Rank and Select on Bits

Difficulty

Asked at Jump Trading

Theory: Data Structures You Implement, Not Import

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xxx xxxxxxxxxx xxxx x xxxxxx xxxx xx xxxxx, xxx xxxxxxx xxxx xxxx xxxxxxxx xxxxxxxx xxxx xxxxxxxxxx, xxxxxxx xxxxx, xxx xxxxx "xxxxx xx xxx x-xx xxxx xxxxx xx xxxx xxxxx" xxxxxxxx xx xxxxx xxxx xxxx. xxxx(x) : xxx xxxx xxx xxxx xxx xxxxxxxx xxxxx xxxxx ( x ). xxxxxx(x) : xxxxx xxx ( x )-xx xxx xxx xx. xxxx xxx xxxxxxxx xx xxxx xxxxx, xxx xxxx xxxx xx xxxxxxxxx. xxxxxxxx xxxx xxxxxxx xx xxxxx xxxxx xx ( x(x) ), xxxxx xx xxxx xx x xxxxxx xx xx xxx xxxxxxx xx xxx xx xxxxxx-xxx xxxxxxx. xxxxxxxxx xxxxxxxxxx xxxx x xxx::xxxxxx<xxx::xxxxxx_x>, xxxx xxx ( x ) xxxxxx xx xxxx ( x / xx ) xx xxx xxxxxxxx ( x xxxx xx ), xxxxx xxxxxxxxxxx xxx xxxxx. xxxx(x) : xxxx(x) xx x xxx xxxx(xxx_xxxxx) xx xxx xxxxxxxxxx. xxxxxx(x) : xxx xxxxx xx xxx ( x )-xx xxx xxx xxxxxxxx xxxx x, xx ( -x ) xx xxxxx xxx xxx xxxx xxxx. xxxxx() : xxx xxxxx xxxxxxxxxx. xxxxxxxxxxxx xxx xxxx ( x(x) ) xxx xxxxx xxxxxxxx xxxxx xx xxxxx; xxxx xxxx xx xxxx xxxx. xxxxxxxx xxxx xxxx x, x xxx x xxx xx xxx xxxxx xxxx xxx xxx xx xxx xx xxx xxxxxx: x.xxxx(x); // x xxxxxxx xxxxx xxxxx x, xxxx x.xxxx(x); // x xxxx x xxx x x.xxxx(xx); // x xxx xx xxxx x.xxxxxx(x); // x x.xxxxxx(x); // xx xxx xxxxxx xxxxxxx xxxx xxx xxxxxx xxxx x.xxxxxx(x); // -x xxxxxxxxxxx xx xx ( x.x xxxxx xx^x ) xxxx xxx ( xx^x ) xxxxxxx. xxx::xxxxxxxx xx xxxxxxxxx xxx xxxxxxxx xx x xxxxxx xxxxxxxxxxx. xxx xx xxxxxx xxxx x xxx-xxxxxxxxx xxxx. xxx xxxx xxxx xxxxxxxx xxx xxxx xxxxx xx xxxxxx xxxxxx x xxxx xx (x << xxxxxx) - x, xxx xxx xxxxx xxxx xx xxxx xx x xx-xxx xxxx. xxxxxxxx x xx-xxx xxxxx xx xx xx xxxxxxxxx xxxxxxxxx, xxx xxxx, xx xx xxxxxx xx xx xxxx xxxxx xxxxx xxx xxxxx. xxxx xxx xxxxxx xxxx xxxxx: xxxx(xxxxxx(x)) == x xxx xxxxx xxxxx ( x ), xxxxx xxx xxxxx xxxxxx xxxxxxxx.

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Language: C++23RankSelect

#include <bit>
#include <cstddef>
#include <cstdint>
#include <vector>

// ...
// ...
// ...
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// ...
// ...
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class RankSelect {
public:
    explicit RankSelect(std::vector<std::uint64_t> words, std::size_t bit_count)
        : words_(std::move(words)), bit_count_(bit_count) {
        // ...
    }

    long long rank(std::size_t index) const {
        // ...
        (void)index;
        return 0;
    }

    long long select(long long k) const {
        // ...
        (void)k;
        return -1;
    }

    long long count() const {
        // ...
        return 0;
    }

private:
    std::vector<std::uint64_t> words_;
    std::size_t bit_count_ = 0;
};

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