Mark's cakewalk

Problem Description

Marc loves cupcakes, but he also likes to stay fit.
Each cupcake has a certain calorie count, and Marc can burn those calories by walking.

If Marc has already eaten j cupcakes and eats a new one with c calories,
he must walk at least: $2^j\times c$ miles to maintain his weight.

Marc can eat the cupcakes in any order.
Your goal is to find the minimum total distance (in miles) he must walk.

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Example

Suppose the calorie values are:

[1, 3, 2]

If Marc eats them in this order (3, 2, 1):

Order	Calories	Miles to walk (2^j × c)	Total so far
1	3	2^0 × 3 = 3	3
2	2	2^1 × 2 = 4	7
3	1	2^2 × 1 = 4	11

✅ Minimum total miles = 11

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Function Description

Write the function:

def marcsCakewalk(calorie: list[int]) -> int:

The function should:

• Take a list of calorie values.
• Return the minimum total miles Marc needs to walk.

Hint.

• use max() Python function to find the maximum value in a list
• list.index(<value>) to find the index of an element given its value in a list
• list.pop(<index>) to remove an element from a list given its index

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Sample Input 1

[1, 3, 2]

Sample Output 1

11

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Sample Input 2

[7, 4, 9, 6]

Sample Output 2

79

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Guided Steps

1. Understand the formula.
   For each cupcake i (in the chosen order), Marc walks 2^j * calorie[i] miles,
   where j is the number of cupcakes already eaten.
   Try computing it for a few small examples.

2. Write pseudocode. Before writing the code, write the pseudocode implementing the following logic:

   • Think about how the order of eating affects the total.

   • To make 2^j * calorie[i] small, should Marc eat the largest or smallest cupcakes first?

   • Keep a variable to track the total miles.
     Initialize it properly, e.g. total = 0.

3. Implement and test.
   Translate your plan into Python.
   Use the sample inputs to check if your result matches the expected outputs.