UVa 944
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[edit] 944 - Happy Numbers
[edit] Summary
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.
[edit] Explanation
Instructions are clear. If you start with S0 = 7
S0 = 7
S1 = 72 = 49
S2 = 42 + 92 = 97
S3 = 92 + 72 = 130
S4 = 12 + 32 = 10
S5 = 12 = 1
If you reach 1 then S0 is Happy else it's Unhappy!
[edit] Gotcha's
- S0 is unhappy when you meet a Si again and it means a loop, so it never meets 1.
- ``if S0 is happy (unhappy), then any number in the sequence S1,S2,S3,... will also be happy (unhappy) , attention , if you know Si is happy (unhappy) don’t waste time and terminate it because the rest of sequence will be happy (unhappy).
- the number of iterations for S0 ,if you meet a happy number in the sequence (Si), simply add the size of current sequence to the number of iterations for Si , then S1 = ( the number of iterations for S0) - 1 and so on.
[edit] Input
7 10 1 7 10 4 10 10 1 1 99970 99999
[edit] Output
7 6 10 2 1 1 7 6 10 2 1 1 99971 7 99973 4 99978 8 99987 8
