Range Mex Query
(data-structure/wavelet-matrix/query/RangeMex.hpp)

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• Last update: 2025-05-12 02:45:56+09:00
• Include: #include "data-structure/wavelet-matrix/query/RangeMex.hpp"

概要

todo

計算量

todo

Depends on

• Wavelet Matrix (Segment Tree) (data-structure/wavelet-matrix/WaveletMatrixSegtree.hpp)

Code

#include "../WaveletMatrixSegtree.hpp"
using S = int;
S op(S a, S b) {
  return min(a, b);
}

S e() {
  return INT_MAX;
}
class RangeMex {
 private:
  int n;
  WaveletMatrix<S, op, e> wm;

 public:
  RangeMex(const vector<int> &v) {
    n = v.size();
    vector<int> x, y, z;
    vector<int> last(n + 1, -1);
    x.reserve(n * 2);
    y.reserve(n * 2);
    z.reserve(n * 2);

    for (int i = 0; i < n; i++) {
      if (v[i] > n) continue;
      x.emplace_back(last[v[i]]);
      y.emplace_back(i);
      z.emplace_back(v[i]);
      last[v[i]] = i;
    }

    for (int i = 0; i < n + 1; i++) {
      x.emplace_back(last[i]);
      y.emplace_back(n);
      z.emplace_back(i);
    }

    wm = WaveletMatrix<S, op, e>(x, y, z);
  }

  int range_mex(int l, int r) {
    return wm.rectangle_prod(-1, l, r, n + 1);
  }
};

#line 1 "data-structure/wavelet-matrix/query/RangeMex.hpp"

#line 1 "data-structure/wavelet-matrix/WaveletMatrixSegtree.hpp"
struct BitVector {
    unsigned sz;
    unsigned blocksize;
    vector<unsigned> bit, sum;

    BitVector() {}

    BitVector(unsigned siz) {
        sz = siz;
        blocksize = (sz + 31) >> 5;
        bit.assign(blocksize, 0U);
        sum.assign(blocksize, 0U);
    }

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

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

    inline bool access(unsigned k) {
        return (bool((bit[k >> 5] >> (k & 31)) & 1));
    }

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

template <class S, auto op, auto e, class T>
class WaveletMatrix {
   private:
    unsigned n;
    unsigned bitsize;
    vector<BitVector> b;
    vector<segtree<S, op, e>> seg;
    vector<unsigned> zero;
    vector<T> cmp;
    T MI, MA;

    inline unsigned compress(const T &x) {
        return lower_bound(cmp.begin(), cmp.end(), x) - begin(cmp);
    }

   public:
    // コンストラクタ
    WaveletMatrix() {}
    WaveletMatrix(vector<T> v) {
        MI = numeric_limits<T>::min();
        MA = numeric_limits<T>::max();
        n = v.size();
        cmp = v;
        sort(cmp.begin(), cmp.end());
        cmp.erase(unique(cmp.begin(), cmp.end()), cmp.end());
        vector<T> tmp(n);
        vector<T> tmpc(n);
        vector<T> compressed(n);
        for (unsigned i = 0; i < n; i++) {
            compressed[i] = distance(cmp.begin(), lower_bound(cmp.begin(), cmp.end(), v[i]));
        }
        bitsize = bit_width(cmp.size());
        b.resize(bitsize + 1);
        seg.resize(bitsize + 1);
        zero.resize(bitsize, 0);
        int cur = 0;
        for (unsigned i = 0; i < bitsize; i++) {
            b[i] = BitVector(n + 1);
            seg[i] = segtree<T, op, e>(v);
            cur = 0;
            for (unsigned j = 0; j < n; j++) {
                if (compressed[j] & (1U << (bitsize - i - 1))) {
                    b[i].set(j);
                } else {
                    zero[i]++;
                    tmpc[cur] = compressed[j];
                    tmp[cur] = v[j];
                    cur++;
                }
            }
            b[i].build();
            for (int j = 0; j < n; j++) {
                if (compressed[j] & (1U << (bitsize - i - 1))) {
                    tmpc[cur] = compressed[j];
                    tmp[cur] = v[j];
                    cur++;
                }
            }
            swap(tmpc, compressed);
            swap(tmp, v);
        }
        b[bitsize] = BitVector(n + 1);
        seg[bitsize] = segtree<T, op, e>(v);
    }

