Atcoder - 随笔分类 - 灰鲭鲨

[ARC132E] Paw

摘要：题目链接考虑最后形态，一定是有某一个区间

[l, r]

$[l,r]$ 保持初始的样子，

l

$l$ 前面都是 <，

r

$r$ 后面都是 >。这个区间一定是某两个相邻圆点的位置。设

f_{i}

$f_i$ 为前

i

$i$ 个数全部被覆盖成 < 的概率。设

x

$x$ 为

l

$l$ 前面圆点的数量，

y

$y$ 阅读全文

posted @ 2023-12-12 12:50 灰鲭鲨阅读(34) 评论(0) 推荐(0) 编辑

[ARC169E] Avoid Boring Matches

摘要：题解链接非常厉害的一道题。考虑无解是什么情况？ R 的个数超过

2^{n - 1}

$2^{n-1}$ 先考虑如何判定。从前往后考虑，如果遇到一个 B，那么如果后面有 R，就选最靠前的 R，否则选最靠后的一个 B.如果遇到 R，就选最靠后的一个 B。但是这个判定很繁琐。我们考虑求出一个合法序列，使得他的 B 阅读全文

posted @ 2023-12-12 12:36 灰鲭鲨阅读(25) 评论(0) 推荐(0) 编辑

[ARC105E] Keep Graph Disconnected

摘要：题目链接好题。如果

1

$1$ 和

n

$n$ 一直联通，开始即结束。如果

n \mod 4 = 1

$n\mod 4=1$ ，那么

\frac{1}{2} x (x + 1) + \frac{1}{2} (n - x) (n - x + 1)

$\frac 12x(x+1)+\frac12(n-x)(n-x+1)$ 为偶数。如果

n \mod 4 = 3

$n\mod 4=3$ ，那么 \(\frac 12x(x+1)+\frac12(n-x 阅读全文

posted @ 2023-11-26 12:49 灰鲭鲨阅读(9) 评论(0) 推荐(0) 编辑

[ABC327G] Many Good Tuple Problems

摘要：题目链接简化题意：有一个

n

$n$ 个点的图，问有多少个长度为

M

$M$ 的边序列，满足连边后图是二分图。

n \leq 30, m \leq 10^{9}

$n\le 30,m\le 10^9$ 考虑先强制要求无重边。定义

f_{i, j}

$f_{i,j}$ 为

i

$i$ 个点，

j

$j$ 条边的图的二分图染色数量（染色方式不同算多次）。这个是阅读全文

posted @ 2023-11-26 12:35 灰鲭鲨阅读(12) 评论(0) 推荐(0) 编辑

[ARC168E] Subsegments with Large Sums

摘要：题目链接看到严格选

k

$k$ 个，不难想到 WQS二分。定义

f (x)

$f(x)$ 为分成

x

$x$ 段，最多有多少个超过

S

$S$ 的。然后你会发现他不是凸的。因为他有很多平段，比如把两个很小的合并不改变答案。换个方向？考虑定义

f (x)

$f(x)$ 为有

x

$x$ 个超过

S

$S$ 的段阅读全文

posted @ 2023-11-26 11:59 灰鲭鲨阅读(28) 评论(0) 推荐(0) 编辑

[ARC122E] Increasing LCMs

摘要：Problem StatementWe have a sequence of

N

$N$ positive integers:

A_{1}, A_{2}, \dots, A_{N}

$A_1,A_2,\cdots,A_N$ . You are to rearrange these integers into another sequence $x_1,x_2 阅读全文

posted @ 2023-11-03 20:36 灰鲭鲨阅读(6) 评论(0) 推荐(0) 编辑

[ARC122D] XOR Game

摘要：Problem StatementThere are

2 N

$2N$ integers written on a blackboard. The

i

$i$ -th integer is

A_{i}

$A_i$ . Alice and Bob will play a game consisting of

N

$N$ rounds 阅读全文

posted @ 2023-11-03 20:27 灰鲭鲨阅读(23) 评论(0) 推荐(0) 编辑

[ARC137E] Baker

摘要：Problem StatementSnuke runs a bakery. He is planning for the next

N

$N$ days. Let us call these days Day

1, 2, \dots, N

$1,2,\cdots,N$ . At the moment, the bakery hires 阅读全文

posted @ 2023-09-25 11:10 灰鲭鲨阅读(17) 评论(0) 推荐(0) 编辑

[AGC030D] Inversion Sum

摘要：Problem StatementYou are given an integer sequence of length

N

$N$ :

