Submission #957255

#	Time	Username	Problem	Language	Result	Execution time	Memory
957255		alextodoran	Chorus (JOI23_chorus)	C++17	100 / 100	2521 ms	45816 KiB

chorus

/**
 _  _   __  _ _ _  _  _ _
 |a  ||t  ||o    d | |o  |
| __    _| | _ | __|  _ |
| __ |/_  | __  /__\ / _\|

**/

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;

const int N_MAX = 1000000;
const ll INF = LLONG_MAX;

int N, K;
int A[N_MAX + 2];
ll suff[N_MAX + 2];

ll dp[N_MAX + 2];
int cnt[N_MAX + 2];

struct Line {
    ll a, b;
    ll f (int x) {
        return a * x + b;
    }
};

Line lines[N_MAX + 2];
deque <int> rel;

bool check (const Line &l1, const Line &l2, const Line &l3) {
    return (l2.b - l1.b) * (l2.a - l3.a) < (l3.b - l2.b) * (l1.a - l2.a);
}

void add_line (int j) {
    while ((int) rel.size() >= 2
           && check(lines[rel.end()[-2]], lines[rel.back()], lines[j]) == false) {
        rel.pop_back();
    }
    rel.push_back(j);
}

pair <ll, int> query (int i) {
    if (rel.empty() == true) {
        return make_pair(INF, 0);
    }
    while ((int) rel.size() >= 2
           && make_pair(lines[rel[0]].f(i), cnt[rel[0]]) >=
              make_pair(lines[rel[1]].f(i), cnt[rel[1]])) {
        rel.pop_front();
    }
    return make_pair(lines[rel.front()].f(i) - suff[i + 1], cnt[rel.front()]);
}

ll solve (ll pen) {
    rel.clear();
    deque <int> dq;
    int curr = 0;
    for (int i = 1; i <= N; i++) {
        for (int j = curr; j < min(A[i] - i, i); j++) {
            // dp[j] + sum(A[i1] + i1 - j | i <= i1 <= i2)
            // dp[j] + suff[i] - suff[i2 + 1] - j * i2 + j * (i - 1)
            lines[j].a = -j;
            lines[j].b = dp[j] + suff[i] + (ll) j * (i - 1);
            add_line(j);
        }
        curr = min(A[i] - i, i);
        while (dq.empty() == false && dp[i - 1] < dp[dq.back()]) {
            dq.pop_back();
        }
        dq.push_back(i - 1);
        while (dq.empty() == false && dq.front() < curr) {
            dq.pop_front();
        }
        tie(dp[i], cnt[i]) = query(i);
        if (dq.empty() == false) {
            int j = dq.front();
            if (make_pair(dp[j], cnt[j]) < make_pair(dp[i], cnt[i])) {
                dp[i] = dp[j]; cnt[i] = cnt[j];
            }
        }
        dp[i] += pen; cnt[i]++;
    }
    return dp[N] - pen * K;
}

int main () {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cin >> N >> K;
    string S;
    cin >> S;
    for (int i = 0, j = 0; i < N * 2; i++) {
        if (S[i] == 'A') {
            A[++j] = i + 1;
        }
    }
    for (int i = N; i >= 1; i--) {
        suff[i] = suff[i + 1] + A[i] - i;
    }
    ll l = 0, r = LLONG_MAX / 2;
    while (l < r) {
        ld mid = (l + r) / 2;
        solve(mid);
        if (cnt[N] <= K) {
            r = mid;
        } else {
            l = mid + 1;
        }
    }
    cout << solve(l) << "\n";

    return 0;
}

• Subtask 1: 16 / 16
• Subtask 2: 24 / 24
• Subtask 3: 21 / 21
• Subtask 4: 26 / 26
• Subtask 5: 13 / 13