# 5 Best Ways to Find the Minimum Cost to Purchase All Items in Python

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π‘ Problem Formulation: Imagine you are given a list of prices for various items at a store and you want to find out the minimum cost required to purchase every item on your list once. The input could be a list of integers representing the prices, and the desired output is a single integer representing the minimum total cost.

## Method 1: Using a Simple Loop

This method involves iterating through the list of item prices using a loop and summing up all the values. The function `calculate_total_cost` is straightforward and efficient for small lists, providing a clear and concise understanding of the total cost calculation.

Here’s an example:

```def calculate_total_cost(prices):
total_cost = 0
for price in prices:
total_cost += price

prices = [5, 20, 9, 15]
print(calculate_total_cost(prices))
```

Output:

```49
```

This snippet defines a function `calculate_total_cost` which takes a list of prices and returns their sum. It works by initializing a total cost variable and then adding up each price in the list to it. Finally, the total cost is returned.

## Method 2: Using Python’s Built-in `sum()` Function

Python provides a built-in function `sum()` that can be used to add all elements in an iterable. This approach is more Pythonic, requires less code, and is usually faster than manual looping for larger datasets.

Here’s an example:

```prices = [5, 20, 9, 15]
total_cost = sum(prices)
print(total_cost)
```

Output:

```49
```

The example shows an elegant way to calculate the total cost by utilizing the `sum` function on the list of prices directly, without the need for defining a custom function.

## Method 3: Using List Comprehension

List comprehension can be used for more complex cases where you may want to apply conditions or transformations to the prices before summing them. This method is compact, and the expression inside the comprehension can be adjusted as needed.

Here’s an example:

```prices = [5, 20, 9, 15]
total_cost = sum([price for price in prices])
print(total_cost)
```

Output:

```49
```

In this code, list comprehension is used for demonstrating the process of iterating over each item. Even though there’s no additional condition or transformation here, this method would be useful when such changes are needed before adding the prices.

## Method 4: Using the `reduce()` Function

The `reduce()` function from the `functools` module is a powerful tool for applying a specific function cumulatively to the items of a list, from left to right. It can be used for summing up the prices in a more functional programming style.

Here’s an example:

```from functools import reduce

prices = [5, 20, 9, 15]
total_cost = reduce(lambda x, y: x + y, prices)
print(total_cost)
```

Output:

```49
```

This snippet uses `reduce()` with a lambda function that adds two arguments together. Applied consecutively across the list of prices, reduce effectively sums all the prices to give the total cost.

## Bonus One-Liner Method 5: Using NumPy

For large datasets, NumPy’s array operations can significantly speed up mathematical computations. By turning the list of prices into a NumPy array, one can leverage optimized array operations to find the sum.

Here’s an example:

```import numpy as np

prices = np.array([5, 20, 9, 15])
total_cost = np.sum(prices)
print(total_cost)
```

Output:

```49
```

Here, `np.sum` computes the sum of the NumPy array `prices`. This method is highly efficient for large arrays and demonstrates the benefit of using NumPy for numerical computations.

## Summary/Discussion

• Method 1: Simple Loop. Straightforward. Leaves room for additional logic. However, it is verbose and not the most Pythonic.
• Method 2: Python’s Built-in `sum()` Function. Clean and concise. Efficient and Pythonic. Lacks flexibility for conditional summing.
• Method 3: List Comprehension. Versatile and compact. Ideal for conditional summing or transformations. Slightly more complex than using `sum()` directly.
• Method 4: `reduce()` Function. Functional programming approach. Flexible and powerful. May be less intuitive for those not familiar with functional concepts.
• Bonus One-Liner Method 5: Using NumPy. Highly efficient for large datasets. Requires an additional library. Overhead for small datasets.