Link to challenge on Advent of Code 2021 website

## Loading the data

The number is again, comma-separated, so `np.loadtxt()`

does the job

```
from numpy import np
pos = np.loadtxt("day_7.txt", delimiter=",")
```

## Part 1

So....this is where I cheat. I'd like to get the job done quickly and go about my day. Python has some great libraries for data science, like `scipy`

which has a nice selection of optimizers. We can use one of them.

The problem boils down to an optimization problem where we are to minimize the distance between a collection of 1D points and some target point. We're trying to minimize the sum of `target - position`

for each of the points.

```
from scipy.optimize import minimize_scalar
res = minimize_scalar(lambda x: np.abs(round(x)-pos).sum())
```

Job done.

## Part 2

Part 2 tells us the cost function isn't linear `target - position`

but is triangle numbers `n(n+1)`

so we simply adjust our cost function accordingly:

```
res = minimize_scalar(lambda x: (np.abs(round(x)-pos)*(np.abs(round(x)-pos)+1)/2).sum())
```

## Full Code

```
import numpy as np
from scipy.optimize import minimize_scalar
pos = np.loadtxt("day_7.txt", delimiter=",", dtype="int32")
res = minimize_scalar(lambda x: np.abs(round(x)-pos).sum())
print("Part 1 result:", round(res.fun))
res = minimize_scalar(lambda x: (np.abs(round(x)-pos)*(np.abs(round(x)-pos)+1)/2).sum())
print("Part 2 result:", round(res.fun))
```

## Discussion (0)