Python Language:Number Grouping ProgramExample: separate (([10, 12, 45, 47, 91, 98, 99]), 3)It should return [[10, 12], [45, 47], [91, 98, 99]]. How can we automatically split seemingly-random data points into meaningful groups? For example,consider the heights of 20 people (in cm) presented in the ascending order:71.4, 72.73, 74.36, 75. 38, 76.15, 76.96, 79.51, 86.82, 87.81, 87.87, 146.38, 150.89,151.16, 152.18, 152.36, 153.27, 155.7, 160.99, 161.36, 164.55Say we happen to know that there are two age groups in this population-kids and adults. How can wetell them apart? It may not be clear at first glance, but plotting this reveals an interesting trend:With the plot, it is visually trivial to split this dataset into two groups: there is a big gap in the mid-dle, separating the heights into two logical sides. The more involved question-and the basis for thisproblem-is, how can we discover thisgap automatically?Answering this and similar questions has been a topic of extensive research, fueled by real-world prob-lems ranging from deciding letter grades to giving suggestions on Facebook (e.g., who are your closefriends?). What we did in our brain was essentially locating the widest gap visually. This makes intuitive andmathematical sense because the widest gap is where our data points are the most dissimilar.Generalizing this idea gives us a simple heuristic that often works okay on real data. Say we want toidentify k groups. We can proceed as follows:Step 1: Find the largest gap in the data.Step 2: Split the data at that point.This gives us 2 groups. To further split the data, we find the largest gap that hasn't been split and splitit there. This gives us one more group. We can repeat this process until we get k groups.Let us illustrate this idea with a simple example. Suppose k = 3 and our input is the following numbers:10, 12,45, 47,91,98,99.They look as follows in plot:As before, we assume the input is sorted from small to large. And we wish to split it into k = 3To begin, we'll treat the input as one big group:groups.[10,12,45,47,91,98,99]Then, we look for the largest gap between two consecutive elements. In this example, the largest gap isin between 47 and 91 (you can check that). That is where we want to split. After that, the list becomes:[10,12,45, 47] [91,98,99]Next, we find the largest gap between two successive elements in all groups. This time, the largest gapis in the first group (to know this, we'll have to check the other group, to0). The overall largest gap isbetween 12 and 45. Hence, we further split it there, leading to the following groups (illustration onright):[10,12] [45,47) [91,98,99]Group 1Group 2Group 3We now have 3 groups, so we can stop and output them.REMARKS: Mathematically, this process partitions a list into k sublists so that the total gap-the sumof all gaps-between sublists is maximized. It makes sense intuitively and aligns with out intuition thatdifferent groups should be dissimilar, so the process attempts to maximize how different they are.YOUR TASK:You will write a functionseparate(data: list[int], k: int) - list[list[int]]that partitions data into k sublists that maximize dissimilarity using the process described above.Importantly: for this task, your implementation must find the largest gap and split the dataset at thegap, repeating this process until you have k groups. If there are ties, pick the left-most gap. To keepthings simple, we will assume that the input list is always ordered from small to large.Hence, for example,separate([10, 12, 45, 47, 91, 98, 99], 3)should return[10, 12], [45, 47], [91, 98, 99]].

Question

Python Language:Number Grouping ProgramExample: separate (([10, 12, 45, 47, 91, 98, 99]), 3)It should return [[10, 12], [45, 47], [91, 98, 99]]. How can we automatically split seemingly-random data points into meaningful groups? For example,consider the heights of 20 people (in cm) presented in the ascending order:71.4, 72.73, 74.36, 75. 38, 76.15, 76.96, 79.51, 86.82, 87.81, 87.87, 146.38, 150.89,151.16, 152.18, 152.36, 153.27, 155.7, 160.99, 161.36, 164.55Say we happen to know that there are two age groups in this population-kids and adults. How can wetell them apart? It may not be clear at first glance, but plotting this reveals an interesting trend:With the plot, it is visually trivial to split this dataset into two groups: there is a big gap in the mid-dle, separating the heights into two logical sides. The more involved question-and the basis for thisproblem-is, how can we discover thisgap automatically?Answering this and similar questions has been a topic of extensive research, fueled by real-world prob-lems ranging from deciding letter grades to giving suggestions on Facebook (e.g., who are your closefriends?). What we did in our brain was essentially locating the widest gap visually. This makes intuitive andmathematical sense because the widest gap is where our data points are the most dissimilar.Generalizing this idea gives us a simple heuristic that often works okay on real data. Say we want toidentify k groups. We can proceed as follows:Step 1: Find the largest gap in the data.Step 2: Split the data at that point.This gives us 2 groups. To further split the data, we find the largest gap that hasn't been split and splitit there. This gives us one more group. We can repeat this process until we get k groups.Let us illustrate this idea with a simple example. Suppose k = 3 and our input is the following numbers:10, 12,45, 47,91,98,99.They look as follows in plot:As before, we assume the input is sorted from small to large. And we wish to split it into k = 3To begin, we'll treat the input as one big group:groups.[10,12,45,47,91,98,99]Then, we look for the largest gap between two consecutive elements. In this example, the largest gap isin between 47 and 91 (you can check that). That is where we want to split. After that, the list becomes:[10,12,45, 47] [91,98,99]Next, we find the largest gap between two successive elements in all groups. This time, the largest gapis in the first group (to know this, we'll have to check the other group, to0). The overall largest gap isbetween 12 and 45. Hence, we further split it there, leading to the following groups (illustration onright):[10,12] [45,47) [91,98,99]Group 1Group 2Group 3We now have 3 groups, so we can stop and output them.REMARKS: Mathematically, this process partitions a list into k sublists so that the total gap-the sumof all gaps-between sublists is maximized. It makes sense intuitively and aligns with out intuition thatdifferent groups should be dissimilar, so the process attempts to maximize how different they are.YOUR TASK:You will write a functionseparate(data: list[int], k: int) -> list[list[int]]that partitions data into k sublists that maximize dissimilarity using the process described above.Importantly: for this task, your implementation must find the largest gap and split the dataset at thegap, repeating this process until you have k groups. If there are ties, pick the left-most gap. To keepthings simple, we will assume that the input list is always ordered from small to large.Hence, for example,separate([10, 12, 45, 47, 91, 98, 99], 3)should return[10, 12], [45, 47], [91, 98, 99]].

Accepted Answer

python code

def separate(list, k):
    temp = None
    data = []
    for number in list:
        if…

Python Language: Number Grouping Program Example: separate (([10, 12, 45, 47, 91, 98, 99]), 3) It should return [[10, 12], [45, 47], [91, 98, 99]].