Submission #641173

#	Time	Username	Problem	Language	Result	Execution time	Memory
641173		cthbst	Let's Win the Election (JOI22_ho_t3)	C++14	100 / 100	990 ms	8412 KiB

Main

#include <algorithm>
#include <iomanip>
#include <iostream>
#include <utility>
#include <vector>

using namespace std;

#define int long long
using pdd = pair<long double, long double>;

const long double INF = 1e18;
const int maxn = 505;

int n, k;
vector<pdd> vc;
long double dp[maxn][maxn];
long double sf[maxn][maxn];  // sf[i][j] 從 A[i~(n-1)] 選 j 個最小的數字

void build_sf() {
    for (int i = 1; i < maxn; i++) {
        fill(sf[i] + 1, sf[i] + maxn, INF);
    }

    for (int i = n - 1; i >= 0; i--) {
        vector<long double> cur;
        for (int j = i; j < n; j++) {
            cur.push_back(vc[j].first);
        }
        sort(cur.begin(), cur.end());
        sf[i][0] = 0;
        for (int j = 1; j <= k; j++) {
            if (j > (int)(cur.size()))
                break;
            else
                sf[i][j] = sf[i][j - 1] + cur[j - 1];
        }
    }
}

long double solve(const int t) {
    for (int i = 0; i < n; i++) {
        fill(dp[i], dp[i] + (t + 1), INF);
    }

    for (int i = 0; i < n; i++) {
        if (i == 0) {
            dp[i][0] = vc[i].first / (t + 1.0);
            dp[i][1] = vc[i].second;
            continue;
        }
        for (int j = 0; j <= t; j++) {
            if (j == 0) {
                dp[i][0] = dp[i - 1][0] + vc[i].first / (t + 1.0);
            } else {
                long double x = dp[i - 1][j] + vc[i].first / (t + 1.0);
                long double y = dp[i - 1][j - 1] + vc[i].second * 1.0 / j;
                dp[i][j] = min(x, y);
            }
        }
    }
    // if (k == n) return dp[n - 1][t];

    long double res = sf[0][k];
    for (int i = 0; i < n; i++) {
        if (k - (i+1) >= 0) {
            res = min(res, dp[i][t] + sf[i + 1][k - (i+1)] / (t + 1));
        }
    }
    return res;
}

signed main() {
    ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    cout << fixed << setprecision(15);

    cin >> n >> k;
    for (int i = 0; i < n; i++) {
        int x, y;
        cin >> x >> y;
        if (y == -1) {
            vc.push_back({x, INF});
        } else {
            vc.push_back({x, y});
        }
    }
    sort(vc.begin(), vc.end(),
         [](pdd a, pdd b) { return a.second < b.second; });
    build_sf();

    long double res = sf[0][k];
    for (int t = 1; t <= k; t++) {
        res = min(res, solve(t));
    }
    cout << res << '\n';

    return 0;
}

• Subtask 1: 5 / 5
• Subtask 2: 5 / 5
• Subtask 3: 11 / 11
• Subtask 4: 12 / 12
• Subtask 5: 33 / 33
• Subtask 6: 11 / 11
• Subtask 7: 23 / 23