Pentomino Solution & Patchwork

# Load required libraries
library(tidyverse)    # Data wrangling and general utilities
library(ggraph)       # Graph visualization
library(tidygraph)    # Graph data structure (tbl_graph) + graph algorithms
library(ggforce)      # Extra geoms for ggplot2
library(cowplot)      # Additional plotting helpers
library(patchwork)    # Combine multiple ggplots effortlessly!

### Read solution data frame from Github 
pento_sol <- read_csv("https://raw.githubusercontent.com/chichacha/pentomino/refs/heads/main/pentomino_solution.csv")

sample_n(pento_sol, size=5) |>
  knitr::kable("markdown")

# Just Prepping some color palette
retro <-  c("#00A0B0", "#6A4A3C", "#CC333F", "#EB6841", "#EDC951")
retro12 <- colorRampPalette(retro)(12)
retro13 <- c(retro12,"#ffffff")

#Assigning names to each color allows direct mapping with scale_color_manual() or scale_fill_manual()
piece <- c("F","I","L","N","P","T","U","V","W","X","Y","Z")
names(retro12) <- piece
names(retro13) <- c(piece,".")

retro12 |> enframe() |>
  ggplot(aes(x=name,y=1)) +
  geom_tile(aes(fill=I(value))) +
  geom_text(aes(label=name), color="white",vjust=-0.5) +
  geom_text(aes(label=value), color="white",vjust=1, size=3) +
  theme_nothing()

### Convert Solution to XY position data frame
pento_sol_df <- pento_sol |>
  mutate(solution_num = row_number()) |>
  mutate(sol_text = str_split(sol_text, " ")) |>
  unnest(sol_text) |>
  group_by(solution_num) |>
  mutate(y = row_number()) |>
  ungroup() |>
  mutate(sol_text = str_split(sol_text, "")) |>
  unnest(sol_text) |>
  group_by(solution_num, y) |>
  mutate(x = row_number()) |>
  ungroup()


# Split the data into chunks programmatically
tables <- pento_sol_df |> 
  filter(dim == "5×3", sol_idx == 1) |>
  select(dim, sol_text, x, y) |>
  group_split(x)

pento_sol_df |> 
  filter(dim == "5×3", sol_idx %in% c(1:6)) |>
  mutate(sol_idx=if_else(sol_idx==1, str_c("1. See Table Below"), as.character(sol_idx))) |>
  ggplot(aes(x=x,y=y)) +
  geom_point(aes(color=sol_text),size=10) +
  geom_text(aes(label=sol_text), color="#fffff3") +
  scale_color_manual(values=retro12, guide="none") +
  theme_minimal() +
  facet_wrap(~sol_idx,ncol=6) +
  coord_fixed() +
  scale_x_continuous(expand=expansion(add=1)) +
  scale_y_continuous(expand=expansion(add=1))

pento_min <- pento_sol_df |>
  filter(sol_text != ".") |>  # exclude the "." cells
  select(x, y, sol_text, solution_num, dim) |>
  nest(.by = c(solution_num, dim))

df_to_graph <- function(data) {
  
  # cross join is expensive, but straightforward: 
  # generate all pairs of cells, then filter to pairs that are adjacent (Manhattan distance = 1).
  tmp <- data |>
    cross_join(data) |>
    filter((abs(x.x - x.y) + abs(y.x - y.y)) == 1) |>
    distinct()
  
  edges <- tmp |>
    transmute(
      from = paste(x.x, y.x, sol_text.x, sep = ","),
      to   = paste(x.y, y.y, sol_text.y, sep = ","),
      w    = if_else(sol_text.x == sol_text.y, 1, 0.1)
    )
  
  # Standardize from/to to avoid duplicate edges in undirected graph
  edges_unique <- edges %>%
    rowwise() %>%
    mutate(
      a = min(from, to),
      b = max(from, to)
    ) %>%
    ungroup() %>%
    distinct(a, b, .keep_all = TRUE) %>%
    select(-a, -b)
  
  graph <- tidygraph::as_tbl_graph(edges_unique, directed = FALSE)
  
  # Add node attributes
  graph <- graph |>
    mutate(
      x     = as.numeric(str_split_i(name, ",", 1)),
      y     = as.numeric(str_split_i(name, ",", 2)),
      piece = str_split_i(name, ",", 3)
    ) |>
    mutate(
      deg   = centrality_degree(weights = w),
      btwn  = centrality_betweenness(weights = w),
      sub_g = centrality_subgraph(),
      idx   = row_number()
    )
  
  return(graph)
}

plot_graph <- function(g) {
  g |>
    activate("nodes") |>
    mutate(comm = group_louvain(weights = w)) |>
    ggraph(layout = "manual", x = x, y = y) +
    
    # 1) Thicker edges for cells in the same piece
    geom_edge_link(
      lineend = "round", linejoin = "mitre", alpha = 0.8,
      aes(edge_color = .N()$piece[from], edge_width = I(if_else(w == 1, 7, w)))
    ) +
    
    # 2) Another edge layer (white dash) just as decoration
    geom_edge_link(
      lineend = "square", linejoin = "round", alpha = 0.8,
      aes(edge_width = I(w)), color = "#ffffff", linetype = 3
    ) +
    
    coord_fixed() +
    theme_nothing() +
    scale_edge_color_manual(values = retro12) +
    scale_x_continuous(expand = expansion(add = 1)) +
    scale_y_reverse(expand = expansion(add = 1))
  
}

indexes <- c(14369:15378) |> sample(size = 24)

list_of_plots <- indexes %>%
  map(~ {
    pento_min$data[[.x]] %>%
      df_to_graph() %>%
      plot_graph()
  })

wrap_plots(list_of_plots, ncol = 3) +
  plot_annotation(
    title = "Collection of Pentomino Solutions (5x12)",
    theme = theme(text = element_text(family = "Roboto Condensed"))
  ) +
  plot_layout()