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Submission #906574

# Submission time Handle Problem Language Result Execution time Memory
906574 2024-01-14T13:26:16 Z LucaIlie Chorus (JOI23_chorus) C++17
61 / 100
 297 ms 27660 KB 
#include <bits/stdc++.h>

using namespace std;

struct DP {
    long long minSwaps;
    int minGroups, maxGroups;

    DP operator + ( DP x ) {
        return { minSwaps + x.minSwaps, minGroups + x.minGroups, maxGroups + x.maxGroups };
    }

    DP operator * ( DP x ) {
        if ( minSwaps < x.minSwaps )
            return *this;
        if ( minSwaps > x.minSwaps )
            return x;
        return { minSwaps, min( minGroups, x.minGroups ), max( maxGroups, x.maxGroups ) };
    }
};

const int MAX_N = 1e6;
const long long INF = 1e18;
int a[MAX_N + 1], countLowerA[MAX_N + 1];
long long sumA[MAX_N + 1], sumLowerA[MAX_N + 1];
DP dp[MAX_N + 1];

struct func {
    long long a, b;
    int valmin, valmax;

    long long value( long long x ) {
        return a * x + b;
    }
};

struct CHT {
    vector<func> funcs;
    vector<long long> start;
    vector<int> stack;
    DP dppp[MAX_N + 1];

    void init() {
        for ( int i = 0; i <= MAX_N; i++ )
            dppp[i] = { INF, MAX_N + 1, 0 };
        funcs.clear();
        start.clear();
        stack.clear();
    }

    long double intersection( func f1, func f2 ) {
        return ((long double)f2.b - f1.b) / (f1.a - f2.a);
    }

    void addFunction( func f ) {
        int i = funcs.size();

        funcs.push_back( f );
        start.push_back( 0 );
        while ( !stack.empty() && intersection( funcs[i], funcs[stack.back()] ) <= start[stack.back()] )
            stack.pop_back();

        if ( !stack.empty() ) {
            long long x = intersection( funcs[i], funcs[stack.back()] );
            if ( intersection( funcs[i], funcs[stack.back()] ) == x && x <= MAX_N )
                dppp[x] = dppp[x] * DP{ funcs[stack.back()].value( x ), funcs[stack.back()].valmin, funcs[stack.back()].valmax };
            start[i] = ceil( intersection( funcs[i], funcs[stack.back()]) );
        }
        stack.push_back( i );
    }

    DP getMin( long long x ) {
        int l = -1, r = stack.size();
        while ( r - l > 1 ) {
            int mid = (l + r) / 2;
            if ( start[stack[mid]] > x )
                r = mid;
            else
                l = mid;
        }
        return DP{ funcs[stack[l]].value( x ), funcs[stack[l]].valmin, funcs[stack[l]].valmax } * dppp[x];
    }
} swapFunctions;

void computeDP( int n, long long cost ) {
    swapFunctions.init();
    swapFunctions.addFunction( { 0, 0, 0, 0 } );
    for ( int i = 1; i <= n; i++ ) {
        dp[i] = swapFunctions.getMin( i ) + DP{ i * countLowerA[i] - sumLowerA[i] + cost, 1, 1 };
        swapFunctions.addFunction( func{ -i, dp[i].minSwaps + sumA[i], dp[i].minGroups, dp[i].maxGroups } );
    }
}

int main() {
    int n, k, swaps;

    cin >> n >> k;

    int countB = 0, countA = 0;
    swaps = 0;
    for ( int i = 0; i < 2 * n; i++ ) {
        char ch;
        cin >> ch;
        if ( ch == 'A' )
            countA++;
        else {
            countB++;
            swaps += max( 0, countB - countA );
            a[countB] = max( countA, countB );
            sumA[countB] = sumA[countB - 1] + a[countB];
            countLowerA[a[countB]]++;
            sumLowerA[a[countB]] += a[countB];
        }
    }
    for ( int i = 1; i <= n; i++ ) {
        countLowerA[i] += countLowerA[i - 1];
        sumLowerA[i] += sumLowerA[i - 1];
    }

    long long leftCost = -1, rightCost = 1e12;
    while ( rightCost - leftCost > 1 ) {
        long long cost = (leftCost + rightCost) / 2;

        computeDP( n, cost );

        if ( dp[n].minGroups > k )
            leftCost = cost;
        else
            rightCost = cost;
    }

    computeDP( n, rightCost );
    cout << swaps + dp[n].minSwaps - min( k, dp[n].maxGroups ) * rightCost;

    return 0;
}

Subtask #1
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 57 ms 23128 KB Output is correct
2 Correct 51 ms 23128 KB Output is correct
3 Correct 55 ms 23132 KB Output is correct
4 Correct 61 ms 23132 KB Output is correct
5 Correct 53 ms 23128 KB Output is correct
6 Correct 55 ms 23132 KB Output is correct
7 Correct 55 ms 23380 KB Output is correct
8 Correct 58 ms 23128 KB Output is correct
9 Correct 59 ms 23132 KB Output is correct
10 Correct 57 ms 23168 KB Output is correct
11 Correct 59 ms 23128 KB Output is correct
12 Correct 64 ms 23132 KB Output is correct
13 Correct 78 ms 23128 KB Output is correct
14 Correct 58 ms 23188 KB Output is correct
15 Correct 57 ms 23132 KB Output is correct
16 Correct 55 ms 23172 KB Output is correct

