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[問題案] Point Set Range Composite (Linear Functions) (point_set_range_composite) #122

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yosupo06 opened this issue Oct 4, 2019 · 4 comments
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@yosupo06 yosupo06 commented Oct 4, 2019

問題概要

  • 問題ID: point_set_range_composite
  • 問題名: Point Set Range Composite (Linear Functions)

1次関数、1点変更 / 区間関数合成

N個の一次関数f_0, f_1, ..., f_{N - 1}が与えられる。f_i = a_i x + b_i。Q個のクエリを処理

  • 0 p c d: f_p(x) = (cx + d)に変更
  • 1 l, r, x: f_r(f_{r-1}(...f_{l+1}(f_l(x))...)を出力

全てmod 998244353

入力

N Q
a_0 b_0
a_1 b_1
:
a_{N - 1} b_{N - 1}
query 0
query 1
:

制約

N, Q <= 500,000
0 <= 値 < 998244353

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@yosupo06 yosupo06 commented Oct 4, 2019

  • 名前をどうするか(Fenwick Treeをpoint_add_range_sumにしたが、これと対応づけられる気がしないなァ)

  • 合成の向きをどっちにするか

@yosupo06 yosupo06 added this to 精査待ち in 問題リスト Oct 4, 2019
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@yosupo06 yosupo06 commented Nov 11, 2019

f_r( ... ( f_l(x) )..)の方向の合成が自然でしょう

@yosupo06 yosupo06 self-assigned this Nov 11, 2019
@yosupo06 yosupo06 changed the title [問題案] 一次関数の一点変更, 区間合成 [問題案] Point Set Range Composite (Linear Functions) Nov 11, 2019
@yosupo06 yosupo06 changed the title [問題案] Point Set Range Composite (Linear Functions) [問題案] Point Set Range Composite (Linear Functions) (point_set_range_composite) Nov 11, 2019
@yosupo06 yosupo06 moved this from 精査待ち to 作業待ち in 問題リスト Nov 12, 2019
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@yosupo06 yosupo06 commented Nov 25, 2019

(adhocにやればa=0でも逆元があるかのように扱えるはずだし)逆元消す理由がないので0<a

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@yosupo06 yosupo06 commented Nov 26, 2019

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