B - The 3n + 1 problem
2016-07-10 09:02
176 查看
Description
Problems in Computer Science are often classified as belonging to a certain class of problems (e.g., NP, Unsolvable, Recursive). In this problem you will be analyzing a property of an algorithm whose classification is not known for
all possible inputs.
Consider the following algorithm:
1. input n
2. print n
3. if n = 1 then STOP
4. if n is odd then n <- 3n + 1
5. else n <- n / 2
6. GOTO 2
Given the input 22, the following sequence of numbers will be printed 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
It is conjectured that the algorithm above will terminate (when a 1 is printed) for any integral input value. Despite the simplicity of the algorithm, it is unknown whether this conjecture is true. It has been verified, however, for all integers n such that
0 < n < 1,000,000 (and, in fact, for many more numbers than this.)
Given an input n, it is possible to determine the number of numbers printed (including the 1). For a given n this is called the cycle-length of n. In the example above, the cycle length of 22 is 16.
For any two numbers i and j you are to determine the maximum cycle length over all numbers between i and j.
Input
The input will consist of a series of pairs of integers i and j, one pair of integers per line. All integers will be less than 1,000,000 and greater than 0.
You should process all pairs of integers and for each pair determine the maximum cycle length over all integers between and including i and j.
You can assume that no opperation overflows a 32-bit integer.
Output
For each pair of input integers i and j you should output i, j, and the maximum cycle length for integers between and including i and j. These three numbers should be separated by at least one space with all three numbers on one line
and with one line of output for each line of input. The integers i and j must appear in the output in the same order in which they appeared in the input and should be followed by the maximum cycle length (on the same line).
Sample Input
1 10
100 200
201 210
900 1000
Sample Output
1 10 20
100 200 125
201 210 89
900 1000 174
so easy
解法 输入两个数(先判断大小 )然后按照题意做啦
![](http://static.blog.csdn.net/xheditor/xheditor_emot/default/laugh.gif)
上代码
#include <iostream>
#include <cmath>
using namespace std;
int main()
{
int a,b,c,n,x=0;
while(cin>>a>>b)
{
cout<<a<<" "<<b;
if(a>b)
{
swap(a,b);
}
x=0;
for(int i=a; i<=b; i++)
{
n=i;
c=1;
while(n!=1)
{
if(n%2==0)
{
n=n/2;
c++;
}
else
{
n=3*n+1;
c++;
}
if(x<c)
{
x=c;
}
}
}
cout<<" "<<x<<endl;
}
return 0;
}
Problems in Computer Science are often classified as belonging to a certain class of problems (e.g., NP, Unsolvable, Recursive). In this problem you will be analyzing a property of an algorithm whose classification is not known for
all possible inputs.
Consider the following algorithm:
1. input n
2. print n
3. if n = 1 then STOP
4. if n is odd then n <- 3n + 1
5. else n <- n / 2
6. GOTO 2
Given the input 22, the following sequence of numbers will be printed 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
It is conjectured that the algorithm above will terminate (when a 1 is printed) for any integral input value. Despite the simplicity of the algorithm, it is unknown whether this conjecture is true. It has been verified, however, for all integers n such that
0 < n < 1,000,000 (and, in fact, for many more numbers than this.)
Given an input n, it is possible to determine the number of numbers printed (including the 1). For a given n this is called the cycle-length of n. In the example above, the cycle length of 22 is 16.
For any two numbers i and j you are to determine the maximum cycle length over all numbers between i and j.
Input
The input will consist of a series of pairs of integers i and j, one pair of integers per line. All integers will be less than 1,000,000 and greater than 0.
You should process all pairs of integers and for each pair determine the maximum cycle length over all integers between and including i and j.
You can assume that no opperation overflows a 32-bit integer.
Output
For each pair of input integers i and j you should output i, j, and the maximum cycle length for integers between and including i and j. These three numbers should be separated by at least one space with all three numbers on one line
and with one line of output for each line of input. The integers i and j must appear in the output in the same order in which they appeared in the input and should be followed by the maximum cycle length (on the same line).
Sample Input
1 10
100 200
201 210
900 1000
Sample Output
1 10 20
100 200 125
201 210 89
900 1000 174
so easy
解法 输入两个数(先判断大小 )然后按照题意做啦
![](http://static.blog.csdn.net/xheditor/xheditor_emot/default/laugh.gif)
上代码
#include <iostream>
#include <cmath>
using namespace std;
int main()
{
int a,b,c,n,x=0;
while(cin>>a>>b)
{
cout<<a<<" "<<b;
if(a>b)
{
swap(a,b);
}
x=0;
for(int i=a; i<=b; i++)
{
n=i;
c=1;
while(n!=1)
{
if(n%2==0)
{
n=n/2;
c++;
}
else
{
n=3*n+1;
c++;
}
if(x<c)
{
x=c;
}
}
}
cout<<" "<<x<<endl;
}
return 0;
}
相关文章推荐
- Spring Cache抽象详解
- Ubuntu系统vi编辑器上下左右键变ABCD的解决方法
- 线性代数(高斯消元):JSOI2008 球形空间产生器sphere
- 通过demo搞懂encode_utf8和decode_utf8
- 通过demo搞懂encode_utf8和decode_utf8
- 编程之美 - 只考加法的算术题
- 郁闷的C小加(三)
- centos7重启apache、nginx、mysql、php-fpm命令
- python 获取 中国证券网 的公告
- Java单元测试(Junit+Mock+代码覆盖率)
- Fedora 23如何安装LAMP服务器
- HDU 4987(概率dp)
- html网页中显示浏览器标题栏小图标
- Mock方法介绍
- SQL Server对文件访问的权限
- lseek详解
- 图文详解mybatis+postgresql平台搭建步骤
- java代码中调用js
- 虚拟机网络不通:
- 一些 Android 重要知识点解析整理