47 lines
1.6 KiB
Markdown
47 lines
1.6 KiB
Markdown
# Funny plant
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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.
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Now you need to calculate after how many weeks, you can support a group of x people, given y fruits to start with.
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## Input Description
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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.
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## Output Description
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The number of weeks before you can feed the entire group of people.
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## Explanation
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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:
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```text
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Plant 1 2 3 4 5 6 7 8 9 10 11 12 13 Total # of fruits in a harvest
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Week
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1 0 - - - - - - - - - - - - 0
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2 1 0 - - - - - - - - - - - 1
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3 2 1 0 0 0 - - - - - - - - 3
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4 3 2 1 1 1 0 0 0 0 0 0 0 0 8
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5 4 3 2 2 2 1 1 1 1 1 1 1 1 21
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```
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At week 1 we have 1 plant giving 0 fruits, because it has just been planted.
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When week 2 comes along we have 1 plant that gives off a fruit and then we use that fruit to plant plant 2.
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Then in week 3 we have 2 fruits from plant 1, 1 from plant 2, so we can plant 3 new plants.
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## Examples
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```text
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input: 200, 15
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output: 5
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input: 50000, 1
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output: 14
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input: 150000, 250
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output: 9
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```
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