結果

問題 No.5020 Averaging
ユーザー square1001
提出日時 2024-02-25 16:24:07
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 808 ms / 1,000 ms
コード長 4,620 bytes
コンパイル時間 2,979 ms
コンパイル使用メモリ 224,320 KB
実行使用メモリ 152,404 KB
スコア 84,845,286
最終ジャッジ日時 2024-02-25 16:25:15
合計ジャッジ時間 43,846 ms
ジャッジサーバーID
（参考情報） 		judge11 / judge10
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ファイルパターン 結果
other AC * 50
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ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
class state {
public:
    double x, y; uint64_t bit; int pre;
    state() : x(0.0), y(0.0), bit(0), pre(-1) {}
    state(double x_, double y_, uint64_t bit_, int pre_) : x(x_), y(y_), bit(bit_), pre(pre_) {}
    double score() const {
        return max(abs(x), abs(y));
    }
    bool operator<(const state& s) const {
        return score() < s.score();
    }
};
int main() {
    // step #1. input
    int N;
    cin >> N;
    vector<double> A(N), B(N);
    for (int i = 0; i < N; i++) {
        cin >> A[i] >> B[i];
        A[i] -= 5.0e+17;
        B[i] -= 5.0e+17;
    }
    
    // step #2. beam search
    constexpr int BEAMWIDTH = 5000;
    constexpr int REMAINS = 6;
    vector<vector<state> > beam(N - REMAINS - 2);
    for (int v1 = 1; v1 < N; v1++) {
        for (int v2 = v1 + 1; v2 < N; v2++) {
            double x = (A[0] + A[v1] + A[v2]) / 4;
            double y = (B[0] + B[v1] + B[v2]) / 4;
            uint64_t bit = ((1ULL << N) - 1) ^ (1ULL << 0) ^ (1ULL << v1) ^ (1ULL << v2);
            beam[0].push_back(state(x, y, bit, -1));
        }
    }
    sort(beam[0].begin(), beam[0].end());
    if (int(beam[0].size()) > BEAMWIDTH) {
        beam[0].resize(BEAMWIDTH);
    }
    for (int level = 1; level <= N - REMAINS - 3; level++) {
        double mul = pow(0.5, level + 2);
        for (int i = 0; i < int(beam[level - 1].size()); i++) {
            state s = beam[level - 1][i];
            uint64_t b = s.bit;
            while (b != 0) {
                int pos = __builtin_ctzll(b);
                b ^= 1ULL << pos;
                double x = s.x + A[pos] * mul;
                double y = s.y + B[pos] * mul;
                uint64_t bit = s.bit ^ (1ULL << pos);
                beam[level].push_back(state(x, y, bit, i));
            }
        }
        sort(beam[level].begin(), beam[level].end());
        if (int(beam[level].size()) > BEAMWIDTH) {
            beam[level].resize(BEAMWIDTH);
        }
        cerr << "level = " << level << ": size = " << beam[level].size() << ", score = " << beam[level][0].score() << ", back = " << beam[level].back
            ().score() << endl;
    }
    
    // step #3. enumerate all remaining combinations
    vector<array<double, REMAINS> > weights;
    vector<int> path;
    auto dfs = [&](auto& self, int depth, int rem, int val) -> void {
        if (rem < val) {
            return;
        }
        if (val == 0) {
            array<double, REMAINS> v;
            for (int i = 0; i < REMAINS; i++) {
                v[i] = (i < int(path.size()) ? pow(2.0, -((N - REMAINS - 1) + path[i])) : 0.0);
            }
            reverse(v.begin(), v.end());
            do {
                weights.push_back(v);
            } while (next_permutation(v.begin(), v.end()));
            return;
        }
        for (int i = 0; i <= rem && i <= val; i++) {
            self(self, depth + 1, rem - i, (val - i) * 2);
            path.push_back(depth);
        }
        while (!path.empty() && path.back() == depth) {
            path.pop_back();
        }
    };
    dfs(dfs, 0, REMAINS, 1);
    const int SUBSTATES = weights.size();
    cerr << "substates = " << SUBSTATES << endl;
    
    // step #4. brute force
    double bestscore = 1.0e+99;
    vector<int> bestdepth;
    for (int i = 0; i < int(beam[N - REMAINS - 3].size()); i++) {
        state s = beam[N - REMAINS - 3][i];
        uint64_t rembit = s.bit;
        array<int, REMAINS> subidx;
        array<double, REMAINS> suba, subb;
        for (int j = 0; j < REMAINS; j++) {
            subidx[j] = __builtin_ctzll(rembit);
            suba[j] = A[subidx[j]];
            subb[j] = B[subidx[j]];
            rembit ^= 1ULL << subidx[j];
        }
        for (int j = 0; j < SUBSTATES; j++) {
            double x = s.x, y = s.y;
            for (int k = 0; k < REMAINS; k++) {
                x += suba[k] * weights[j][k];
                y += subb[k] * weights[j][k];
            }
            double score = max(abs(x), abs(y));
            if (bestscore > score) {
                // reconstruction
                vector<int> depth(N, -1);
                for (int k = 0; k < REMAINS; k++) {
                    if (weights[j][k] != 0.0) {
                        depth[subidx[k]] = int(-log2(weights[j][k]) + 0.5);
                    }
                }
                int idx = i;
                uint64_t prebit = s.bit;
                for (int k = N - REMAINS - 3; k >= 0; k--) {
                    uint64_t nxtbit = (k != 0 ? beam[k - 1][beam[k][idx].pre].bit : (1ULL << N) - 1);
                    uint64_t bitdiff = prebit ^ nxtbit;
                    while (bitdiff != 0) {
                        int pos = __builtin_ctzll(bitdiff);
                        depth[pos] = k + 2;
                        bitdiff ^= 1ULL << pos;
                    }
                    prebit = nxtbit;
                    if (k != 0) {
                        idx = beam[k][idx].pre;
                    }
                }
                bestscore = score;
                bestdepth = depth;
            }
        }
    }
    cerr << "bestscore = " << bestscore << endl;
    
    // step #5. construction
    vector<array<int, 2> > answer;
    vector<int> curdepth = bestdepth;
    while (curdepth[0] != 0) {
        int p1 = max_element(curdepth.begin(), curdepth.end()) - curdepth.begin();
        int p2 = max_element(curdepth.begin() + p1 + 1, curdepth.end()) - curdepth.begin();
        answer.push_back({p1, p2});
        curdepth[p1] -= 1;
        curdepth[p2] = -1;
    }
    
    // step #6. output
    cout << answer.size() << endl;
    for (array<int, 2> v : answer) {
        cout << v[0] + 1 << ' ' << v[1] + 1 << endl;
    }
    
    return 0;
}
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