A14901 | Arithmetic Operations
时间限制1s
内存限制256MB
通过 / 提交0/0
题目描述
You are given an array of integers $a_1, a_2, \ldots, a_n$ .
You can do the following operation any number of times (possibly zero):
- Choose any index $i$ and set $a_i$ to any integer (positive, negative or $0$ ).
What is the minimum number of operations needed to turn $a$ into an arithmetic progression? The array $a$ is an arithmetic progression if $a_{i+1}-a_i=a_i-a_{i-1}$ for any $2 \leq i \leq n-1$ .
You can do the following operation any number of times (possibly zero):
- Choose any index $i$ and set $a_i$ to any integer (positive, negative or $0$ ).
What is the minimum number of operations needed to turn $a$ into an arithmetic progression? The array $a$ is an arithmetic progression if $a_{i+1}-a_i=a_i-a_{i-1}$ for any $2 \leq i \leq n-1$ .
输入格式
The first line contains a single integer $n$ ( $1 \le n \le 10^5$ ).
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq 10^5$ ).
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq 10^5$ ).
输出格式
Print a single integer: the minimum number of operations needed to turn $a$ into an arithmetic progression.
输入输出样例
输入 #1
9 3 2 7 8 6 9 5 4 1
输出 #1
6
输入 #2
14 19 2 15 8 9 14 17 13 4 14 4 11 15 7
输出 #2
10
输入 #3
10 100000 1 60000 2 20000 4 8 16 32 64
输出 #3
7
输入 #4
4 10000 20000 10000 1
输出 #4
2
In the first test, you can get the array $a = [11, 10, 9, 8, 7, 6, 5, 4, 3]$ by performing $6$ operations:
- Set $a_3$ to $9$ : the array becomes $[3, 2, 9, 8, 6, 9, 5, 4, 1]$ ;
- Set $a_2$ to $10$ : the array becomes $[3, 10, 9, 8, 6, 9, 5, 4, 1]$ ;
- Set $a_6$ to $6$ : the array becomes $[3, 10, 9, 8, 6, 6, 5, 4, 1]$ ;
- Set $a_9$ to $3$ : the array becomes $[3, 10, 9, 8, 6, 6, 5, 4, 3]$ ;
- Set $a_5$ to $7$ : the array becomes $[3, 10, 9, 8, 7, 6, 5, 4, 3]$ ;
- Set $a_1$ to $11$ : the array becomes $[11, 10, 9, 8, 7, 6, 5, 4, 3]$ .
$a$ is an arithmetic progression: in fact, $a_{i+1}-a_i=a_i-a_{i-1}=-1$ for any $2 \leq i \leq n-1$ .
There is no sequence of less than $6$ operations that makes $a$ an arithmetic progression.
In the second test, you can get the array $a = [-1, 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38]$ by performing $10$ operations.
In the third test, you can get the array $a = [100000, 80000, 60000, 40000, 20000, 0, -20000, -40000, -60000, -80000]$ by performing $7$ operations.
- Set $a_3$ to $9$ : the array becomes $[3, 2, 9, 8, 6, 9, 5, 4, 1]$ ;
- Set $a_2$ to $10$ : the array becomes $[3, 10, 9, 8, 6, 9, 5, 4, 1]$ ;
- Set $a_6$ to $6$ : the array becomes $[3, 10, 9, 8, 6, 6, 5, 4, 1]$ ;
- Set $a_9$ to $3$ : the array becomes $[3, 10, 9, 8, 6, 6, 5, 4, 3]$ ;
- Set $a_5$ to $7$ : the array becomes $[3, 10, 9, 8, 7, 6, 5, 4, 3]$ ;
- Set $a_1$ to $11$ : the array becomes $[11, 10, 9, 8, 7, 6, 5, 4, 3]$ .
$a$ is an arithmetic progression: in fact, $a_{i+1}-a_i=a_i-a_{i-1}=-1$ for any $2 \leq i \leq n-1$ .
There is no sequence of less than $6$ operations that makes $a$ an arithmetic progression.
In the second test, you can get the array $a = [-1, 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38]$ by performing $10$ operations.
In the third test, you can get the array $a = [100000, 80000, 60000, 40000, 20000, 0, -20000, -40000, -60000, -80000]$ by performing $7$ operations.
C++ 编辑器
输入
输出
可保存默认模板；新题优先使用已保存模板。
当前快捷键仅展示，暂不支持修改。
- 撤销
Ctrl / ⌘ + Z - 重做
Ctrl / ⌘ + Y - 查找
Ctrl / ⌘ + F - 全选
Ctrl / ⌘ + A - 复制
Ctrl / ⌘ + C - 剪切
Ctrl / ⌘ + X - 粘贴
Ctrl / ⌘ + V - 自动排版
工具栏排版按钮 - 草稿保存
编辑时自动保存到本机
历史
提交记录
状态说明时间源码
AI
作答助手
你好，我是作答助手。可以问思路、复杂度、样例含义或代码报错原因；不会直接给出完整 AC 代码。
确定要清空代码吗？
提交通过
评测结果：Accepted