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Distance Formula

Manhattan Distance

**Manhattan Distance** is extremely similar to Euclidean distance. Rather than summing the squared difference between each dimension, we instead sum the absolute value of the difference between each dimension. It’s called Manhattan distance because it’s similar to how you might navigate when walking city blocks. If you’ve ever wondered “how many blocks will it take me to get from point A to point B”, you’ve computed the Manhattan distance.

The equation is shown below:

`$\mid a_1 - b_1 \mid + \mid a_2 - b_2 \mid + \ldots + \mid a_n - b_n \mid$`

Note that Manhattan distance will always be greater than or equal to Euclidean distance. Take a look at the image below visualizing Manhattan Distance:

`$d = \mid a_1 - b_1 \mid + \mid a_2 - b_2 \mid$`

Below `euclidean_distance()`

, create a function called `manhattan_distance()`

that takes two lists named `pt1`

and `pt2`

as parameters.

In the function, create a variable named `distance`

, set it equal to `0`

, and return it.

After defining `distance`

, create a `for`

loop to loop through the dimensions of each point.

Add the absolute value of the difference between each dimension to `distance`

.

Remember, in Python, you can take the absolute value of `num`

by using `abs(num)`

You’re done with `manhattan_distance()`

! Go ahead and find the Manhattan distance between the same points as last time.

Below the print statements for Euclidean distance, print the Manhattan distance between `[1, 2]`

and `[4, 0]`

.

Also print the Manhattan distance between `[5, 4, 3]`

and `[1, 7, 9]`

.