Analisis De Algoritmos
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Publicado: 21 de abril de 2012
1.6. Problems
15
1.6 Problems
1.6.1 The 3n + 1 Problem
PC/UVa IDs: 110101/100, Popularity: A, Success rate: low Level: 1 Consider the followingalgorithm to generate a sequence of numbers. Start with an integer n. If n is even, divide by 2. If n is odd, multiply by 3 and add 1. Repeat this process withthe new value of n, terminating when n = 1. For example, the following sequence of numbers will be generated for n = 22: 22 11 34 17 52 26 13 40 20 10 5 168 4 2 1 It is conjectured (but not yet proven) that this algorithm will terminate at n = 1 for every integer n. Still, the conjecture holds for allintegers up to at least 1, 000, 000. For an input n, the cycle-length of n is the number of numbers generated up to and including the 1. In the example above, thecycle length of 22 is 16. Given any two numbers i and j, you are to determine the maximum cycle length over all numbers between i and j, including bothendpoints.
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 1,000,000and greater than 0.
Output
For each pair of input integers i and j, output i, j in the same order in which they appeared in the input and then the maximumcycle length for integers between and including i and j. These three numbers should be separated by one space, with all three numbers on one line and withone line of output for each line of input.
Sample Input
1 10 100 200 201 210 900 1000
Sample Output
1 10 20 100 200 125 201 210 89 900 1000 174
15
1.6 Problems
1.6.1 The 3n + 1 Problem
PC/UVa IDs: 110101/100, Popularity: A, Success rate: low Level: 1 Consider the followingalgorithm to generate a sequence of numbers. Start with an integer n. If n is even, divide by 2. If n is odd, multiply by 3 and add 1. Repeat this process withthe new value of n, terminating when n = 1. For example, the following sequence of numbers will be generated for n = 22: 22 11 34 17 52 26 13 40 20 10 5 168 4 2 1 It is conjectured (but not yet proven) that this algorithm will terminate at n = 1 for every integer n. Still, the conjecture holds for allintegers up to at least 1, 000, 000. For an input n, the cycle-length of n is the number of numbers generated up to and including the 1. In the example above, thecycle length of 22 is 16. Given any two numbers i and j, you are to determine the maximum cycle length over all numbers between i and j, including bothendpoints.
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 1,000,000and greater than 0.
Output
For each pair of input integers i and j, output i, j in the same order in which they appeared in the input and then the maximumcycle length for integers between and including i and j. These three numbers should be separated by one space, with all three numbers on one line and withone line of output for each line of input.
Sample Input
1 10 100 200 201 210 900 1000
Sample Output
1 10 20 100 200 125 201 210 89 900 1000 174
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