Data Structures

Binary Heap With Decrease-Key

Difficulty

Asked at Citadel Securities

Theory: Data Structures You Implement, Not Import

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Available in C++ and Python. You are solving it in C++. Switch to Python

xxxxxxxxx xxxxxxxxxxxxxx, x xxxxxx xxx-xxxx xxxx xxxxxx xxxxxxx xxxx xxxx xxxxxxx xxxxxxxxxx. xx xxxxxxxx xxxxxxxx_xxx, xxxxx xxxxxx xxx xxxxxxxx xx x xxx xxxx xx xxxxxxx xx xxx xxxx. xxxxxxxx xx xx (xxxxxxxx, xxx) xxxxxxxxx: xxxxx xxxxxxxx xxxxx, xxxx xxxxxx xx xxxxxxx xxx, xxxxx xxxxx xxxxx xxxxxxxxx xxxxxxxxxxxxx. xxx xxxxxxxx xxxxxxx'x xxxxxxxx xxxxx xxxxxx xxxxx xx xxxxxxx xx xxx xxxxxx xx xxxxxx xxx xxxxxxxx. xxxxxxxx'x xxxxxxxxxx xxxx, xxxxxxxxxxx xxxxx-xxxx xxxxxx xxx xxx xxxxx xxxxx xxxx xxxxxx xxxxxxxxx xxxx xxxx. xxx xxx xx x xxxx xxxx xxxxxx xxxxx xxxxx xxx xxxxx, xx xxx xxxx xxxxx xxx xxx xxxxx xxxx xxxx xxxxxxxxxx xxxxxxx xxxxx xxxxxxxx. xxxxx xxxxxxxxxxxxxx { xxxxxx: xxxx xxxxxx(xxxx xxxx xxx, xxxx xxxx xxxxxxxx); xxx::xxxxxxxx<xxx::xxxx<xxxx xxxx, xxxx xxxx>> xxxxxxx_xxx(); xxxx xxxxxxxx_xxx(xxxx xxxx xxx, xxxx xxxx xxxxxxxxxxx); xxx::xxxx_x xxxx() xxxxx; }; xxxx xxxxxx(xxxx xxxx xxx, xxxx xxxx xxxxxxxx): xxxx xxx xxx. xxxxxxx xxxxx (xxx xxxxxxx xxxxxxx) xx xxx xxx xx xxxxxxx xxxxxxx. xxx::xxxxxxxx<xxx::xxxx<xxxx xxxx, xxxx xxxx>> xxxxxxx_xxx(): xxxxxxx xxx xxxxxxx (xxx, xxxxxxxx) xxx xxx xxxxxxxx xxxxxxx, xxx::xxxxxxx xx xxxxx. x xxx xxxxxxxxx xxxxxxx xxx xx xxxxxxxx xxxxx xxxxx. xxxx xxxxxxxx_xxx(xxxx xxxx xxx, xxxx xxxx xxxxxxxxxxx): xxxx xxx xxx'x xxxxxxxx xx xxxxxxxxxxx xx xxx xxx xx xxxxxxx xxx xxxxxxxxxxx xx xxxxxxxx xxxxx xxxx xxx xxxxxxx xxxxxxxx; xxxxxxx xxxxxxx xx xxx. xxx::xxxx_x xxxx() xxxxx: xxx xxxxxx xx xxxx xxxxxxxx. xxx::xxxxxxxx_xxxxx xx xxxxxx. xxx xx xxxxx-xxxxxx xxxxxx xxxx xxxx x xxx xxxx xxx xx xxxx xxxxx, xxx xxxx xxxx xxxxx xxxxxxx xxxxxxx xxxxx xxxx: xxxxxx xxx xxxxxxxx_xxx xxxx xx, xxxxxxx_xxx xxxxx xxx xxxx xxxxxxx xxxx xxx xxxx xxx xxxxx xxxx. xxxxxxxx xxxxxxxxxxxxxx x; x.xxxxxx(xxx, x); x.xxxxxx(xxx, x); x.xxxxxx(xxx, x); x.xxxx(); // x x.xxxxxxx_xxx(); // {xxx, x}, xxxxxxxx x xxxxx x.xxxxxxx_xxx(); // {xxx, x}, xxx xxx xxxxxxxx-x xxxx xxxxxxx xx xxx xxxxx x.xxxxxxx_xxx(); // {xxx, x} x.xxxxxxx_xxx(); // xxx::xxxxxxx x.xxxx(); // x xxxxxxxxxxxxxx x; x.xxxxxx(x, xx); x.xxxxxx(x, xx); x.xxxxxx(x, xx); x.xxxxxxxx_xxx(x, xx); // xxxx, xxx x xxxxx xxx xxxxx x.xxxxxxxx_xxx(x, xx); // xxxxx, x xxxxx xx xxxxxxxx x.xxxxxxxx_xxx(xx, x); // xxxxx, xxxxxxx xxx x.xxxxxx(x, x); // xxxxx, xxx x xx xxxxxxx xxxxxxx x.xxxxxxx_xxx(); // {x, xx} x.xxxxxxx_xxx(); // {x, xx} x.xxxxxxxx_xxx(x, xx); // xxxx x.xxxxxxx_xxx(); // {x, xx} xxxxxxxxxxx xxxx xxx xxxxxxxxxx xxx xxxxxxxx; xxxx xxx xxxxxx xxxxx xxxx xxxxxxxx. xxxx xxx xxxxxxxxxx xxxx xxxx xxxx. xxx xxxxxxxxxx (x(xxx x)) (xxxxxxxx x(x) xxx xxx xxxxx-xxx xxxxxxx). xxx xxxxxx xxxxxxxxxxx xxxx xxxxxxx xxx,xxx xxxx, xxxxxxx xxx,xxx xxxxxxxxx xxx xxxxxx xxx xxxx, xxxxxxxxx xxx xxxxxxxxxx xxxxxxxx xx xxxxxx; xx xxxxxxx_xxx xxxx xxxxx xxx xxx xxxxxxx xxxxx xxxx xx xxxxxxx xx xx, xxxxxxx xxxx xxx xxxxxxxxx. x xxxxxx xxxx xxxxxxx xxxxxxxxx xx xxxxxxxxxxx xxxxxxxxxx xxxxxxx x xxxxx-xxxxx xxxxxx, xx xxxxx xxxx (xxxxxxxx xx xxx xxxx, xxxxxxxx xxxx xxxx xxx xxxxx x xxxxxx, xxxxxxx-xxxx-xxxxxxxx) xxxx xx xxxxx.

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Language:

C++23 Python 3.12

IndexedMinHeap

#include <cstddef>
#include <optional>
#include <unordered_map>
#include <utility>
#include <vector>

// ...
// ...
// ...
// ...
// ...
class IndexedMinHeap {
public:
    bool insert(long long key, long long priority) {
        // ...
        (void)key;
        (void)priority;
        return false;
    }

    std::optional<std::pair<long long, long long>> extract_min() {
        // ...
        return std::nullopt;
    }

    bool decrease_key(long long key, long long newPriority) {
        // ...
        // ...
        (void)key;
        (void)newPriority;
        return false;
    }

    std::size_t size() const {
        // ...
        return 0;
    }
};

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