{"id":86950,"date":"2021-05-07T12:26:29","date_gmt":"2021-05-07T16:26:29","guid":{"rendered":"https:\/\/ibkrcampus.com\/?p=86950"},"modified":"2022-11-21T09:47:27","modified_gmt":"2022-11-21T14:47:27","slug":"how-to-solve-sudoku-with-r-open-source-automation","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/how-to-solve-sudoku-with-r-open-source-automation\/","title":{"rendered":"How to Solve Sudoku with R – Open Source Automation"},"content":{"rendered":"\n

In this post we discuss how to write an R script to solve any Sudoku puzzle<\/a>. There are some R packages to handle this, but in our case, we\u2019ll write our own solution. For our purposes, we\u2019ll assume the input Sudoku is a 9\u00d79 grid. At the end result, each row, column, and 3\u00d73 box needs to contain exactly one of each integer 1 through 9.<\/p>\n\n\n\n

Learn more about data science by checking out the great curriculum at 365 Data Science!<\/a><\/em><\/p>\n\n\n\n

Step 0) Define a sample board<\/strong><\/h2>\n\n\n\n

Let\u2019s define a sample Sudoku board for testing. Empty cells will be represented as zeroes.<\/p>\n\n\n\n

\nboard <- matrix(
\n     c(0,0,0,0,0,6,0,0,0,
\n     0,9,5,7,0,0,3,0,0,
\n     4,0,0,0,9,2,0,0,5,
\n     7,6,4,0,0,0,0,0,3,
\n     0,0,0,0,0,0,0,0,0,
\n     2,0,0,0,0,0,9,7,1,
\n     5,0,0,2,1,0,0,0,9,
\n     0,0,7,0,0,5,4,8,0,
\n     0,0,0,8,0,0,0,0,0),

\n \n     byrow = T,
\n     ncol = 9
\n)\n<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Step 1) Find the empty cells<\/strong><\/h2>\n\n\n\n

In the first step, let\u2019s write a function that will find all of the empty cells on the board.<\/p>\n\n\n\n

\n     find_empty_cells <- function(board) {

\n      which(board == 0, arr.ind = TRUE)

\n \n}\n<\/p>\n\n\n\n

Step 2) Make sure cell placement is valid<\/strong><\/h2>\n\n\n\n

Next, we need a function that will check if a cell placement is valid. In other words, if we try putting a number into a particular cell, we need to ensure that the number appears only once in that row, column, and box. Otherwise, the placement would not be valid.<\/p>\n\n\n\n

\nis_valid <- function(board, num, row, col) {

\n \n    # Check if any cell in the same row has value = num
\n    if(any(board[row, ] == num)) {

\n \n        return(FALSE)

\n \n    }

\n \n    # Check if any cell in the same column has value = num
\n    if(any(board[, col] == num)) {

\n \n        return(FALSE)

\n \n    }

\n \n    # Get cells in num’s box
\n    box_x <- floor((row - 1) \/ 3) + 1
\n    box_y <- floor((col - 1) \/ 3) + 1

\n \n    # Get subset of matrix containing num’s box
\n    box <- board[(3 * box_x - 2):(3 * box_x), (3 * box_y - 2):(3 * box_y)]

\n \n    # Check if the number appears elsewhere in its box
\n    if(any(box == num)) {

\n \n        return(FALSE)

\n \n    }

\n \n        return(TRUE)

\n \n    }
\n<\/p>\n\n\n\n

Step 3) Recursively solve the Sudoku<\/strong><\/h2>\n\n\n\n

In the third step, we write our function to solve the Sudoku. This function will return\u00a0TRUE<\/strong>\u00a0if the input Sudoku is solvable. Otherwise, it will return\u00a0FALSE<\/strong>. The final result will be stored in a separate variable.<\/p>\n\n\n\n

\nsolve_sudoku <- function(board, needed_cells = NULL, index = 1) {

\n \n    # Find all empty cells
\n    if(is.null(needed_cells))
\n        needed_cells <- find_empty_cells(board)

\n \n    if(index > nrow(needed_cells)) {

\n \n        # Set result equal to current value of board
\n        # and return TRUE
\n        result <<- board
\n        return(TRUE)

\n \n    } else {

\n \n        row <- needed_cells[index, 1]
\n        col <- needed_cells[index, 2]
\n    }

\n \n    # Solve the Sudoku
\n    for(num in 1:9) {
\n \n        # Test for valid answers
\n        if(!is_valid(board, num, row, col)) {next} else{
\n \n            board2 = board
\n            board2[row, col] <- num

\n \n        # Retest with input
\n        if(solve_sudoku(board2, needed_cells, index + 1)) {
\n        return(TRUE)

\n \n            }

\n \n        }

\n \n    }

\n \n    # If not solvable, return FALSE
\n    return(FALSE)

\n \n}\n<\/p>\n\n\n\n

Calling the Sudoku solver<\/strong><\/h2>\n\n\n\n

Lastly, we call our Sudoku solver. The result is stored in the variable \u201cresult\u201d, as can be seen below.<\/p>\n\n\n\n

\nsolve_sudoku(board)\n<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Conclusion<\/strong><\/h2>\n\n\n\n

That\u2019s it for this post! If you enjoyed reading this and want to learn more about R or Python, check out the great data science program at 365 Data Science<\/a>.<\/p>\n\n\n\n

Visit TheAutomatic.net<\/strong> for additional insight on this topic: https:\/\/theautomatic.net\/2020\/11\/25\/how-to-solve-sudoku-with-r\/<\/a>.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

Andrew Treadway shows us how to write our own solution in R to solve a Sudoku puzzle as a 9\u00d79 grid.<\/p>\n","protected":false},"author":388,"featured_media":80184,"comment_status":"closed","ping_status":"open","sticky":true,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[339,343,338,341,352,344,342],"tags":[806,487,6591,508],"contributors-categories":[13695],"class_list":["post-86950","post","type-post","status-publish","format-standard","has-post-thumbnail","category-data-science","category-programing-languages","category-ibkr-quant-news","category-quant-development","category-quant-north-america","category-quant-regions","category-r-development","tag-data-science","tag-r","tag-rstats","tag-rstudio","contributors-categories-theautomatic-net"],"pp_statuses_selecting_workflow":false,"pp_workflow_action":"current","pp_status_selection":"publish","acf":[],"yoast_head":"\nHow to Solve Sudoku with R – Open Source Automation<\/title>\n<meta name=\"description\" content=\"Andrew Treadway shows us how to write our own solution in R to solve a Sudoku puzzle as a 9\u00d79 grid.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.interactivebrokers.com\/campus\/wp-json\/wp\/v2\/posts\/86950\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to Solve Sudoku with R - 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