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Problem solution · Python

ABC306 E — Best Performances

ABC306 E — Best Performances: a Python solution using heap or priority queue. Learn the idea, check the complexity, and read the full code, with credit to KATO-Hiro AtCoder Solutions.

Technique
Heap or priority queue
Source
KATO-Hiro AtCoder Solutions
Length
126 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Heap or priority queue

For ABC306 E — Best Performances, the implementation repeatedly takes the currently best candidate from a heap while inserting newly available choices.

  1. Define the priority key and whether the smallest or largest item should lead.
  2. Push each candidate when it becomes eligible.
  3. Discard stale entries when necessary and process the best live candidate.

Code notes

  • 126 lines of Python from the credited upstream file abc306_e.py.
  • The implementation visibly relies on sequence storage, hash lookup, ordered lookup, work queue.
  • No explicit loop blocks detected.

Complexity

Count heap pushes and pops; each normally contributes a logarithmic factor in the heap size.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from KATO-Hiro AtCoder Solutions by KATO-Hiro and is used under the CC0-1.0 licence.

Open problem ↗Original source ↗
Full codeABC306 E — Best Performances · PythonPython
Use this to learn the idea, then write your own version.
# -*- coding: utf-8 -*- from collections import defaultdictfrom heapq import heappop, heappush  class SumOfTopKth:    """Sum of the k-th number from the smallest (largest) to the k-th.     See:    https://atcoder.jp/contests/abc306/submissions/42339375    """     __slots__ = (        "_summed",        "_k",        "_in",        "_out",        "_d_in",        "_d_out",        "_freq",        "_ascending_order",    )     def __init__(self, k: int, ascending_order=True) -> None:        self._k = k        self._summed = 0        self._in = []        self._out = []        self._d_in = []        self._d_out = []        self._ascending_order = ascending_order        self._freq = defaultdict(int)     def query(self) -> int:        return self._summed if self._ascending_order else -self._summed     def add(self, x: int) -> None:        if not self._ascending_order:            x = -x         self._freq[x] += 1        heappush(self._in, -x)        self._summed += x        self._modify()     def discard(self, x: int) -> None:        if not self._ascending_order:            x = -x        if self._freq[x] == 0:            return         self._freq[x] -= 1         if self._in and -self._in[0] == x:            self._summed -= x            heappop(self._in)        elif self._in and -self._in[0] > x:            self._summed -= x            heappush(self._d_in, -x)        else:            heappush(self._d_out, x)         self._modify()     def set_k(self, k: int) -> None:        self._k = k        self._modify()     def get_k(self) -> int:        return self._k     def _modify(self) -> None:        while self._out and (len(self._in) - len(self._d_in) < self._k):            p = heappop(self._out)             if self._d_out and p == self._d_out[0]:                heappop(self._d_out)            else:                self._summed += p                heappush(self._in, -p)         while len(self._in) - len(self._d_in) > self._k:            p = -heappop(self._in)             if self._d_in and p == -self._d_in[0]:                heappop(self._d_in)            else:                self._summed -= p                heappush(self._out, p)         while self._d_in and self._in[0] == self._d_in[0]:            heappop(self._in)            heappop(self._d_in)     def __len__(self) -> int:        return len(self._in) + len(self._out) - len(self._d_in) - len(self._d_out)     def __contains__(self, x: int) -> bool:        if not self._ascending_order:            x = -x        return self._freq[x] > 0  def main():    import sys     input = sys.stdin.readline     n, k, q = map(int, input().split())    a = [0] * n    s = SumOfTopKth(k, ascending_order=False)     for _ in range(q):        xi, yi = map(int, input().split())        xi -= 1         s.discard(a[xi])        s.add(yi)        print(s.query())        a[xi] = yi  if __name__ == "__main__":    main()

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