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Submission #940494

# Submission time Handle Problem Language Result Execution time Memory
940494 2024-03-07T09:57:33 Z LucaIlie The short shank; Redemption (BOI21_prison) C++17
35 / 100
 2000 ms 115676 KB 
#include <bits/stdc++.h>

using namespace std;

const int MAX_N = 2e6;
const long double INF = 1e15;
const long double eps = 1e-7;

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() {
    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 1 ms 4444 KB Output is correct
2 Correct 23 ms 4444 KB Output is correct
3 Correct 23 ms 4444 KB Output is correct
4 Correct 29 ms 4444 KB Output is correct
5 Correct 29 ms 4444 KB Output is correct
6 Correct 29 ms 4444 KB Output is correct
7 Correct 27 ms 4444 KB Output is correct
8 Correct 26 ms 4660 KB Output is correct
9 Correct 27 ms 4444 KB Output is correct
10 Correct 26 ms 4444 KB Output is correct
11 Correct 26 ms 4444 KB Output is correct

Subtask #2
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4444 KB Output is correct
2 Execution timed out 2056 ms 115676 KB Time limit exceeded
3 Halted 0 ms 0 KB -

Subtask #3
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4444 KB Output is correct
2 Correct 23 ms 4444 KB Output is correct
3 Correct 23 ms 4444 KB Output is correct
4 Correct 29 ms 4444 KB Output is correct
5 Correct 29 ms 4444 KB Output is correct
6 Correct 29 ms 4444 KB Output is correct
7 Correct 27 ms 4444 KB Output is correct
8 Correct 26 ms 4660 KB Output is correct
9 Correct 27 ms 4444 KB Output is correct
10 Correct 26 ms 4444 KB Output is correct
11 Correct 26 ms 4444 KB Output is correct
12 Correct 1 ms 4444 KB Output is correct
13 Correct 30 ms 4620 KB Output is correct
14 Correct 23 ms 4444 KB Output is correct
15 Correct 29 ms 4444 KB Output is correct
16 Correct 29 ms 4444 KB Output is correct
17 Correct 29 ms 4440 KB Output is correct
18 Correct 27 ms 4440 KB Output is correct
19 Correct 26 ms 4444 KB Output is correct
20 Correct 27 ms 4652 KB Output is correct
21 Correct 29 ms 4656 KB Output is correct
22 Correct 30 ms 4444 KB Output is correct
23 Correct 319 ms 5376 KB Output is correct
24 Correct 326 ms 5212 KB Output is correct
25 Correct 304 ms 5208 KB Output is correct
26 Correct 342 ms 5380 KB Output is correct
27 Correct 315 ms 5460 KB Output is correct
28 Correct 305 ms 5376 KB Output is correct
29 Correct 311 ms 5456 KB Output is correct
30 Correct 269 ms 5412 KB Output is correct
31 Correct 276 ms 5460 KB Output is correct
32 Correct 305 ms 5380 KB Output is correct
33 Correct 285 ms 5212 KB Output is correct
34 Correct 349 ms 5212 KB Output is correct
35 Correct 300 ms 5208 KB Output is correct

Subtask #4
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4440 KB Output is correct
2 Execution timed out 2009 ms 20976 KB Time limit exceeded
3 Halted 0 ms 0 KB -

Subtask #5
0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4444 KB Output is correct
2 Correct 23 ms 4444 KB Output is correct
3 Correct 23 ms 4444 KB Output is correct
4 Correct 29 ms 4444 KB Output is correct
5 Correct 29 ms 4444 KB Output is correct
6 Correct 29 ms 4444 KB Output is correct
7 Correct 27 ms 4444 KB Output is correct
8 Correct 26 ms 4660 KB Output is correct
9 Correct 27 ms 4444 KB Output is correct
10 Correct 26 ms 4444 KB Output is correct
11 Correct 26 ms 4444 KB Output is correct
12 Correct 1 ms 4444 KB Output is correct
13 Correct 30 ms 4620 KB Output is correct
14 Correct 23 ms 4444 KB Output is correct
15 Correct 29 ms 4444 KB Output is correct
16 Correct 29 ms 4444 KB Output is correct
17 Correct 29 ms 4440 KB Output is correct
18 Correct 27 ms 4440 KB Output is correct
19 Correct 26 ms 4444 KB Output is correct
20 Correct 27 ms 4652 KB Output is correct
21 Correct 29 ms 4656 KB Output is correct
22 Correct 30 ms 4444 KB Output is correct
23 Correct 319 ms 5376 KB Output is correct
24 Correct 326 ms 5212 KB Output is correct
25 Correct 304 ms 5208 KB Output is correct
26 Correct 342 ms 5380 KB Output is correct
27 Correct 315 ms 5460 KB Output is correct
28 Correct 305 ms 5376 KB Output is correct
29 Correct 311 ms 5456 KB Output is correct
30 Correct 269 ms 5412 KB Output is correct
31 Correct 276 ms 5460 KB Output is correct
32 Correct 305 ms 5380 KB Output is correct
33 Correct 285 ms 5212 KB Output is correct
34 Correct 349 ms 5212 KB Output is correct
35 Correct 300 ms 5208 KB Output is correct
36 Correct 1 ms 4440 KB Output is correct
37 Execution timed out 2009 ms 20976 KB Time limit exceeded
38 Halted 0 ms 0 KB -

Subtask #6
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4444 KB Output is correct
2 Correct 23 ms 4444 KB Output is correct
3 Correct 23 ms 4444 KB Output is correct
4 Correct 29 ms 4444 KB Output is correct
5 Correct 29 ms 4444 KB Output is correct
6 Correct 29 ms 4444 KB Output is correct
7 Correct 27 ms 4444 KB Output is correct
8 Correct 26 ms 4660 KB Output is correct
9 Correct 27 ms 4444 KB Output is correct
10 Correct 26 ms 4444 KB Output is correct
11 Correct 26 ms 4444 KB Output is correct
12 Correct 1 ms 4444 KB Output is correct
13 Execution timed out 2056 ms 115676 KB Time limit exceeded
14 Halted 0 ms 0 KB -