結果

問題 No.1919 Many Monster Battles
ユーザー ei1333333ei1333333
提出日時 2022-04-29 22:52:56
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,378 ms / 2,000 ms
コード長 5,420 bytes
コンパイル時間 4,886 ms
コンパイル使用メモリ 270,924 KB
最終ジャッジ日時 2025-01-28 23:37:50
ジャッジサーバーID
（参考情報） 		judge1 / judge1
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ファイルパターン 結果
sample AC * 3
other AC * 32
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include<bits/stdc++.h>
#include<atcoder/all>

using namespace std;

using mint = atcoder::modint1000000007;
const int inf = (1 << 30) - 1;

/**
 * @brief Succinct Indexable Dictionary(完備辞書)
 */
struct SuccinctIndexableDictionary {
  size_t length;
  size_t blocks;
  vector< unsigned > bit, sum;

  SuccinctIndexableDictionary() = default;

  SuccinctIndexableDictionary(size_t length) : length(length), blocks((length + 31) >> 5) {
    bit.assign(blocks, 0U);
    sum.assign(blocks, 0U);
  }

  void set(int k) {
    bit[k >> 5] |= 1U << (k & 31);
  }

  void build() {
    sum[0] = 0U;
    for(int i = 1; i < blocks; i++) {
      sum[i] = sum[i - 1] + __builtin_popcount(bit[i - 1]);
    }
  }

  bool operator[](int k) {
    return (bool((bit[k >> 5] >> (k & 31)) & 1));
  }

  int rank(int k) {
    return (sum[k >> 5] + __builtin_popcount(bit[k >> 5] & ((1U << (k & 31)) - 1)));
  }

  int rank(bool val, int k) {
    return (val ? rank(k) : k - rank(k));
  }
};

/*
 * @brief Wavelet Matrix Rectangle Sum
 * @docs docs/wavelet-matrix-rectangle-sum.md
 */
template< typename T, int MAXLOG, typename D >
struct WaveletMatrixRectangleSum {
  size_t length;
  SuccinctIndexableDictionary matrix[MAXLOG];
  vector< D > ds[MAXLOG];
  int mid[MAXLOG];

  WaveletMatrixRectangleSum() = default;

  WaveletMatrixRectangleSum(const vector< T > &v, const vector< D > &d) : length(v.size()) {
    assert(v.size() == d.size());
    vector< int > l(length), r(length), ord(length);
    iota(begin(ord), end(ord), 0);
    for(int level = MAXLOG - 1; level >= 0; level--) {
      matrix[level] = SuccinctIndexableDictionary(length + 1);
      int left = 0, right = 0;
      for(int i = 0; i < length; i++) {
        if(((v[ord[i]] >> level) & 1)) {
          matrix[level].set(i);
          r[right++] = ord[i];
        } else {
          l[left++] = ord[i];
        }
      }
      mid[level] = left;
      matrix[level].build();
      ord.swap(l);
      for(int i = 0; i < right; i++) {
        ord[left + i] = r[i];
      }
      ds[level].resize(length + 1);
      ds[level][0] = D();
      for(int i = 0; i < length; i++) {
        ds[level][i + 1] = ds[level][i] + d[ord[i]];
      }
    }
  }

  pair< int, int > succ(bool f, int l, int r, int level) {
    return {matrix[level].rank(f, l) + mid[level] * f, matrix[level].rank(f, r) + mid[level] * f};
  }

  // count d[i] s.t. (l <= i < r) && (v[i] < upper)
  D rect_sum(int l, int r, T upper) {
    D ret = 0;
    for(int level = MAXLOG - 1; level >= 0; level--) {
      bool f = ((upper >> level) & 1);
      if(f) ret += ds[level][matrix[level].rank(false, r)] - ds[level][matrix[level].rank(false, l)];
      tie(l, r) = succ(f, l, r, level);
    }
    return ret;
  }

  D rect_sum(int l, int r, T lower, T upper) {
    return rect_sum(l, r, upper) - rect_sum(l, r, lower);
  }
};

template< typename T, int MAXLOG, typename D >
struct CompressedWaveletMatrixRectangleSum {
  WaveletMatrixRectangleSum< int, MAXLOG, D > mat;
  vector< T > ys;

  CompressedWaveletMatrixRectangleSum(const vector< T > &v, const vector< D > &d) : ys(v) {
    sort(begin(ys), end(ys));
    ys.erase(unique(begin(ys), end(ys)), end(ys));
    vector< int > t(v.size());
    for(int i = 0; i < v.size(); i++) t[i] = get(v[i]);
    mat = WaveletMatrixRectangleSum< int, MAXLOG, D >(t, d);
  }

  inline int get(const T &x) {
    return lower_bound(begin(ys), end(ys), x) - begin(ys);
  }

  D rect_sum(int l, int r, T upper) {
    return mat.rect_sum(l, r, get(upper));
  }

  D rect_sum(int l, int r, T lower, T upper) {
    return mat.rect_sum(l, r, get(lower), get(upper));
  }
};

mint solve(const vector< int > &A, const vector< int > &B) {
  int N = (int) A.size();
  mint ret = 0;
  vector< int > ord(N);
  iota(begin(ord), end(ord), 0);
  {
    sort(begin(ord), end(ord), [&](int a, int b) {
      return A[a] < A[b];
    });
    vector< pair< int, int > > pts(N);
    for(int i = 0; i < N; i++) pts[i] = {A[i] - B[i], A[i] + B[i]};
    sort(begin(pts), end(pts));
    vector< int > xs(pts.size()), ys(pts.size()), ds(pts.size(), 1);
    for(int i = 0; i < (int) pts.size(); i++) {
      tie(xs[i], ys[i]) = pts[i];
    }
    auto bs = CompressedWaveletMatrixRectangleSum< int, 18, int >(ys, ds);
    for(int i: ord) {
      {
        int left = lower_bound(begin(xs), end(xs), A[i] - B[i]) - begin(xs);
        int right = (int) pts.size();
        int pct = bs.rect_sum(0, left, A[i] + B[i]);
        ret += mint(A[i]) * pct;
      }
    }
  }

  {
    reverse(begin(ord), end(ord));
    vector< pair< int, int > > pts(N);
    for(int i = 0; i < N; i++) pts[i] = {-(A[i] + B[i]), -(A[i] - B[i])};
    sort(begin(pts), end(pts));
    vector< int > xs(pts.size()), ys(pts.size()), ds(pts.size(), 1);
    for(int i = 0; i < (int) pts.size(); i++) {
      tie(xs[i], ys[i]) = pts[i];
    }
    auto bs = CompressedWaveletMatrixRectangleSum< int, 18, int >(ys, ds);
    for(int i: ord) {
      {
        int left = lower_bound(begin(xs), end(xs), -(A[i] + B[i])) - begin(xs);
        int right = (int) pts.size();
        int pct = bs.rect_sum(0, left, -(A[i] - B[i]));
        ret -= mint(A[i]) * pct;
      }
    }
  }
  return ret * 2;
}

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  int N;
  cin >> N;
  vector< int > A(N), B(N);
  for(auto &a: A) cin >> a;
  for(auto &b: B) cin >> b;
  cout << solve(A, B).val() << " " << solve(B, A).val() << "\n";
}
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