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UVA 100

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UVA 100 - The 3n + 1 problem

The 3n + 1 problem

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 morenumbers than this.)

Given an input n, it is possible to determine the number of numbers printed before and including the 1 is printed. 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 and including both 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 10,000 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 operation 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).

範例:

input:

1
2
3
4
1 10
100 200
201 210
900 1000

output:

1
2
3
4
1 10 20
100 200 125
201 210 89
900 1000 174

題意:

就在i到j之間經過上面的演算法做一串數列計算它的長度取其中的最大值。

思路:

把循環的演算法先寫出來回傳它的長度，在i到j的數計算每個數進入演算法重複的次數，取最大的一個，把i，j和最大的數印出。

程式碼: