From 80846a1f699be708559f76b0165a807a56d8a927 Mon Sep 17 00:00:00 2001 From: Zengtudor Date: Tue, 6 Aug 2024 08:31:25 +0800 Subject: [PATCH] update problems --- .vscode/launch.json | 14 +++++++ day4/T435167/T435167.md | 72 ++++++++++++++++++++++++++++++++ day4/U287193/U287193.md | 77 +++++++++++++++++++++++++++++++++++ day4/U461920/U461920.md | 88 ++++++++++++++++++++++++++++++++++++++++ day4/U76034/U76034.cpp | 0 day4/U76034/U76034.md | 79 ++++++++++++++++++++++++++++++++++++ day4/U76034/U76034.pdf | Bin 0 -> 124183 bytes day4/U76034/chat.md | 17 ++++++++ 8 files changed, 347 insertions(+) create mode 100644 day4/T435167/T435167.md create mode 100644 day4/U287193/U287193.md create mode 100644 day4/U461920/U461920.md create mode 100644 day4/U76034/U76034.cpp create mode 100644 day4/U76034/U76034.md create mode 100644 day4/U76034/U76034.pdf create mode 100644 day4/U76034/chat.md diff --git a/.vscode/launch.json b/.vscode/launch.json index 4cd01e5..d26621e 100644 --- a/.vscode/launch.json +++ b/.vscode/launch.json @@ -4,6 +4,20 @@ // 欲了解更多信息,请访问: https://go.microsoft.com/fwlink/?linkid=830387 "version": "0.2.0", "configurations": [ + { + "type": "gdb", + "request": "launch", + "name": "GDB", + "program": "${workspaceFolder}/${command:AskForProgramName}", + "stopOnEntry": true + }, + { + "type": "by-gdb", + "request": "launch", + "name": "Launch(gdb)", + "program": "${fileBasenameNoExtension}", + "cwd": "${workspaceRoot}" + }, { "type": "lldb", "request": "launch", diff --git a/day4/T435167/T435167.md b/day4/T435167/T435167.md new file mode 100644 index 0000000..9251b03 --- /dev/null +++ b/day4/T435167/T435167.md @@ -0,0 +1,72 @@ +# 01 Sort + +## 题目描述 + +给定两个长度为 $n$ 的序列 $a[1...n]$ 和 $b[1...n]$,其中每个 $a[i]$ 都对应一个属性 $b[i]$,并且 $b[i]$ 的取值只能为 $0$ 或者 $1$。 + +定义一次操作的规则如下: + +- 选择满足 $b[i]\neq b[j]$ 的两个数 $i$ 和 $j \ (1\le i,j\le n, i\neq j)$,分别交换对应的 $a[i],a[j]$ 和 $b[i], b[j]$ + +你最多可以执行 $x\in [0, 10^5]$ 次操作,请你判断能否在规定次数内,使得序列 $a[1...n]$ 排序成非降顺序吗?如果可以,请你输出一种可能的操作方案;如果不可以,则输出 $-1$。 + +## 输入格式 + +第一行包含一个整数 $t$,代表 $t$ 组数据 + +每组数据的第一行保包含 $1$ 个整数 $n$,表示序列长度 + +每组数据的第二行 $n$ 个整数 $a[1...n]$ + +每组数据的第三行 $n$ 个整数 $b[1...n]$,表示每个 $a[i]$ 对应的属性 $0$ 或 $1$ + +## 输出格式 + +请你分别输出 $t$ 组数据的答案。 + +对于每组数据,第一行输出一个整数 $x \ (x\in [0, 10^5])$ 代表操作次数,若无解则输出 $-1$。接下来的 $x$ 行,每行两个整数 $i$ 和 $j$,代表一次操作。 + +如果有多个答案,则打印其中任何一个。你不必尽量减少移动的次数。 + +## 样例 #1 + +### 样例输入 #1 + +``` +5 +4 +10 20 20 30 +0 1 0 1 +3 +3 1 2 +0 1 1 +4 +2 2 4 8 +1 1 1 1 +3 +5 15 4 +0 0 0 +4 +20 10 100 50 +1 0 0 1 +``` + +### 样例输出 #1 + +``` +0 +2 +1 2 +2 3 +0 +-1 +2 +1 2 +3 4 +``` + +## 提示 + +对于 $20\%$ 数据,$1\le t\le 10$,$1\le n\le 100$,$1\le a[i]\le 100$,所有 $b[i]=0$ + +对于 $100\%$ 数据,$1\le t\le 100$,$1\le n\le 10^3$,$1\le a[i]\le 10^5$,$b[i]\in \{0,1\}$ \ No newline at end of file diff --git a/day4/U287193/U287193.md b/day4/U287193/U287193.md new file mode 100644 index 0000000..8b16663 --- /dev/null +++ b/day4/U287193/U287193.md @@ -0,0 +1,77 @@ +# 冒泡 + +## 题目描述 + +对于一个 $1\sim n$ 的排列 $a$ 和一个数 $m$,定义 $f(a,m)$ 为恰好经过 $m$ 轮冒泡排序后变为 $a$ 的不同排列数量。 + +一轮冒泡排序的过程如下:从小到大依次考虑每个 $i \in [1,n)$,如果 $a[i]>a[i+1]$,那么就交换 $a[i]$ 和 $a[i+1]$。 + +给定 $n,m$ 和一个长度为 $n$ 的序列 $lim$。一个排列 $a$ 合法当且仅当 $\forall i$,如果 $lim[i]\ne 0$,那么 $a[i] = lim[i]$。 + +你需要求出所有合法的 $a$ 的 $f(a,m)$ 之和。答案对 $998244353$ 取模。 + +## 输入格式 + +第一行,共两个数,表示 $n,m$。 + +第二行,共 $n$ 个数,表示 $lim[1...n]$。 + +## 输出格式 + +共一行,一个数,表示答案。 + +## 样例 #1 + +### 样例输入 #1 + +``` +6 2 +0 0 0 0 0 0 +``` + +### 样例输出 #1 + +``` +720 +``` + +## 样例 #2 + +### 样例输入 #2 + +``` +6 0 +6 0 1 4 0 0 +``` + +### 样例输出 #2 + +``` +6 +``` + +## 样例 #3 + +### 样例输入 #3 + +``` +见下发样例 +``` + +### 样例输出 #3 + +``` + +``` + +## 提示 + +对于 100% 的数据,$1\le n\le 5000, 0\le m\le n, 0\le lim[i]\le n$,保证 $lim[i]$ 互不相同。 + +子任务1(10pts):$n\le 8$ + +子任务2(40pts):所有 $lim[i]\ne 0$ + +子任务3(20pts):$n\le 100$ + +子任务4(30pts):无特殊限制 \ No newline at end of file diff --git a/day4/U461920/U461920.md b/day4/U461920/U461920.md new file mode 100644 index 0000000..5a03012 --- /dev/null +++ b/day4/U461920/U461920.md @@ -0,0 +1,88 @@ +# 中位数 + +## 题目背景 + +1.5s, 512MB + +定义一个序列 $A[0,1,...,N-1]$ 的中位数为将 $A$ 升序排序之后的中间元素 $A'[N/2]$;如果 $N$ 为偶数,则序列可以有 $2$ 个中位数。 + +定义 $f(A)$ 为序列 $A$ 的中位数在序列中的出现次数,如果序列有 $2$ 个不同中位数,则为它们出现次数的**较大值**。 + +## 题目描述 + +现在给定序列 $A[0,1,...,N-1]$,请你计算其所有子段 $f$ 值的最大值: +$$ +max_{0\le l \le r< N}\{ f(A[l...r])\} +$$ + +## 输入格式 + +第 $1$ 行: $N$ + +第 $2$ 行: $A[0] A[1] \cdots A[N-1]$ + +## 输出格式 + +输出1行1个整数代表答案 + +## 样例 #1 + +### 样例输入 #1 + +``` +7 +1 2 3 1 2 1 3 +``` + +### 样例输出 #1 + +``` +3 +``` + +## 样例 #2 + +### 样例输入 #2 + +``` +9 +1 1 2 3 4 3 2 1 1 +``` + +### 样例输出 #2 + +``` +2 +``` + +## 样例 #3 + +### 样例输入 #3 + +``` +14 +2 6 2 5 3 4 2 1 4 3 5 6 3 2 +``` + +### 样例输出 #3 + +``` +3 +``` + +## 提示 + +### 约束条件 + +- $1 \leq N \leq 5 \times 10^{5}$ +- $1 \leq A[i] \leq N$ + +### 子任务 + +1. (11 分):$N \leq 100$ 。 +2. (17 分):$N \le 2 \times 10^{3}$ 。 +3. 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