제출 #1276488

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1276488		mehrzad	Festival (IOI25_festival)	C++17	12 / 100	1038 ms	2162688 KiB

festival

#include <bits/stdc++.h>
using namespace std;

struct ScalingCoupon {
    int price;
    int mult;          // T[i] ( > 1 )
    int idx;           // original index
};

struct CheapCoupon {
    int price;
    int idx;
};

static const long long INF = 4000000000000000000LL;   // 4·10^18

// comparator: a before b  <=>  Pa*Ta/(Ta-1)  <  Pb*Tb/(Tb-1)
bool scalingCmp(const ScalingCoupon& a, const ScalingCoupon& b) {
    __int128 left  = (__int128)a.price * a.mult * (b.mult - 1);
    __int128 right = (__int128)b.price * b.mult * (a.mult - 1);
    if (left != right) return left < right;
    if (a.price != b.price) return a.price < b.price;
    return a.idx < b.idx;
}

vector<int> max_coupons(int A, vector<int> P, vector<int> T) {
    const int N = (int)P.size();
    vector<ScalingCoupon> scaling;
    vector<CheapCoupon> cheap;

    for (int i = 0; i < N; ++i) {
        if (T[i] == 1) {
            cheap.push_back({P[i], i});
        } else {
            scaling.push_back({P[i], T[i], i});
        }
    }

    /* sort scaling coupons by the optimal order (Lemma 3) */
    sort(scaling.begin(), scaling.end(), scalingCmp);

    /* sort cheap coupons by price, they will be taken greedily */
    sort(cheap.begin(), cheap.end(),
         [](const CheapCoupon& a, const CheapCoupon& b) {
             if (a.price != b.price) return a.price < b.price;
             return a.idx < b.idx;
         });

    int m = (int)scaling.size();
    int c1 = (int)cheap.size();

    /* DP: dp[i][k] – max tokens after first i scaling coupons,
                    having taken exactly k of them                 */
    vector<vector<long long>> dp(m + 1, vector<long long>(m + 1, -1));
    vector<vector<char>> take(m + 1, vector<char>(m + 1, 0));
    dp[0][0] = A;

    for (int i = 1; i <= m; ++i) {
        const ScalingCoupon& cur = scaling[i - 1];
        for (int k = 0; k <= i; ++k) {
            // skip current coupon
            if (dp[i - 1][k] > dp[i][k]) {
                dp[i][k] = dp[i - 1][k];
                take[i][k] = 0;
            }
            // take current coupon
            if (k > 0 && dp[i - 1][k - 1] >= cur.price) {
                __int128 tmp = (__int128)(dp[i - 1][k - 1] - cur.price) * cur.mult;
                long long nxt = (tmp > INF ? INF : (long long)tmp);
                if (nxt > dp[i][k]) {
                    dp[i][k] = nxt;
                    take[i][k] = 1;
                }
            }
        }
    }

    /* prefix sums of cheap coupons */
    vector<long long> pref(c1 + 1, 0);
    for (int i = 0; i < c1; ++i) pref[i + 1] = pref[i] + cheap[i].price;

    /* choose the best k */
    int bestTotal = -1;
    int bestK = 0;
    int bestCheapCnt = 0;
    long long bestTokens = 0;

    for (int k = 0; k <= m; ++k) {
        long long tok = dp[m][k];
        if (tok < 0) continue;
        // maximal cheap coupons affordable
        int cheapCnt = (int)(upper_bound(pref.begin(), pref.end(), tok) - pref.begin()) - 1;
        int total = k + cheapCnt;
        if (total > bestTotal) {
            bestTotal = total;
            bestK = k;
            bestCheapCnt = cheapCnt;
            bestTokens = tok;
        }
    }

    /* reconstruct scaling part */
    vector<int> answer;
    int i = m, k = bestK;
    while (i > 0) {
        if (take[i][k]) {
            answer.push_back(scaling[i - 1].idx);
            --k;
        }
        --i;
    }
    reverse(answer.begin(), answer.end());

    /* add cheap coupons (cheapest first) */
    for (int i = 0; i < bestCheapCnt; ++i) {
        answer.push_back(cheap[i].idx);
    }
    return answer;
}

• Subtask 0: 0 / 0
• Subtask 1: 5 / 5
• Subtask 2: 7 / 7
• Subtask 3: 0 / 12
• Subtask 4: 0 / 15
• Subtask 5: 0 / 27
• Subtask 6: 0 / 16
• Subtask 7: 0 / 18