HDU1032&Uva100 The 3n + 1 problem
2015-11-22 16:44
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Problem 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 possibleinputs.
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 andwith 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 水题,给出a,b,找到在这个范围包括两个端点中进行上述算法的循环最大长度; 因为a不一定小于b,所以先要进行一个比较交换,然后吧循环最大长度找到。 代码如下:#include <stdio.h> #include <stdlib.h> /* run this program using the console pauser or add your own getch, system("pause") or input loop */ int main(int argc, char *argv[]) { int a,b,i,c,max,t; while(scanf("%d%d",&a,&b)!=-1) { printf("%d %d ",a,b); if(a>b) { t=a;a=b;b=t; } max=0; for(t=a;t<=b;t++) { i=t;c=1; while(i!=1) { if(i%2!=0) i=3*i+1; else i=i/2; c++; } if(c>max) max=c; } printf("%d\n",max); } return 0; }
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