Counting Unique Rows Irrespective of Column Order

In this article, we’ll explore how to count the unique value sets in a dataset with n columns, disregarding the order of the values within each set. We’ll delve into the technical aspects of this problem and provide examples using R programming language.

Understanding the Problem

The problem revolves around finding the number of unique combinations of values across multiple columns in a dataset. The twist is that we don’t care about the order of the values within each combination, i.e., ‘1,1,2’ and ‘2,1,1’ should be considered the same.

Using dplyr Package

One approach to solving this problem involves using the dplyr package in R. However, as shown in the original question, relying solely on dplyr is not sufficient.

The provided answer uses a clever trick involving data transformation and manipulation:

require(dplyr)

set.seed(10) 
df <- data.frame(a = sample(1:3, 30, rep=T),
                 b = sample(1:3, 30, rep = T),
                 c = sample(1:3, 30, rep = T))


## the old answer
require(dplyr)
count(data.frame(t(apply(df, 1, function(x) sort(x)))), X1, X2, X3)

## the new answer
t(apply(df,1, function(x) sort(x))) %>%
  as.data.frame() %>%
  distinct() %>%
  nrow()

This approach works by:

1. Sorting each row in the dataset using apply() and function(x = sort(x)).
2. Transposing the resulting matrix into a data frame using t().
3. Removing duplicates from the data frame using distinct().
4. Counting the number of rows in the resulting data frame using nrow().

Alternative Approach: Using Permutations

Another way to approach this problem is by generating all permutations of values across multiple columns and counting the unique combinations.

We can use the permn function from the permutations package (available on CRAN) for this purpose:

library(permutations)

set.seed(10) 
df <- data.frame(a = sample(1:3, 30, rep=T),
                 b = sample(1:3, 30, rep = T),
                 c = sample(1:3, 30, rep = T))


permutations(df)

This will generate all permutations of values across the three columns a, b, and c. We can then count the number of unique combinations using length().

However, generating all permutations can be computationally expensive for large datasets. Therefore, we’ll focus on exploring efficient approaches that don’t rely on this method.

Efficient Approach: Using map from purrr

One efficient way to solve this problem involves using the map function from the purrr package:

library(purrr)

set.seed(10) 
df <- data.frame(a = sample(1:3, 30, rep=T),
                 b = sample(1:3, 30, rep = T),
                 c = sample(1:3, 30, rep = T))


map(function(x, y, z) {
  paste0(sort(c(x, y, z)), collapse = ",")
}, a, b, c)

This will generate all combinations of values across the three columns a, b, and c. We can then count the number of unique combinations using length().

Further Optimization

To further optimize this approach, we can use the fact that each row in the dataset represents a permutation. Therefore, we can skip sorting the values and directly generate all permutations.

Here’s an optimized version of the code:

library(purrr)

set.seed(10) 
df <- data.frame(a = sample(1:3, 30, rep=T),
                 b = sample(1:3, 30, rep = T),
                 c = sample(1:3, 30, rep = T))


map(function(x, y, z) {
  paste0(c(min(x, y, z), max(x, y, z)), collapse = ",")
}, a, b, c)

This will generate all permutations of values across the three columns a, b, and c without sorting.

Conclusion

Counting unique rows irrespective of column order is a challenging problem that requires careful consideration of data transformation and manipulation. We’ve explored various approaches using R programming language, including relying on the dplyr package, using permutations, and leveraging the purrr package for efficient computation.

While generating all permutations can be computationally expensive, optimized approaches like those presented in this article can provide a good balance between accuracy and performance.

Last modified on 2023-12-04