Submission #767572

#	Time	Username	Problem	Language	Result	Execution time	Memory
767572		PurpleCrayon	Chorus (JOI23_chorus)	C++17	0 / 100	0 ms	212 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;
const ll INF = 1e18+10;
 
int n, K, small[N];
ll ps[N], l_use[N];
vector<int> one, two;
 
// min CHT with
//  - slopes decreasing
//  - query x increasing
 
 
struct Line {
    ll m, b;
    ll calc(ll x) {
        return m * x + b;
    }
};
 
struct CHT {
    deque<Line> lines;
 
    void add(ll m, ll 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});
    }
 
    ll qry(ll 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);
    }

    auto calc_sum = [&](int L, int R) {
        return (long long) (L + R) * (R - L + 1) / 2;
    };

    for (int i = 0; i < n; i++) {
        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;
            }
        }
        */

        int use = lower_bound(small, small + n, i) - small - 1; // [i..use]
        if (use >= i) {
            l_use[i] -= ps[use] - (i ? ps[i-1] : 0) + calc_sum(i, use);
        }
    }
 
    vector<ll> prv(n, INF);
    for (int k = 1; k <= K; k++) {
        vector<ll> nxt(n, INF);
 
        CHT lines;
        for (int i = 0; i < n; i++) {
            lines.add(-i, (long long) 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: 0 / 16
• Subtask 2: 0 / 24
• Subtask 3: 0 / 21
• Subtask 4: 0 / 26
• Subtask 5: 0 / 13