For example, suppose there are 50 data points which need to be clustered into seven parts, in a way so that each cluster contains at least five and at most 10 data points.
I'm not aware of any implementation that clusters data according to the number of points.
I would suggest that you iteratively search and optimize the number of clusters to reach your desired goal.
The paper DOI: 10.1007/978-3-319-19644-2_22 has implemented this type of k-means clustering.
The maximum possible number of clusters will be equal to the number of observations in the dataset.
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