correct 20 ms 4680 KB Output is correct
10 Correct 23 ms 4696 KB Output is correct
11 Correct 19 ms 4444 KB Output is correct

Subtask #2
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4444 KB Output is correct
2 Execution timed out 2084 ms 115660 KB Time limit exceeded
3 Halted 0 ms 0 KB -

Subtask #3
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4440 KB Output is correct
2 Correct 20 ms 4652 KB Output is correct
3 Correct 17 ms 4440 KB Output is correct
4 Correct 22 ms 4440 KB Output is correct
5 Correct 22 ms 4440 KB Output is correct
6 Correct 21 ms 4444 KB Output is correct
7 Correct 20 ms 4444 KB Output is correct
8 Correct 20 ms 4676 KB Output is correct
9 Correct 20 ms 4680 KB Output is correct
10 Correct 23 ms 4696 KB Output is correct
11 Correct 19 ms 4444 KB Output is correct
12 Correct 1 ms 4440 KB Output is correct
13 Correct 17 ms 4440 KB Output is correct
14 Correct 18 ms 4444 KB Output is correct
15 Correct 22 ms 4444 KB Output is correct
16 Correct 22 ms 4440 KB Output is correct
17 Correct 22 ms 4444 KB Output is correct
18 Correct 21 ms 4444 KB Output is correct
19 Correct 20 ms 4444 KB Output is correct
20 Correct 20 ms 4440 KB Output is correct
21 Correct 20 ms 4444 KB Output is correct
22 Correct 19 ms 4444 KB Output is correct
23 Correct 226 ms 5212 KB Output is correct
24 Correct 240 ms 5404 KB Output is correct
25 Correct 225 ms 5212 KB Output is correct
26 Correct 225 ms 5212 KB Output is correct
27 Correct 227 ms 5208 KB Output is correct
28 Correct 224 ms 5212 KB Output is correct
29 Correct 224 ms 5208 KB Output is correct
30 Correct 207 ms 5408 KB Output is correct
31 Correct 203 ms 5212 KB Output is correct
32 Correct 213 ms 5212 KB Output is correct
33 Correct 226 ms 5460 KB Output is correct
34 Correct 223 ms 5208 KB Output is correct
35 Correct 224 ms 5208 KB Output is correct

Subtask #4
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4696 KB Output is correct
2 Execution timed out 2057 ms 21076 KB Time limit exceeded
3 Halted 0 ms 0 KB -

Subtask #5
0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4440 KB Output is correct
2 Correct 20 ms 4652 KB Output is correct
3 Correct 17 ms 4440 KB Output is correct
4 Correct 22 ms 4440 KB Output is correct
5 Correct 22 ms 4440 KB Output is correct
6 Correct 21 ms 4444 KB Output is correct
7 Correct 20 ms 4444 KB Output is correct
8 Correct 20 ms 4676 KB Output is correct
9 Correct 20 ms 4680 KB Output is correct
10 Correct 23 ms 4696 KB Output is correct
11 Correct 19 ms 4444 KB Output is correct
12 Correct 1 ms 4440 KB Output is correct
13 Correct 17 ms 4440 KB Output is correct
14 Correct 18 ms 4444 KB Output is correct
15 Correct 22 ms 4444 KB Output is correct
16 Correct 22 ms 4440 KB Output is correct
17 Correct 22 ms 4444 KB Output is correct
18 Correct 21 ms 4444 KB Output is correct
19 Correct 20 ms 4444 KB Output is correct
20 Correct 20 ms 4440 KB Output is correct
21 Correct 20 ms 4444 KB Output is correct
22 Correct 19 ms 4444 KB Output is correct
23 Correct 226 ms 5212 KB Output is correct
24 Correct 240 ms 5404 KB Output is correct
25 Correct 225 ms 5212 KB Output is correct
26 Correct 225 ms 5212 KB Output is correct
27 Correct 227 ms 5208 KB Output is correct
28 Correct 224 ms 5212 KB Output is correct
29 Correct 224 ms 5208 KB Output is correct
30 Correct 207 ms 5408 KB Output is correct
31 Correct 203 ms 5212 KB Output is correct
32 Correct 213 ms 5212 KB Output is correct
33 Correct 226 ms 5460 KB Output is correct
34 Correct 223 ms 5208 KB Output is correct
35 Correct 224 ms 5208 KB Output is correct
36 Correct 1 ms 4696 KB Output is correct
37 Execution timed out 2057 ms 21076 KB Time limit exceeded
38 Halted 0 ms 0 KB -

Subtask #6
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4440 KB Output is correct
2 Correct 20 ms 4652 KB Output is correct
3 Correct 17 ms 4440 KB Output is correct
4 Correct 22 ms 4440 KB Output is correct
5 Correct 22 ms 4440 KB Output is correct
6 Correct 21 ms 4444 KB Output is correct
7 Correct 20 ms 4444 KB Output is correct
8 Correct 20 ms 4676 KB Output is correct
9 Correct 20 ms 4680 KB Output is correct
10 Correct 23 ms 4696 KB Output is correct
11 Correct 19 ms 4444 KB Output is correct
12 Correct 2 ms 4444 KB Output is correct
13 Execution timed out 2084 ms 115660 KB Time limit exceeded
14 Halted 0 ms 0 KB -