HPYNOS - Happy Numbers I
The process of “breaking” an integer is defined as summing the squares of its digits. For example, the result of breaking the integer 125 is (12 + 22 + 52) = 30. An integer N is happy if after “breaking” it repeatedly the result reaches 1. If the result never reaches 1 no matter how many times the “breaking” is repeated, then N is not a happy number.
TASK
Write a program that given an integer N, determines whether it is a happy number or not.
CONSTRAINTS
2 ≤ N ≤ 2,147,483,647
Input
A single line containing a single integer N.
Output
A single line containing a single integer T which is the number of times the process had to be done to determine that N is happy, or -1 if N is not happy.
Example
Input: 19 Output: 4
1) 19 : 12 + 92 = 82 2) 82 : 82 + 22 = 68 3) 68 : 62 + 82 = 100 4) 100 : 12 + 02 + 02 = 1
The solution is 4 because we discovered that the integer 19 is happy after we repeated the process 4 times.
Input: 204 Output: -1
204 –> 20 –> 4 –> 16 –> 37 –> 58 –> 89 –> 145 –> 42 –> 20 –> 4 –> 16 –> 37 –> 58 –> 89 –> 145 ……
204 is not a happy number because after breaking it several times the results start repeating so we can deduce that if we continue breaking it, the result will never reach 1.
Number of input files is 32.
Don't use pre-calculated values (Don't Cheat)!!!
hide comments
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jayeshd:
2017-09-08 20:42:23
The theoretical maxima of a loop length will be very less and can be a good problem in itself (given N ≤ 2,147,483,647). The max sum of squares can be 1^2 + 81*9 = 730, in the next step the number would become even lesser. So we can be pretty sure that even if there is a loop its length will be in 3 digits. Though actually, the highest loop size is just 20 given N ≤ 2,147,483,647. Last edit: 2017-09-08 20:42:55 |
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addy1397:
2017-07-24 10:56:17
7 sucks ...right! |
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ramesh_961:
2017-06-04 14:04:09
can Learn Floyd's cycle detection!! Easy!! |
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akababa:
2017-04-26 07:25:00
How would you even use pre-calculated valuess... lol |
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visu27:
2017-03-23 10:21:21
easy one AC in one go |
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stark_attack:
2017-02-23 11:34:14
very easy , with just two loops .AC in first go ..... |
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cake_is_a_lie:
2017-02-11 00:37:59
Lots of ways to solve this, but for me the thought pattern was "if only I could easily find a bound on the number of iterations it might take to reach 1"... |
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aditya9125:
2016-12-30 11:17:27
Can be done without map or sets.Read few lines about happy numbers n you'll be able to figure out the rest. |
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avi892nash:
2016-12-27 20:23:09
How can we say that breaking the number would lead to a cycle or it become 1....is there is any case in which breaking of a number goes to infinity but 1 does not appear and cycle also not appear |
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nolex:
2016-12-13 01:51:46
Does output have to be in file or on console... If it is file, do I need one more scanf for file for output? Last edit: 2016-12-13 19:41:18 |
| Added by: | Rofael Emil |
| Date: | 2010-11-03 |
| Time limit: | 1s |
| Source limit: | 50000B |
| Memory limit: | 1536MB |
| Cluster: | Cube (Intel G860) |
| Languages: | All |
| Resource: | Egyptian Olympiad in Informatics ( EOI ) 2009, August 14 - 21, Cairo |
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