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Problem solution · Python

ABC339 E — Smooth Subsequence

ABC339 E — Smooth Subsequence: a Python solution using segment tree or range structure. Learn the idea, check the complexity, and read the full code, with credit to KATO-Hiro AtCoder Solutions.

Technique
Segment tree or range structure
Source
KATO-Hiro AtCoder Solutions
Length
172 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

Segment tree or range structure

For ABC339 E — Smooth Subsequence, the implementation stores interval information in a range-query data structure so updates and queries avoid rescanning the full input.

  1. Choose the aggregate stored for each interval or prefix.
  2. Build or initialize the structure from the input.
  3. Apply updates and combine the affected nodes to answer each query.

Code notes

  • 172 lines of Python from the credited upstream file abc339_e.py.
  • The implementation visibly relies on sequence storage, ordered lookup.
  • 1 loop block detected.

Complexity

Count the build once, then multiply the logarithmic update or query path by the number of operations.

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 codeABC339 E — Smooth Subsequence · PythonPython
Use this to learn the idea, then write your own version.
# -*- coding: utf-8 -*-  import typing  # See:# ac-library-python# https://github.com/not522/ac-library-python/blob/master/atcoder/segtree.pydef _ceil_pow2(n: int) -> int:    x = 0     while (1 << x) < n:        x += 1     return x  class SegTree:    def __init__(        self,        op: typing.Callable[[typing.Any, typing.Any], typing.Any],        e: typing.Any,        v: typing.Union[int, typing.List[typing.Any]],    ) -> None:        self._op = op        self._e = e         if isinstance(v, int):            v = [e] * v         self._n = len(v)        self._log = _ceil_pow2(self._n)        self._size = 1 << self._log        self._d = [e] * (2 * self._size)         for i in range(self._n):            self._d[self._size + i] = v[i]        for i in range(self._size - 1, 0, -1):            self._update(i)     def set(self, p: int, x: typing.Any) -> None:        assert 0 <= p < self._n         p += self._size        self._d[p] = x         for i in range(1, self._log + 1):            self._update(p >> i)     def get(self, p: int) -> typing.Any:        assert 0 <= p < self._n         return self._d[p + self._size]     def prod(self, left: int, right: int) -> typing.Any:        assert 0 <= left <= right <= self._n         sml = self._e        smr = self._e        left += self._size        right += self._size         while left < right:            if left & 1:                sml = self._op(sml, self._d[left])                left += 1             if right & 1:                right -= 1                smr = self._op(self._d[right], smr)             left >>= 1            right >>= 1         return self._op(sml, smr)     def all_prod(self) -> typing.Any:        return self._d[1]     def max_right(self, left: int, f: typing.Callable[[typing.Any], bool]) -> int:        assert 0 <= left <= self._n        assert f(self._e)         if left == self._n:            return self._n         left += self._size        sm = self._e        first = True         while first or (left & -left) != left:            first = False             while left % 2 == 0:                left >>= 1             if not f(self._op(sm, self._d[left])):                while left < self._size:                    left *= 2                     if f(self._op(sm, self._d[left])):                        sm = self._op(sm, self._d[left])                        left += 1                return left - self._size             sm = self._op(sm, self._d[left])            left += 1         return self._n     def min_left(self, right: int, f: typing.Callable[[typing.Any], bool]) -> int:        assert 0 <= right <= self._n        assert f(self._e)         if right == 0:            return 0         right += self._size        sm = self._e         first = True         while first or (right & -right) != right:            first = False            right -= 1             while right > 1 and right % 2:                right >>= 1             if not f(self._op(self._d[right], sm)):                while right < self._size:                    right = 2 * right + 1                    if f(self._op(self._d[right], sm)):                        sm = self._op(self._d[right], sm)                        right -= 1                return right + 1 - self._size             sm = self._op(self._d[right], sm)         return 0     def _update(self, k: int) -> None:        self._d[k] = self._op(self._d[2 * k], self._d[2 * k + 1])  def main():    import sys     input = sys.stdin.readline     n, d = map(int, input().split())    a = list(map(int, input().split()))    m = 5 * 10**5 + 10    # 最後にajを選んだときに条件を満たす最大値    dp = [0] * m    st = SegTree(op=max, e=0, v=dp)     for aj in a:        left = max(0, aj - d)        right = min(aj + d, m - 1)        value = st.prod(left, right + 1) + 1         st.set(aj, value)     ans = st.all_prod()    print(ans)  if __name__ == "__main__":    main()

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