atcoder/waveletmatrix.hpp

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• Last update: 2021-10-21 18:06:39+09:00
• Include: #include "atcoder/waveletmatrix.hpp"
• Link: https://ei1333.github.io/library/structure/wavelet/succinct-indexable-dictionary.cpp
• Link: https://ei1333.github.io/library/structure/wavelet/wavelet-matrix.cpp

Verified with

• test/waveletmatrix.test.cpp

Code

#ifndef ATCODER_WAVELETMATRIX_HPP
#define ATCODER_WAVELETMATRIX_HPP 1

#include <cassert>
#include <tuple>
#include <vector>

namespace atcoder {

// Reference: https://ei1333.github.io/library/structure/wavelet/succinct-indexable-dictionary.cpp

struct SuccinctIndexableDictionary {
    int length;
    int blocks;
    std::vector< unsigned > bit, sum;

    SuccinctIndexableDictionary() = default;

    explicit SuccinctIndexableDictionary(int 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 int(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));
    }
};


// Reference: https://ei1333.github.io/library/structure/wavelet/wavelet-matrix.cpp

template< typename T, int MAXLOG >
struct WaveletMatrix {
    int length;
    SuccinctIndexableDictionary matrix[MAXLOG];
    int mid[MAXLOG];

    WaveletMatrix() = default;

    explicit WaveletMatrix(std::vector< T > v) : length(int(v.size())) {
        std::vector< T > l(length), r(length);
        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[i] >> level) & 1)) {
                    matrix[level].set(i);
                    r[right++] = v[i];
                } else {
                    l[left++] = v[i];
                }
            }
            mid[level] = left;
            matrix[level].build();
            v.swap(l);
            for(int i = 0; i < right; i++) {
                v[left + i] = r[i];
            }
        }
    }

    std::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};
    }

    // v[k]
    T access(int k) {
        T ret = 0;
        for(int level = MAXLOG - 1; level >= 0; level--) {
            bool f = matrix[level][k];
            if(f) ret |= T(1) << level;
            k = matrix[level].rank(f, k) + mid[level] * f;
        }
        return ret;
    }

    T operator[](const int &k) {
        return access(k);
    }

    // count i s.t. (0 <= i < r) && v[i] == x
    int rank(const T &x, int r) {
        int l = 0;
        for(int level = MAXLOG - 1; level >= 0; level--) {
            std::tie(l, r) = succ((x >> level) & 1, l, r, level);
        }
        return r - l;
    }

    // k-th(0-indexed) smallest number in v[l,r)
    T kth_smallest(int l, int r, int k) {
        assert(0 <= k && k < r - l);
        T ret = 0;
        for(int level = MAXLOG - 1; level >= 0; level--) {
            int cnt = matrix[level].rank(false, r) - matrix[level].rank(false, l);
            bool f = cnt <= k;
            if(f) {
                ret |= T(1) << level;
                k -= cnt;
            }
            std::tie(l, r) = succ(f, l, r, level);
        }
        return ret;
    }

    // k-th(0-indexed) largest number in v[l,r)
    T kth_largest(int l, int r, int k) {
        return kth_smallest(l, r, r - l - k - 1);
    }

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

    // count i s.t. (l <= i < r) && (lower <= v[i] < upper)
    int range_freq(int l, int r, T lower, T upper) {
        return range_freq(l, r, upper) - range_freq(l, r, lower);
    }

    // max v[i] s.t. (l <= i < r) && (v[i] < upper)
    T prev_value(int l, int r, T upper) {
        int cnt = range_freq(l, r, upper);
        return cnt == 0 ? T(-1) : kth_smallest(l, r, cnt - 1);
    }

    // min v[i] s.t. (l <= i < r) && (lower <= v[i])
    T next_value(int l, int r, T lower) {
        int cnt = range_freq(l, r, lower);
        return cnt == r - l ? T(-1) : kth_smallest(l, r, cnt);
    }
};

}  // namespace atcoder

#endif  // ATCODER_WAVELETMATRIX_HPP

#line 1 "atcoder/waveletmatrix.hpp"



#include <cassert>
#include <tuple>
#include <vector>

namespace atcoder {

// Reference: https://ei1333.github.io/library/structure/wavelet/succinct-indexable-dictionary.cpp

struct SuccinctIndexableDictionary {
    int length;
    int blocks;
    std::vector< unsigned > bit, sum;

    SuccinctIndexableDictionary() = default;

    explicit SuccinctIndexableDictionary(int 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 int(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));
    }
};


// Reference: https://ei1333.github.io/library/structure/wavelet/wavelet-matrix.cpp

template< typename T, int MAXLOG >
struct WaveletMatrix {
    int length;
    SuccinctIndexableDictionary matrix[MAXLOG];
    int mid[MAXLOG];

    WaveletMatrix() = default;

    explicit WaveletMatrix(std::vector< T > v) : length(int(v.size())) {
        std::vector< T > l(length), r(length);
        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[i] >> level) & 1)) {
                    matrix[level].set(i);
                    r[right++] = v[i];
                } else {
                    l[left++] = v[i];
                }
            }
            mid[level] = left;
            matrix[level].build();
            v.swap(l);
            for(int i = 0; i < right; i++) {
                v[left + i] = r[i];
            }
        }
    }

    std::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};
    }

    // v[k]
    T access(int k) {
        T ret = 0;
        for(int level = MAXLOG - 1; level >= 0; level--) {
            bool f = matrix[level][k];
            if(f) ret |= T(1) << level;
            k = matrix[level].rank(f, k) + mid[level] * f;
        }
        return ret;
    }

    T operator[](const int &k) {
        return access(k);
    }

    // count i s.t. (0 <= i < r) && v[i] == x
    int rank(const T &x, int r) {
        int l = 0;
        for(int level = MAXLOG - 1; level >= 0; level--) {
            std::tie(l, r) = succ((x >> level) & 1, l, r, level);
        }
        return r - l;
    }

    // k-th(0-indexed) smallest number in v[l,r)
    T kth_smallest(int l, int r, int k) {
        assert(0 <= k && k < r - l);
        T ret = 0;
        for(int level = MAXLOG - 1; level >= 0; level--) {
            int cnt = matrix[level].rank(false, r) - matrix[level].rank(false, l);
            bool f = cnt <= k;
            if(f) {
                ret |= T(1) << level;
                k -= cnt;
            }
            std::tie(l, r) = succ(f, l, r, level);
        }
        return ret;
    }

    // k-th(0-indexed) largest number in v[l,r)
    T kth_largest(int l, int r, int k) {
        return kth_smallest(l, r, r - l - k - 1);
    }

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

    // count i s.t. (l <= i < r) && (lower <= v[i] < upper)
    int range_freq(int l, int r, T lower, T upper) {
        return range_freq(l, r, upper) - range_freq(l, r, lower);
    }

    // max v[i] s.t. (l <= i < r) && (v[i] < upper)
    T prev_value(int l, int r, T upper) {
        int cnt = range_freq(l, r, upper);
        return cnt == 0 ? T(-1) : kth_smallest(l, r, cnt - 1);
    }

    // min v[i] s.t. (l <= i < r) && (lower <= v[i])
    T next_value(int l, int r, T lower) {
        int cnt = range_freq(l, r, lower);
        return cnt == r - l ? T(-1) : kth_smallest(l, r, cnt);
    }
};

}  // namespace atcoder

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