Submission #767523

#	Time	Username	Problem	Language	Result	Execution time	Memory
767523		PurpleCrayon	Chorus (JOI23_chorus)	C++17	61 / 100	426 ms	1996 KiB

chorus

#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 - B.m) <= (B.b - A.b) * (A.m - m)) lines.pop_back();
            else break;
        }
        lines.push_back({m, b});
    }
 
    int qry(int x) {
        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 / 16
• Subtask 2: 24 / 24
• Subtask 3: 21 / 21
• Subtask 4: 0 / 26
• Subtask 5: 0 / 13