Time Complexity of dplyr functions

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The time complexity of basic dplyr functions like filter(), select(), mutate(), rename(), summarize(), count(), separate(), unite(), spread(), and gather() is generally considered O(N), where N is the number of rows in the data frame. Assuming mutate operates in O(1), this holds true for single data frames. For operations involving two data frames, such as inner_join, left_join, and outer_join, the time complexity is O(N + M), where N and M are the row counts of the respective data frames. This reflects the need to process both data frames during the join operations. Understanding these complexities is crucial for optimizing data manipulation tasks in R using dplyr.
Trollfaz
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For R's dplyr package this is my query.
Suppose I have a data frame/tibble of n observations or n rows. Let's call it df1. Is the time complexity for dplyr's basic manipulation functions O(N)
filter()
select()
mutate() assuming mutate is O(1)
rename()
summarize()
count()
separate()
unite()
spread()
gather()
If I have another data frame/tibble df2 of m rows, then are the following functions of time complexity O(N+M)
inner_join(df1,df2)
right/left_join(df1,df2)
outer_join(df1,df2)
 
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