제출 #1276471

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1276471		mehrzad	Festival (IOI25_festival)	C++17	5 / 100	1097 ms	14268 KiB

festival

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

using i128 = __int128_t;

struct Coupon {
    int idx;
    long long P;
    int T;
};

static bool cmpMul(const Coupon& a, const Coupon& b) {
    // Compare a.P * a.T / (a.T-1)  <  b.P * b.T / (b.T-1) safely
    __int128 left  = (__int128)a.P * a.T * (b.T - 1);
    __int128 right = (__int128)b.P * b.T * (a.T - 1);
    return left < right;
}

static bool cmpOne(const Coupon& a, const Coupon& b) {
    return a.P < b.P;
}

// Greedy feasibility: starting with 'tokens', can we take at least 'need' coupons
// from mul[l..M-1] in-order?
static bool can_take_at_least(const vector<Coupon>& mul, int l, int need, i128 tokens) {
    const i128 INF = (i128)1 << 120;
    int taken = 0;
    for (int i = l; i < (int)mul.size() && taken < need; ++i) {
        const auto& c = mul[i];
        if (tokens >= (i128)c.P) {
            tokens = (tokens - (i128)c.P) * (i128)c.T;
            if (tokens > INF) tokens = INF;
            ++taken;
        }
    }
    return taken >= need;
}

vector<int> max_coupons(int A, vector<int> P, vector<int> T) {
    int N = (int)P.size();
    vector<Coupon> mul, one;
    mul.reserve(N);
    one.reserve(N);
    for (int i = 0; i < N; ++i) {
        Coupon c{ i, (long long)P[i], T[i] };
        if (T[i] == 1) one.push_back(c);
        else mul.push_back(c);
    }

    // Sort as before
    sort(mul.begin(), mul.end(), cmpMul);
    sort(one.begin(), one.end(), cmpOne);

    const i128 INF = (i128)1 << 120;

    // ---- 1-D DP over number of T>1 picks ----
    int M = (int)mul.size();
    vector<i128> dp(M + 1, -1), next_dp(M + 1, -1);
    dp[0] = (i128)A;

    for (int i = 1; i <= M; ++i) {
        fill(next_dp.begin(), next_dp.begin() + i + 1, (i128)-1);
        const auto& c = mul[i - 1];

        // skip
        for (int k = 0; k <= i - 1; ++k) if (dp[k] != -1) {
            if (next_dp[k] < dp[k]) next_dp[k] = dp[k];
        }
        // take
        for (int k = 1; k <= i; ++k) if (dp[k - 1] != -1) {
            i128 prev = dp[k - 1];
            if (prev >= (i128)c.P) {
                i128 after = (prev - (i128)c.P) * (i128)c.T;
                if (after < 0) after = 0;
                if (after > INF) after = INF;
                if (next_dp[k] < after) next_dp[k] = after;
            }
        }
        dp.swap(next_dp);
    }

    // ---- choose best k and # of T=1 you can buy afterwards ----
    int N1 = (int)one.size();
    vector<i128> pref(N1 + 1, 0);
    for (int i = 1; i <= N1; ++i) pref[i] = pref[i - 1] + (i128)one[i - 1].P;

    auto max_ones = [&](i128 tokens) {
        int lo = 0, hi = N1;
        while (lo < hi) {
            int mid = (lo + hi + 1) >> 1;
            if (pref[mid] <= tokens) lo = mid;
            else hi = mid - 1;
        }
        return lo;
    };

    int bestK = 0, bestOneCnt = 0, bestTotal = 0;
    for (int k = 0; k <= M; ++k) if (dp[k] != -1) {
        int cntOne = max_ones(dp[k]);
        int total = k + cntOne;
        if (total > bestTotal) {
            bestTotal = total;
            bestK = k;
            bestOneCnt = cntOne;
        }
    }

    // ---- reconstruct a valid set of multipliers with exactly bestK picks ----
    vector<int> orderMul;
    orderMul.reserve(bestK);
    i128 cur = (i128)A;
    int need = bestK;
    for (int i = 0; i < M && need > 0; ++i) {
        const auto& c = mul[i];
        // If we skip this coupon, can we still reach 'need' picks from the suffix?
        bool ok_to_skip = can_take_at_least(mul, i + 1, need, cur);
        if (!ok_to_skip) {
            // Must take this one (feasibility would be lost otherwise).
            if (cur < (i128)c.P) {
                // Should not happen if DP logic was correct.
                // Fall back: skip (keeps algorithm robust).
                continue;
            }
            cur = (cur - (i128)c.P) * (i128)c.T;
            if (cur > INF) cur = INF;
            orderMul.push_back(c.idx);
            --need;
        }
        // else skip
    }

    // ---- take first bestOneCnt cheap T=1 coupons ----
    vector<int> orderOne;
    orderOne.reserve(bestOneCnt);
    for (int i = 0; i < bestOneCnt; ++i) orderOne.push_back(one[i].idx);

    // ---- concatenate ----
    vector<int> res;
    res.reserve(bestTotal);
    res.insert(res.end(), orderMul.begin(), orderMul.end());
    res.insert(res.end(), orderOne.begin(), orderOne.end());
    return res;
}

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