The problem of computing means of subsets using indices of equal size is a common task in data analysis and statistics. It involves *splitting a dataset into equal-sized subsets based on some indexing variable and then computing the mean of each subset*. This type of operation is often used to summarize or aggregate data and can provide insight into the distribution of values across different groups or categories. The following are the approaches that can be taken to do this:

#### 1. Using "np.unique()" and "np.mean()":

The code functions as follows:

- Import the NumPy library, which provides support for arrays and mathematical operations on them.
- Generate an array of
`100`

random numbers between`0`

and`1`

. - Generate an array of
`100`

random integers between`0`

and`9`

. - Find the unique values in
`S`

and their corresponding indices. - Create an array of zeros with the same length as the number of unique values in
`S`

, to store the mean of`D`

values for each unique value. - Loop over each unique value in
`S`

. - Calculate the mean of the
`D`

values that correspond to the current unique value in`S`

, by using boolean indexing to select the`D`

values with the same index as the current unique value. - Print the mean of the
`D`

values for each unique value in`S`

.

Using this code allows for efficient calculation of means for unique values in an array, but it may not be the most concise or intuitive approach.

#### 2. Using "np.reduceat()" and "np.concatenate()":

The code functions as follows:

- Imports the NumPy library, which provides support for arrays and mathematical operations on them.
- Generate an array of
`100`

random numbers between`0`

and`1`

. - Generate an array of
`100`

random integers between`0`

and`9`

. - Count the number of occurrences of each value in
`S`

. - Find the unique values in
`S`

and their corresponding indices. - Sum the
`D`

values for each group of unique values in`S`

, by first calculating the cumulative sum of the group counts and using it to slice the`D`

array. - Calculate the mean of the
`D`

values for each group of unique values in`S`

. - Print the mean of the
`D`

values for each group of unique values in`S`

.

The merit of this code is that it uses NumPy’s built-in functions to efficiently calculate the mean of the values in array D for each group of unique values in array S. However, a potential demerit is that the code may be difficult to understand for someone not familiar with NumPy’s syntax and functions.

#### 3. Using "np.bincount()" and "np.arange()":

The code functions as follows:

- The code imports the NumPy library as
`np`

. - An array
`D`

is generated using NumPy’s`random.uniform()`

function, which generates 100 random numbers between 0 and 1. - Another array
`S`

is generated using NumPy’s`random.randint()`

function, which generates 100 random integers between 0 and 9. - NumPy’s
`bincount()`

function is used on the array`S`

to count the number of occurrences of each value in the array. - NumPy’s
`unique`

function is used on the array`S`

to find the unique values in the array and their corresponding indices. - NumPy’s
`add.reduceat()`

function is used to sum the values in the array`D`

for each group of unique values in the array`S`

. - The mean of the values in the array
`D`

for each group of unique values in the array`S`

is calculated using a loop that checks for a zero count before dividing by the count. - The means are stored in an array called
`D_means`

. - Finally, the means are printed to the console using the
`print()`

function.

The merit of this code is that it efficiently calculates the mean of the D values for each unique value in S using NumPy functions, while the demerit is that the code may be difficult to understand for those unfamiliar with NumPy.