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2016-01-challenge: Funny plant

Challenge for the January 2016 meetup

Description Scientist have discovered a new plant. The fruit of the plant can feed 1 person for a whole week and best of all, the plant never dies. Fruits needs 1 week to grow, so each weak you can harvest it fruits. Also the plant gives 1 fruit more than the week before and to get more plants you need to plant a fruit.

Now you need to calculate after how many weeks, you can support a group of x people, given y fruits to start with.

Input

15 1

Output

5

Input description

The input gives you 2 positive integers x and y, being x the number of people needed to be fed and y the number of fruits you start with.

Output description

The number of weeks before you can feed the entire group of people. Explanation Here you have a table that shows the growth when starting with 1 fruit. It shows when the plant came into existence (is planted) and how may fruit it bears each week

  Plant   1  2  3  4  5  6  7  8  9 10 11 12 13    Total # of fruits in a harvest
Week
1       0  -  -  -  -  -  -  -  -  -  -  -  -     0
2       1  0  -  -  -  -  -  -  -  -  -  -  -     1
3       2  1  0  0  0  -  -  -  -  -  -  -  -     3
4       3  2  1  1  1  0  0  0  0  0  0  0  0     8
5       4  3  2  2  2  1  1  1  1  1  1  1  1    21  

At week 1 we have 1 plant giving 0 fruits, because it has just been planted.

When week 2 comes along we have 1 plant that gives off a fruit and then we use that fruit to plant plant 2.

Then in week 3 we have 2 fruits from plant 1, 1 from plant 2, so we can plant 3 new plants.

Challenge

Challenge Input

200 15

50000 1

150000 250

Challenge Output

5

14

9

TIP

Don't look beyond here if you don't want a tip!

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Look up Go generator pattern. Disclaimer: it might or might not be an idiomatic Go option for solving this.

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