Happy

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  • Publicado : 17 de diciembre de 2011
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Happy Numbers
Let the sum of the squares of the digits of a positive integer s 0 be represented by s1. In a similar way, let the sum of the squares of the digits of s1 be represented by s2, and soon. If si=1 for some i>=1, then the original integer s0 is said to be happy. For example, starting with 7 gives the sequence 7,49(=7^2), 97 (=4^2+9^2), 130 (=9^2+7^2), 10 (=1^2+3^2), 1 (=1^2), so 7 isa happy number. The first few happy numbers are 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, .... The number of iterations i required for these to reach 1 are,respectively, 1,6,2,3,5,4,4,3,4,5,5,3, A number that is not happy is called unhappy. Once it is known whether a number is happy (unhappy), then any number in the sequence s1, s2, s3, ... will also be happy(unhappy). Unhappy numbers have eventually periodic sequences of si which do not reach 1 (e.g., 4, 16, 37, 58, 89, 145, 42, 20, 4, ...). Any permutation of the digits of a happy (unhappy) number mustalso be happy (unhappy). This follows from the fact that addition is commutative. Moreover, the product of a happy (unhappy) number by any power of ten is a happy (unhappy) number. Example: 58 is anunhappy number; then, so are 85, 580, 850, 508, 805, 5800, 5080, 5008, 8050, 8500, and so on. Problem Decide which numbers, in a given closed interval, are happy numbers. Input The input has n lineseach of them corresponding to a test case. Every line contains two positive integers between 1 and 99999 (inclusive) each; the first integer, L, is the low limit of the closed interval; the second one,H, is the high limit (L ≤ H). Output The output is composed of the happy numbers that lie in the interval [L,H], together with the number of iterations required for the corresponding sequences ofsquares to reach 1. There must be a line for each happy number containing the happy number followed by a space and the number of iterations required for the sequence of squares to reach 1. Print a blank...
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