C++写Bob has a magic computer which has infinite USB ports. But there is a problem with this computer——it can only read and write the two most recently inserted USB disks. Initially, Bob has n USB disks and every USB disk has one unique file. He wants to insert all the n USB disks into his computer. Since his computer is old, he must insert USB disk in the following way: Select 2 unplugged USB disks, insert them into computer. The two USB disks inserted in the previous step will share the files with each other, which means after that both two USB disks will have all files either in the first one or in the second one. If all the n USB disks are in the computer, the task is finished. Otherwise, choose one USB disk in the computer, unplug it and go to step 1 . Bob wants to know the minimum number of n such that there is a sequence of operations that ends up with at least k different files in each USB disk. Input Only one number,k (2≤k≤100000 ),meaning that finally each USB disk owns at least k different files. Output You need to output one number n , which means the minimum number of USB disks in module 998244353.
时间: 2024-01-29 15:04:35 浏览: 45
以下是使用 C++ 解决此问题的代码:
```cpp
#include <iostream>
#include <cstdio>
using namespace std;
const int mod = 998244353;
int k;
int pow_mod(int x, int p) {
int res = 1;
while (p) {
if (p & 1) res = (long long)res * x % mod;
x = (long long)x * x % mod;
p >>= 1;
}
return res;
}
int main() {
scanf("%d", &k);
int ans = 1;
while (ans < k) ans <<= 1;
printf("%d\n", pow_mod(2, ans - 1));
return 0;
}
```
解释:首先将 n 设为 1,然后每次将 n 左移一位(即乘以 2),直到 n 大于等于 k。这样就可以保证最终每个 USB 盘上的文件数都至少为 k。根据题意,只需要算出插入 n 个 USB 盘的方案数,即 C(n, 2)C(n-2, 2)C(n-4, 2)...C(4, 2)C(2, 2),可以化简为 2^(n-1),所以最后的答案为 2^(n-1) % 998244353。
相关问题
C++写Bob has a magic computer which has infinite USB ports. But there is a problem with this computer——it can only read and write the two most recently inserted USB disks. Initially, Bob has n USB disks and every USB disk has one unique file. He wants to insert all the n USB disks into his computer. Since his computer is old, he must insert USB disk in the following way: Select 2 unplugged USB disks, insert them into computer. The two USB disks inserted in the previous step will share the files with each other, which means after that both two USB disks will have all files either in the first one or in the second one. If all the n USB disks are in the computer, the task is finished. Otherwise, choose one USB disk in the computer, unplug it and go to step 1 . Bob wants to know the minimum number of n such that there is a sequence of operations that ends up with at least k different files in each USB disk. Input Only one number,k (2≤k≤100000 ),meaning that finally each USB disk owns at least k different files. Output You need to output one number n , which means the minimum number of USB disks in module 998244353.
以下是C++代码实现:
```cpp
#include <bits/stdc++.h>
using namespace std;
const int mod = 998244353;
int k, ans = 1;
int main()
{
cin >> k;
while (ans < k) ans <<= 1; // 找到第一个大于等于k的2的幂
cout << ans % mod << endl;
return 0;
}
```
思路解析:
由题目中的要求可知,每个USB都需要至少k个文件,而每次插入两个USB后,它们会共享文件,也就是说,它们中的每个USB都会有另一个USB中没有的新文件。因此,每次插入两个USB后,文件数至少会增加k个。
而最终要求每个USB都至少有k个文件,因此,我们只需要找到第一个大于等于k的2的幂,这样,只需要进行log2(k)次操作,就可以使所有USB中都有至少k个文件。
所以,本题的答案就是2的幂次方,满足大于等于k。
Write a few lines of C++ code to show an example of an infinite loop. Explain why it is an infinite loop
Here's an example of an infinite loop in C++:
```c++
while(true){
// code that never exits the loop
}
```
In this example, the `while` loop condition is always `true`, which means the loop will never exit. The loop will continue to execute the block of code inside the curly braces indefinitely.
This is an infinite loop because the loop condition is always true and there is no way for the loop to terminate on its own. The only way to exit the loop is to use a `break` statement or an external event (such as terminating the program).