Bacterial Colony Growth

A microbiologist is monitoring the evolution of a bacterial colony inside a controlled environment.
This time, the colony’s growth depends on both multiplication and decay effects happening simultaneously.

The growth rule is now:

• The colony grows proportionally to twice yesterday’s population

• …but also loses a fraction tied to the population from two days ago

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Problem Description

Given three integers p1, p2, and n, representing the number of bacteria on day 1, day 2, and the day to predict, compute the population on day n according to the rule:

$p_n=2\cdot p_{n-1}-p_{n-2}$

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Example

Input

3 5 6

Output

21

Explanation

Day 1: p1 = 3  
Day 2: p2 = 5  
Day 3: p3 = 2*5 - 3 = 7  
Day 4: p4 = 2*7 - 5 = 9  
Day 5: p5 = 2*9 - 7 = 11  
Day 6: p6 = 2*11 - 9 = 13  

So on day 6, the colony contains 13 bacteria.

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Function Description

Implement the following function:

def bacteriaGrowth(p1: int, p2: int, n: int) -> int:
    # Write your code here

Parameters

• p1: bacteria count on day 1
• p2: bacteria count on day 2
• n: the day to compute

Returns

• int: population on day n

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Modeling Hint

Before coding, identify:

1. What type of recurrence this is and whether you prefer recursion or iteration
2. Which base cases correspond to days 1 and 2
3. How each step depends on the previous two populations