    WaveletMatrix(vector<T> v, vector<S> w) {
        MI = numeric_limits<T>::min();
        MA = numeric_limits<T>::max();
        n = v.size();
        cmp = v;
        sort(cmp.begin(), cmp.end());
        cmp.erase(unique(cmp.begin(), cmp.end()), cmp.end());
        vector<S> tmp(n);
        vector<T> tmpc(n);
        vector<T> compressed(n);
        for (unsigned i = 0; i < n; i++) {
            compressed[i] = distance(cmp.begin(), lower_bound(cmp.begin(), cmp.end(), v[i]));
        }
        bitsize = bit_width(cmp.size());
        b.resize(bitsize + 1);
        seg.resize(bitsize + 1);
        zero.resize(bitsize, 0);
        int cur = 0;
        for (unsigned i = 0; i < bitsize; i++) {
            b[i] = BitVector(n + 1);
            seg[i] = segtree<S, op, e>(w);
            cur = 0;
            for (unsigned j = 0; j < n; j++) {
                if (compressed[j] & (1U << (bitsize - i - 1))) {
                    b[i].set(j);
                } else {
                    zero[i]++;
                    tmpc[cur] = compressed[j];
                    tmp[cur] = w[j];
                    cur++;
                }
            }
            b[i].build();
            for (int j = 0; j < n; j++) {
                if (compressed[j] & (1U << (bitsize - i - 1))) {
                    tmpc[cur] = compressed[j];
                    tmp[cur] = w[j];
                    cur++;
                }
            }
            swap(tmpc, compressed);
            swap(tmp, w);
        }
        b[bitsize] = BitVector(n + 1);
        seg[bitsize] = segtree<S, op, e>(w);
    }

    void set(int p, S x) {
        unsigned cur = p;
        for (unsigned i = 0; i < bitsize; i++) {
            seg[i].set(cur, x);
            if (b[i].access(cur)) {
                cur = zero[i] + b[i].rank(cur);
            } else {
                cur -= b[i].rank(cur);
            }
        }
        seg[bitsize].set(cur, x);
    }

    S get(int p) {
        return seg[0].get(p);
    }

    // v[l,r) の中で[mink,maxk)に入る値の総積を返す
    S range_prod(int vl, int vr, T mink, T maxk) {
        int D = compress(mink);
        int U = compress(maxk);
        S res = e();
        auto dfs = [&](auto &rec, int d, int L, int R, int A, int B) -> void {
            if (U <= A or B <= D) return;
            if (D <= A and B <= U) {
                res = op(res, seg[d].prod(L, R));
                return;
            }
            if (d == bitsize) {
                if (D <= A and A < U) {
                    res = op(res, seg[bitsize].prod(L, R));
                }
                return;
            }
            int C = (A + B) >> 1;
            int rank0_l = L - b[d].rank(L);
            int rank0_r = R - b[d].rank(R);
            int rank1_l = b[d].rank(L) + zero[d];
            int rank1_r = b[d].rank(R) + zero[d];

            rec(rec, d + 1, rank0_l, rank0_r, A, C);
            rec(rec, d + 1, rank1_l, rank1_r, C, B);
        };
        dfs(dfs, 0, vl, vr, 0, 1 << bitsize);
        return res;
    }
};
#line 3 "data-structure/wavelet-matrix/query/RangeMex.hpp"
using S = int;
S op(S a, S b) {
  return min(a, b);
}

S e() {
  return INT_MAX;
}
class RangeMex {
 private:
  int n;
  WaveletMatrix<S, op, e> wm;

 public:
  RangeMex(const vector<int> &v) {
    n = v.size();
    vector<int> x, y, z;
    vector<int> last(n + 1, -1);
    x.reserve(n * 2);
    y.reserve(n * 2);
    z.reserve(n * 2);

    for (int i = 0; i < n; i++) {
      if (v[i] > n) continue;
      x.emplace_back(last[v[i]]);
      y.emplace_back(i);
      z.emplace_back(v[i]);
      last[v[i]] = i;
    }

    for (int i = 0; i < n + 1; i++) {
      x.emplace_back(last[i]);
      y.emplace_back(n);
      z.emplace_back(i);
    }

    wm = WaveletMatrix<S, op, e>(x, y, z);
  }

  int range_mex(int l, int r) {
    return wm.rectangle_prod(-1, l, r, n + 1);
  }
};

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