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Problem solution · Python

ABC340 E — Mancala 2

ABC340 E — Mancala 2: a Python solution using sliding window or two pointers. Learn the idea, check the complexity, and read the full code, with credit to KATO-Hiro AtCoder Solutions.

Technique
Sliding window or two pointers
Source
KATO-Hiro AtCoder Solutions
Length
267 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

Sliding window or two pointers

For ABC340 E — Mancala 2, the implementation maintains a moving interval and updates only the information that enters or leaves the window.

  1. Choose the invariant that makes a window valid or useful.
  2. Advance the right boundary and add the new element.
  3. Move the left boundary only as needed while maintaining the invariant and updating the answer.

Code notes

  • 267 lines of Python from the credited upstream file abc340_e.py.
  • The implementation visibly relies on sequence storage, ordered lookup.
  • 1 loop block detected.

Complexity

Confirm that neither pointer moves backwards; if so, the scan is usually linear apart from the window’s data-structure 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 codeABC340 E — Mancala 2 · PythonPython
Use this to learn the idea, then write your own version.
# -*- coding: utf-8 -*-  import typing  def _ceil_pow2(n: int) -> int:    x = 0    while (1 << x) < n:        x += 1     return x  class LazySegTree:    def __init__(        self,        op: typing.Callable[[typing.Any, typing.Any], typing.Any],        e: typing.Any,        mapping: typing.Callable[[typing.Any, typing.Any], typing.Any],        composition: typing.Callable[[typing.Any, typing.Any], typing.Any],        id_: typing.Any,        v: typing.Union[int, typing.List[typing.Any]],    ) -> None:        self._op = op        self._e = e        self._mapping = mapping        self._composition = composition        self._id = id_         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)        self._lz = [self._id] * 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        for i in range(self._log, 0, -1):            self._push(p >> i)        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         p += self._size        for i in range(self._log, 0, -1):            self._push(p >> i)        return self._d[p]     def prod(self, left: int, right: int) -> typing.Any:        assert 0 <= left <= right <= self._n         if left == right:            return self._e         left += self._size        right += self._size         for i in range(self._log, 0, -1):            if ((left >> i) << i) != left:                self._push(left >> i)            if ((right >> i) << i) != right:                self._push(right >> i)         sml = self._e        smr = self._e        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 apply(        self,        left: int,        right: typing.Optional[int] = None,        f: typing.Optional[typing.Any] = None,    ) -> None:        assert f is not None         if right is None:            p = left            assert 0 <= left < self._n             p += self._size            for i in range(self._log, 0, -1):                self._push(p >> i)            self._d[p] = self._mapping(f, self._d[p])            for i in range(1, self._log + 1):                self._update(p >> i)        else:            assert 0 <= left <= right <= self._n            if left == right:                return             left += self._size            right += self._size             for i in range(self._log, 0, -1):                if ((left >> i) << i) != left:                    self._push(left >> i)                if ((right >> i) << i) != right:                    self._push((right - 1) >> i)             l2 = left            r2 = right            while left < right:                if left & 1:                    self._all_apply(left, f)                    left += 1                if right & 1:                    right -= 1                    self._all_apply(right, f)                left >>= 1                right >>= 1            left = l2            right = r2             for i in range(1, self._log + 1):                if ((left >> i) << i) != left:                    self._update(left >> i)                if ((right >> i) << i) != right:                    self._update((right - 1) >> i)     def max_right(self, left: int, g: typing.Callable[[typing.Any], bool]) -> int:        assert 0 <= left <= self._n        assert g(self._e)         if left == self._n:            return self._n         left += self._size        for i in range(self._log, 0, -1):            self._push(left >> i)         sm = self._e        first = True        while first or (left & -left) != left:            first = False            while left % 2 == 0:                left >>= 1            if not g(self._op(sm, self._d[left])):                while left < self._size:                    self._push(left)                    left *= 2                    if g(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, g: typing.Any) -> int:        assert 0 <= right <= self._n        assert g(self._e)         if right == 0:            return 0         right += self._size        for i in range(self._log, 0, -1):            self._push((right - 1) >> i)         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 g(self._op(self._d[right], sm)):                while right < self._size:                    self._push(right)                    right = 2 * right + 1                    if g(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 _all_apply(self, k: int, f: typing.Any) -> None:        self._d[k] = self._mapping(f, self._d[k])        if k < self._size:            self._lz[k] = self._composition(f, self._lz[k])     def _push(self, k: int) -> None:        self._all_apply(2 * k, self._lz[k])        self._all_apply(2 * k + 1, self._lz[k])        self._lz[k] = self._id  def main():    import sys     input = sys.stdin.readline     n, m = map(int, input().split())    inf = 10**18    a = list(map(int, input().split())) + [inf] * 5    b = list(map(int, input().split()))     def mapping(x, y):        return x + y     def composition(x, y):        return x + y     lazy_st = LazySegTree(        op=min, e=inf, mapping=mapping, composition=composition, id_=0, v=a    )     for bi in b:        ai = lazy_st.get(bi)         if ai == 0:            continue         p, q = divmod(ai, n)        lazy_st.set(bi, 0)        lazy_st.apply(0, n, p)        diff = (n - 1) - bi         if 1 <= q <= diff:            lazy_st.apply(bi + 1, bi + q + 1, 1)        elif q > diff:            lazy_st.apply(bi + 1, n, 1)            lazy_st.apply(0, q - diff, 1)         ans = list()     for i in range(n):        ans.append(lazy_st.get(i))     print(*ans)  if __name__ == "__main__":    main()

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