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Submission #767491

# Submission time Handle Problem Language Result Execution time Memory
767491 2023-06-26T19:40:21 Z PurpleCrayon Chorus (JOI23_chorus) C++17
40 / 100
 7000 ms 468 KB 
#include <bits/stdc++.h>
using namespace std;

#define sz(v) int(v.size())
#define ar array
typedef long long ll;
const int N = 5e3+10, MOD = 1e9+7;

int n, K, small[N];
int ps[N], l_use[N];
vector<int> one, two;

// min CHT with
//  - slopes decreasing
//  - query x increasing


struct Line {
    int m, b;
    int calc(int x) {
        return m * x + b;
    }
};

struct CHT {
    deque<Line> lines;

    void add(int m, int b) {
        while (sz(lines) >= 2) {
            auto A = lines.end()[-2];
            auto B = lines.end()[-1];
            if ((b - A.b) * (A.m - m) <= (B.b - A.b) * (A.m - B.m)) lines.pop_back();
            else break;
        }
        lines.push_back({m, b});
    }

    int qry(int x) {
        int ans = MOD;
        for (auto line : lines) ans = min(ans, line.calc(x));
        return ans;

        /*
        while (sz(lines) >= 2 && lines[0].calc(x) >= lines[1].calc(x)) {
            lines.pop_front();
        }

        return lines[0].calc(x);
        */
    }
};

void solve() {
    cin >> n >> K;
    for (int i = 0; i < 2 * n; i++) {
        char c; cin >> c;
        if (c == 'A') one.push_back(i);
        else two.push_back(i);
    }

    for (int i = 0; i < n; i++) {
        small[i] = lower_bound(two.begin(), two.end(), one[i]) - two.begin();
    }

    for (int i = 0; i < n; i++) {
        ps[i] = small[i] + (i ? ps[i-1] : 0);
        l_use[i] = -(i ? ps[i-1] : 0);
        for (int j = i; j < n; j++) {
            if (small[j] < i) {
                l_use[i] -= small[j] - i;
            }
        }
    }

    vector<int> prv(n, MOD);
    for (int k = 1; k <= K; k++) {
        vector<int> nxt(n, MOD);

        CHT lines;
        for (int i = 0; i < n; i++) {
            lines.add(-i, i * i - i + l_use[i] + (i == 0 ? 0 : prv[i-1]));
            nxt[i] = lines.qry(i) + ps[i];

            int l = small[i];
            if (l <= i) {
                nxt[i] = min(nxt[i], (l == 0 ? 0 : prv[l-1]));
            }
        }
        swap(prv, nxt);
    }

    cout << prv[n-1] << '\n';
}

int main() {
    ios::sync_with_stdio(false); cin.tie(0);
    int T = 1;
    // cin >> T;
    while (T--) solve();
}

Subtask #1
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 0 ms 212 KB Output is correct

Subtask #2
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 2 ms 212 KB Output is correct
18 Correct 13 ms 340 KB Output is correct
19 Correct 37 ms 340 KB Output is correct
20 Correct 0 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 66 ms 212 KB Output is correct
23 Correct 71 ms 340 KB Output is correct
24 Correct 2 ms 340 KB Output is correct
25 Correct 72 ms 340 KB Output is correct
26 Correct 57 ms 340 KB Output is correct
27 Correct 23 ms 340 KB Output is correct
28 Correct 26 ms 340 KB Output is correct

Subtask #3
0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 2 ms 212 KB Output is correct
18 Correct 13 ms 340 KB Output is correct
19 Correct 37 ms 340 KB Output is correct
20 Correct 0 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 66 ms 212 KB Output is correct
23 Correct 71 ms 340 KB Output is correct
24 Correct 2 ms 340 KB Output is correct
25 Correct 72 ms 340 KB Output is correct
26 Correct 57 ms 340 KB Output is correct
27 Correct 23 ms 340 KB Output is correct
28 Correct 26 ms 340 KB Output is correct
29 Execution timed out 7032 ms 468 KB Time limit exceeded
30 Halted 0 ms 0 KB -

Subtask #4
0 / 26.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 2 ms 212 KB Output is correct
18 Correct 13 ms 340 KB Output is correct
19 Correct 37 ms 340 KB Output is correct
20 Correct 0 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 66 ms 212 KB Output is correct
23 Correct 71 ms 340 KB Output is correct
24 Correct 2 ms 340 KB Output is correct
25 Correct 72 ms 340 KB Output is correct
26 Correct 57 ms 340 KB Output is correct
27 Correct 23 ms 340 KB Output is correct
28 Correct 26 ms 340 KB Output is correct
29 Execution timed out 7032 ms 468 KB Time limit exceeded
30 Halted 0 ms 0 KB -

Subtask #5
0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 2 ms 212 KB Output is correct
18 Correct 13 ms 340 KB Output is correct
19 Correct 37 ms 340 KB Output is correct
20 Correct 0 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 66 ms 212 KB Output is correct
23 Correct 71 ms 340 KB Output is correct
24 Correct 2 ms 340 KB Output is correct
25 Correct 72 ms 340 KB Output is correct
26 Correct 57 ms 340 KB Output is correct
27 Correct 23 ms 340 KB Output is correct
28 Correct 26 ms 340 KB Output is correct
29 Execution timed out 7032 ms 468 KB Time limit exceeded
30 Halted 0 ms 0 KB -