暑假热身H题

本文介绍了一种名为CatFurrierTransform的算法,该算法通过特定的操作序列将任意整数转换为2的幂次减一的形式,以创造出“完美长猫”。文章详细解释了操作流程,并提供了一个示例程序。

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http://codeforces.com/problemset/problem/1152/B
Cat Furrier Transform is a popular algorithm among cat programmers to create longcats. As one of the greatest cat programmers ever exist, Neko wants to utilize this algorithm to create the perfect longcat.

Assume that we have a cat with a number x. A perfect longcat is a cat with a number equal 2m−1 for some non-negative integer m. For example, the numbers 0, 1, 3, 7, 15 and so on are suitable for the perfect longcats.

In the Cat Furrier Transform, the following operations can be performed on x:

(Operation A): you select any non-negative integer n and replace x with x⊕(2n−1), with ⊕ being a bitwise XOR operator.
(Operation B): replace x with x+1.
The first applied operation must be of type A, the second of type B, the third of type A again, and so on. Formally, if we number operations from one in the order they are executed, then odd-numbered operations must be of type A and the even-numbered operations must be of type B.

Neko wants to produce perfect longcats at industrial scale, thus for each cat Neko only wants to perform at most 40 operations. Can you help Neko writing a transformation plan?

Note that it is not required to minimize the number of operations. You just need to use no more than 40 operations.

Input
The only line contains a single integer x (1≤x≤106).

Output
The first line should contain a single integer t (0≤t≤40) — the number of operations to apply.

Then for each odd-numbered operation print the corresponding number ni in it. That is, print ⌈t2⌉ integers ni (0≤ni≤30), denoting the replacement x with x⊕(2ni−1) in the corresponding step.

If there are multiple possible answers, you can print any of them. It is possible to show, that there is at least one answer in the constraints of this problem.

Examples
Input
39
Output
4
5 3
Input
1
Output
0
Input
7
Output
0
Note
In the first test, one of the transforms might be as follows: 39→56→57→62→63. Or more precisely:

Pick n=5. x is transformed into 39⊕31, or 56.
Increase x by 1, changing its value to 57.
Pick n=3. x is transformed into 57⊕7, or 62.
Increase x by 1, changing its value to 63=26−1.
In the second and third test, the number already satisfies the goal requirement.

给你一个数字x,循环进行两种操作,x和(2^n-1)异或,x+1;直到x等于2的m次方减一
输出操作次数和每次异或操作的n。
每次用x最高位1对应的n与之异或,例如8(1000)和15(1111)异或,39(100111)和63(111111)异或,直到满足条件为止。

#include<stdio.h>
int x,t;
int find(int m)
{
	int i;
	t=0;
	for(i=1;;i=i<<1,t++)
	{
		if(i>m)
		break;
	}
	return i;
}
int main()
{
	scanf("%d",&x);
		int ans[35],cout=0,num=0;
		while((find(x)-1)!=x)
		{
			int a=find(x)-1;
			x=x^a;
			ans[num++]=t;
			cout++;
			if((find(x)-1)==x)
			break;
			x++;
			cout++;
		}
		printf("%d\n",cout);
		int i;
		for(i=0;i<num-1;i++)
		printf("%d ",ans[i]);
		if(cout>0)
		printf("%d\n",ans[i]);
}
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