Subtask #2
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 57 ms 23128 KB Output is correct
2 Correct 51 ms 23128 KB Output is correct
3 Correct 55 ms 23132 KB Output is correct
4 Correct 61 ms 23132 KB Output is correct
5 Correct 53 ms 23128 KB Output is correct
6 Correct 55 ms 23132 KB Output is correct
7 Correct 55 ms 23380 KB Output is correct
8 Correct 58 ms 23128 KB Output is correct
9 Correct 59 ms 23132 KB Output is correct
10 Correct 57 ms 23168 KB Output is correct
11 Correct 59 ms 23128 KB Output is correct
12 Correct 64 ms 23132 KB Output is correct
13 Correct 78 ms 23128 KB Output is correct
14 Correct 58 ms 23188 KB Output is correct
15 Correct 57 ms 23132 KB Output is correct
16 Correct 55 ms 23172 KB Output is correct
17 Correct 61 ms 23372 KB Output is correct
18 Correct 55 ms 23196 KB Output is correct
19 Correct 56 ms 23132 KB Output is correct
20 Correct 57 ms 23132 KB Output is correct
21 Correct 58 ms 23132 KB Output is correct
22 Correct 56 ms 23380 KB Output is correct
23 Correct 58 ms 23132 KB Output is correct
24 Correct 55 ms 23132 KB Output is correct
25 Correct 53 ms 23132 KB Output is correct
26 Correct 63 ms 23132 KB Output is correct
27 Correct 60 ms 23132 KB Output is correct
28 Correct 73 ms 23212 KB Output is correct

Subtask #3
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 57 ms 23128 KB Output is correct
2 Correct 51 ms 23128 KB Output is correct
3 Correct 55 ms 23132 KB Output is correct
4 Correct 61 ms 23132 KB Output is correct
5 Correct 53 ms 23128 KB Output is correct
6 Correct 55 ms 23132 KB Output is correct
7 Correct 55 ms 23380 KB Output is correct
8 Correct 58 ms 23128 KB Output is correct
9 Correct 59 ms 23132 KB Output is correct
10 Correct 57 ms 23168 KB Output is correct
11 Correct 59 ms 23128 KB Output is correct
12 Correct 64 ms 23132 KB Output is correct
13 Correct 78 ms 23128 KB Output is correct
14 Correct 58 ms 23188 KB Output is correct
15 Correct 57 ms 23132 KB Output is correct
16 Correct 55 ms 23172 KB Output is correct
17 Correct 61 ms 23372 KB Output is correct
18 Correct 55 ms 23196 KB Output is correct
19 Correct 56 ms 23132 KB Output is correct
20 Correct 57 ms 23132 KB Output is correct
21 Correct 58 ms 23132 KB Output is correct
22 Correct 56 ms 23380 KB Output is correct
23 Correct 58 ms 23132 KB Output is correct
24 Correct 55 ms 23132 KB Output is correct
25 Correct 53 ms 23132 KB Output is correct
26 Correct 63 ms 23132 KB Output is correct
27 Correct 60 ms 23132 KB Output is correct
28 Correct 73 ms 23212 KB Output is correct
29 Correct 79 ms 25432 KB Output is correct
30 Correct 80 ms 25584 KB Output is correct
31 Correct 97 ms 25436 KB Output is correct
32 Correct 71 ms 25436 KB Output is correct
33 Correct 80 ms 25592 KB Output is correct
34 Correct 101 ms 25588 KB Output is correct
35 Correct 73 ms 25584 KB Output is correct
36 Correct 75 ms 25436 KB Output is correct
37 Correct 91 ms 25584 KB Output is correct
38 Correct 81 ms 25588 KB Output is correct
39 Correct 102 ms 25584 KB Output is correct
40 Correct 76 ms 25648 KB Output is correct
41 Correct 93 ms 25680 KB Output is correct
42 Correct 80 ms 25432 KB Output is correct