A_{1}, A_{2}, . . ., A_{N}

$A_1,A_2,...,A_N$ . Let us perform

Q

$Q$ operations in order. The

i

$i$ -th operation is d 阅读全文

posted @ 2023-09-22 20:50 灰鲭鲨阅读(8) 评论(0) 推荐(0) 编辑

[ARC165E] Random Isolation

摘要：Problem StatementThere is a tree with

N

$N$ vertices numbered

1

$1$ to

N

$N$ . The

i

$i$ -th edge connects vertices

A_{i}

$A_i$ and

B_{i}

$B_i$ . Let us keep performing the 阅读全文

posted @ 2023-09-22 20:06 灰鲭鲨阅读(31) 评论(0) 推荐(0) 编辑

[ARC165D] Substring Comparison

摘要：Problem StatementFor an integer sequence

X = (X_{1}, X_{2}, \dots, X_{n})

$X=(X_1,X_2,\dots,X_n)$ , let

X [L, R]

$X[L,R]$ denote the integer sequence

(X_{L}, X_{L + 1}, \dots, X_{R})

$(X_L,X_{L+1},\dots,X_{R})$ . You are given 阅读全文

posted @ 2023-09-22 19:56 灰鲭鲨阅读(14) 评论(0) 推荐(0) 编辑

[ABC309Ex] Simple Path Counting Problem

摘要：Problem StatementWe have a grid with

N

$N$ rows and

M

$M$ columns. We denote by

(i, j)

$(i,j)$ the cell in the

i

$i$ -th row from the top and

j

$j$ -th column from the 阅读全文

posted @ 2023-09-22 19:35 灰鲭鲨阅读(39) 评论(0) 推荐(0) 编辑

[AGC003D] Anticube

摘要：Problem StatementSnuke got positive integers

s_{1}, . . ., s_{N}

$s_1,...,s_N$ from his mother, as a birthday present. There may be duplicate elements. He will circle som 阅读全文

posted @ 2023-09-09 16:09 灰鲭鲨阅读(11) 评论(0) 推荐(0) 编辑

[ABC317G] Rearranging

摘要：Problem StatementThere is a grid with

N

$N$ rows and

M

$M$ columns. The square at the

i

$i$ -th row from the top and the

j

$j$ -th column from the left contains 阅读全文

posted @ 2023-09-04 10:36 灰鲭鲨阅读(41) 评论(0) 推荐(1) 编辑

[ABC318G] Typical Path Problem

摘要：Problem StatementYou are given a simple connected undirected graph

G

$G$ with

N

$N$ vertices and

M

$M$ edges. The vertices and edges of

G

$G$ are numbered as 阅读全文

posted @ 2023-09-04 10:28 灰鲭鲨阅读(18) 评论(0) 推荐(0) 编辑

[ABC313F] Flip Machines

摘要：Problem StatementThere are

N

$N$ cards numbered

1

$1$ through

N

$N$ . Each face of a card has an integer written on it; card

i

$i$ has

A_{i}

$A_i$ on its front and $ 阅读全文

posted @ 2023-08-24 23:02 灰鲭鲨阅读(11) 评论(0) 推荐(0) 编辑

[ARC093F] Dark Horse

摘要：Problem StatementThere are

2^{N}

$2^N$ players, numbered

1, 2, . . ., 2^{N}

$1, 2, ..., 2^N$ . They decided to hold a tournament. The tournament proceeds as follows: Choose a p 阅读全文

posted @ 2023-08-03 20:21 灰鲭鲨阅读(18) 评论(0) 推荐(0) 编辑

[AGC024F] Simple Subsequence Problem

摘要：Problem StatementYou are given a set

S

$S$ of strings consisting of 0 and 1, and an integer

K

$K$ . Find the longest string that is a subsequence of

K

$K$ or 阅读全文

posted @ 2023-07-26 12:09 灰鲭鲨阅读(11) 评论(0) 推荐(0) 编辑

[ARC150F] Constant Sum Subsequence

摘要：Problem StatementWe have a sequence of positive integers of length

N^{2}

$N^2$ ,

A = (A_{1}, A_{2}, \dots, A_{N^{2}})

$A=(A_1,\ A_2,\ \dots,\ A_{N^2})$ , and a positive integer

S

$S$ . For this sequ 阅读全文

posted @ 2023-07-25 19:46 灰鲭鲨阅读(10) 评论(0) 推荐(0) 编辑

[ABC309G] Ban Permutation

摘要：Problem StatementFind the number, modulo

998244353

$998244353$ , of permutations

P = (P_{1}, P_{2}, \dots, P_{N})

$P=(P_1,P_2,\dots,P_N)$ of

(1, 2, \dots, N)

$(1,2,\dots,N)$ such that:

| P_{i} - i | \geq X

$|P_i - i| \ge X$ for all 阅读全文

posted @ 2023-07-25 19:27 灰鲭鲨阅读(23) 评论(0) 推荐(0) 编辑

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