UVa 944

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944 - Happy Numbers[edit]

Summary[edit]

Read 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). 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 of squares to reach 1.

Explanation[edit]

Instructions are clear. If you start with S_{0}=7

S_{0}=7

S_{1}=7^{2}=49

S_{2}=4^{2}+9^{2}=97

S_{3}=9^{2}+7^{2}=130

S_{4}=1^{2}+3^{2}=10

S_{5}=1^{2}=1


If you reach 1 then S_{0} is Happy else it's Unhappy!

Gotcha's[edit]

  • S_{0} is unhappy when you meet a S_{i} again and it means a loop, so it never meets 1.
  • ``if S_{0} is happy (unhappy), then any number in the sequence S_{1},S_{2},S_{3},... will also be happy (unhappy) , attention , if you know S_{i} is happy (unhappy) don’t waste time and terminate it because the rest of sequence will be happy (unhappy).
  • the number of iterations for S_{0} ,if you meet a happy number in the sequence (S_{i}), simply add the size of current sequence to the number of iterations for S_{i} , then S_{1} = ( the number of iterations for S_{0}) - 1 and so on.

Input[edit]

7 10
1 7
10 4
10 10
1 1
99970 99999

Output[edit]

7 6
10 2

1 1
7 6

10 2

1 1

99971 7
99973 4
99978 8
99987 8