hdu 1032 The 3n + 1 problem
2016-04-06 11:49
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The 3n + 1 problem
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 32980 Accepted Submission(s):
11928
[align=left]Problem Description[/align]
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.
[align=left]Input[/align]
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.
[align=left]Output[/align]
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).
[align=left]Sample Input[/align]
1 10
100 200
201 210
900 1000
[align=left]Sample Output[/align]
1 10 20
100 200 125
201 210 89
900 1000 174
[align=left]Source[/align]
UVA
[align=left]Recommend[/align]
mcqsmall | We have carefully selected several
similar problems for you: 1048 1062 1056 1073 1038
简单题,直接暴力就可以了。
题意:输入两个数(注意,这里没有说第一个数一定要小与第二个数),然后对这两个数之间的所有整数包括端点的数,进行一种规律运算,并求出运算的次数,比较所有的数规律运算次数,输出最大的.
附上代码:
#include <iostream> #include <cstdio> #include <cstring> using namespace std; int main() { int a,b,i,j,n,m,t; while(~scanf("%d%d",&a,&b)) { printf("%d %d ",a,b); if(a>b) { t=a; a=b; b=t; } int max=0; for(i=a; i<=b; i++) { n=i; m=1; while(n!=1) { if(n%2) n=n*3+1; else n=n/2; m++; } if(max<m) max=m; } printf("%d\n",max); } return 0; }
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