Finding all the combinations of k elements among n columns in tidyverse

Introduction

The problem at hand is to find all possible combinations of k players from a set of n players. In this context, we are dealing with data where each player has multiple roles or positions represented by distinct letters (e.g., A, B, C). We need to compute stats for basketball lineups given the play-by-play data.

Given the dataframe structure and requirements outlined in the question, we’ll explore possible solutions using tidyverse functions. The primary goal is to avoid manual self-joins when feasible and leverage existing functions within tidyverse to achieve this task efficiently.

Prerequisites

To solve this problem, you need:

1. Familiarity with tidyverse packages, specifically dplyr, tidyr, and purrr.
2. Knowledge of base R’s combn function.
3. Understanding of data manipulation concepts (e.g., grouping, joining, reshaping).

Background

The original solution provided involves using apply(across), combn, and other tidyverse functions to generate combinations of player positions (p_comb1 and p_comb2). While this approach works, it may not be the most efficient or elegant way to solve this problem.

To improve upon the original solution, we’ll explore alternative approaches that utilize built-in functions in tidyverse more effectively.

Problem Breakdown

We can break down the problem into three key steps:

1. Group by game_id and action_id: Ensure that all combinations are within the same group.
2. Generate combinations of player positions: Use an efficient method to generate all possible combinations of k players from n.
3. Unnest and unpack the results: Combine the generated combinations into a single, long format for easy analysis.

Solution Overview

Our approach will involve using tidyverse functions to streamline the process:

1. Group by game_id and action_id columns.
2. Generate combinations of player positions using a built-in function or an efficient base R method.
3. Unnest and unpack the results into a long format.

Step 1: Group by game_id and action_id

To ensure that all combinations are within the same group, we first need to group our data by these two columns.

# Load necessary libraries
library(tidyverse)

# Create sample dataframe (inplace)
df %>% 
  mutate(comb = apply(across(num_range('p', 1:5)), 1, function(x) as.data.frame(t(combn(x, 2))))) %>%
  unnest_longer(comb) %>%
  unpack(comb)

# Group by game_id and action_id
df %>% 
  group_by(game_id, action_id)

Step 2: Generate Combinations of Player Positions

To generate all possible combinations of k players from n, we can use a combination of base R’s combn function and the purrr package. We’ll also consider using across from tidyverse to simplify the process.

# Define variables for k and n
k <- 2  # Number of positions to combine
n <- 5  # Total number of player positions

# Generate combinations using combn and purrr
combinations <- map2(k, n, function(k_value, n_value) {
  combn(n_value, k_value)
}) %>% 
  unlist() %>% 
  unique()

# Convert the result to a data frame for easy manipulation
combination_df <- as.data.frame(combinations)

Step 3: Unnest and Pack the Results

Now that we have all possible combinations of k players from n, we need to nest these combinations into our original dataframe.

# Nest combinations into the original dataframe
df %>% 
  group_by(game_id, action_id) %>%
  mutate(
    p_comb1 = map(combinations, ~first),
    p_comb2 = map(combinations, ~last)
  )

Alternative Approach

The above solution leverages base R functions to generate combinations and tidyverse functions for data manipulation. However, there is another approach that uses across from tidyverse to simplify the process.

# Define a function to generate combinations of player positions
generate_combinations <- function(df, k) {
  df %>% 
    group_by(game_id, action_id) %&gt;%
    mutate(
      comb = map(across(num_range('p', 1:5)), 1, function(x) combn(x, k)),
      p_comb1 = map(combinations, ~first),
      p_comb2 = map(combinations, ~last)
    )
}

# Create a sample dataframe
df <- tibble(
  game_id = c("G1", "G1", "G1"),
  action_id = c(1, 2, 1),
  team_id = c("H", "V", "H"),
  event = c("3PA", "REB", "3PA"),
  p1 = c("A", "A", "A"),
  p2 = c("B", "B", "C"),
  p3 = c("D", "E", "F"),
  p4 = c("G", "H", "I"),
  p5 = c("J", "K", "L")
)

# Generate combinations of player positions using generate_combinations
df %>% 
  mutate(comb = map(across(num_range('p', 1:5)), 1, function(x) as.data.frame(t(combn(x, 2))))) %&gt;%
  unnest_longer(comb) %&gt;%
  unpack(comb)

Conclusion

This article presented a solution to finding all combinations of k elements among n columns in tidyverse. We explored two approaches: one using base R functions for combination generation and another utilizing tidyverse functions, particularly across, for simplifying the process.

Both methods aim to provide an efficient way to generate combinations while ensuring that they are within the same group, as specified in the problem statement.

In conclusion, understanding how to leverage tidyverse packages effectively can significantly streamline data manipulation tasks. By applying these principles and exploring alternative approaches, you can develop robust solutions for complex problems like this one.

Last modified on 2023-07-16