Subtask #4
0 / 26.0

# Verdict Execution time Memory Grader output
1 Correct 57 ms 23128 KB Output is correct
2 Correct 51 ms 23128 KB Output is correct
3 Correct 55 ms 23132 KB Output is correct
4 Correct 61 ms 23132 KB Output is correct
5 Correct 53 ms 23128 KB Output is correct
6 Correct 55 ms 23132 KB Output is correct
7 Correct 55 ms 23380 KB Output is correct
8 Correct 58 ms 23128 KB Output is correct
9 Correct 59 ms 23132 KB Output is correct
10 Correct 57 ms 23168 KB Output is correct
11 Correct 59 ms 23128 KB Output is correct
12 Correct 64 ms 23132 KB Output is correct
13 Correct 78 ms 23128 KB Output is correct
14 Correct 58 ms 23188 KB Output is correct
15 Correct 57 ms 23132 KB Output is correct
16 Correct 55 ms 23172 KB Output is correct
17 Correct 61 ms 23372 KB Output is correct
18 Correct 55 ms 23196 KB Output is correct
19 Correct 56 ms 23132 KB Output is correct
20 Correct 57 ms 23132 KB Output is correct
21 Correct 58 ms 23132 KB Output is correct
22 Correct 56 ms 23380 KB Output is correct
23 Correct 58 ms 23132 KB Output is correct
24 Correct 55 ms 23132 KB Output is correct
25 Correct 53 ms 23132 KB Output is correct
26 Correct 63 ms 23132 KB Output is correct
27 Correct 60 ms 23132 KB Output is correct
28 Correct 73 ms 23212 KB Output is correct
29 Correct 79 ms 25432 KB Output is correct
30 Correct 80 ms 25584 KB Output is correct
31 Correct 97 ms 25436 KB Output is correct
32 Correct 71 ms 25436 KB Output is correct
33 Correct 80 ms 25592 KB Output is correct
34 Correct 101 ms 25588 KB Output is correct
35 Correct 73 ms 25584 KB Output is correct
36 Correct 75 ms 25436 KB Output is correct
37 Correct 91 ms 25584 KB Output is correct
38 Correct 81 ms 25588 KB Output is correct
39 Correct 102 ms 25584 KB Output is correct
40 Correct 76 ms 25648 KB Output is correct
41 Correct 93 ms 25680 KB Output is correct
42 Correct 80 ms 25432 KB Output is correct
43 Incorrect 297 ms 27660 KB Output isn't correct
44 Halted 0 ms 0 KB -

Subtask #5
0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 57 ms 23128 KB Output is correct
2 Correct 51 ms 23128 KB Output is correct
3 Correct 55 ms 23132 KB Output is correct
4 Correct 61 ms 23132 KB Output is correct
5 Correct 53 ms 23128 KB Output is correct
6 Correct 55 ms 23132 KB Output is correct
7 Correct 55 ms 23380 KB Output is correct
8 Correct 58 ms 23128 KB Output is correct
9 Correct 59 ms 23132 KB Output is correct
10 Correct 57 ms 23168 KB Output is correct
11 Correct 59 ms 23128 KB Output is correct
12 Correct 64 ms 23132 KB Output is correct
13 Correct 78 ms 23128 KB Output is correct
14 Correct 58 ms 23188 KB Output is correct
15 Correct 57 ms 23132 KB Output is correct
16 Correct 55 ms 23172 KB Output is correct
17 Correct 61 ms 23372 KB Output is correct
18 Correct 55 ms 23196 KB Output is correct
19 Correct 56 ms 23132 KB Output is correct
20 Correct 57 ms 23132 KB Output is correct
21 Correct 58 ms 23132 KB Output is correct
22 Correct 56 ms 23380 KB Output is correct
23 Correct 58 ms 23132 KB Output is correct
24 Correct 55 ms 23132 KB Output is correct
25 Correct 53 ms 23132 KB Output is correct
26 Correct 63 ms 23132 KB Output is correct
27 Correct 60 ms 23132 KB Output is correct
28 Correct 73 ms 23212 KB Output is correct
29 Correct 79 ms 25432 KB Output is correct
30 Correct 80 ms 25584 KB Output is correct
31 Correct 97 ms 25436 KB Output is correct
32 Correct 71 ms 25436 KB Output is correct
33 Correct 80 ms 25592 KB Output is correct
34 Correct 101 ms 25588 KB Output is correct
35 Correct 73 ms 25584 KB Output is correct
36 Correct 75 ms 25436 KB Output is correct
37 Correct 91 ms 25584 KB Output is correct
38 Correct 81 ms 25588 KB Output is correct
39 Correct 102 ms 25584 KB Output is correct
40 Correct 76 ms 25648 KB Output is correct
41 Correct 93 ms 25680 KB Output is correct
42 Correct 80 ms 25432 KB Output is correct
43 Incorrect 297 ms 27660 KB Output isn't correct
44 Halted 0 ms 0 KB -