// Input: nothing to use the default test cases or // multiple lines of integers making the square // matrix. // Created for this code golf challenge: // https://codegolf.stackexchange.com/q/181742 // Is this Pascal's Matrix? // In Pascal's triangle each number is the sum of the two numbers directly above it, treating empty spots as zero: // Source: https://en.wikipedia.org/wiki/File:Pascal_triangle_small.png // By rotating the triangle, we can cut out square matrices of varying sizes and rotations which I will call Pascal's matrices. Note that those matrices always need to contain the top 1 // Here are some examples: // 1 1 1 1 // 1 2 3 4 // 1 3 6 10 // 1 4 10 20 // 6 3 1 // 3 2 1 // 1 1 1 // 1 5 15 35 70 // 1 4 10 20 35 // 1 3 6 10 15 // 1 2 3 4 5 // 1 1 1 1 1 // 1 // 1 1 // 2 1 // The Task // Given a square matrix containing positive numbers in any reasonable format, decide if it is a Pascal's matrix. // Decide means to either return truthy or falsy values depending on whether the input is a Pascal's matrix, or to fix two constant values and return one for the true inputs and the other for false inputs. // This is code-golf, so try to use as few bytes as possible in the language of your choice. The shortest code in each language wins, thus I will not accept an answer. // Test cases // True // [[1, 1, 1, 1], [1, 2, 3, 4], [1, 3, 6, 10], [1, 4, 10, 20]] // [[6, 3, 1], [3, 2, 1], [1, 1, 1]] // [[1, 5, 15, 35, 70], [1, 4, 10, 20, 35], [1, 3, 6, 10, 15], [1, 2, 3, 4, 5], [1, 1, 1, 1, 1]] // [[1]] // [[1, 1], [2, 1]] // False // [[2]] // [[1, 2], [2, 1]] // [[1, 1], [3, 1]] // [[1, 1, 1, 1], [1, 2, 3, 4], [1, 4, 6, 10], [1, 4, 10, 20]] // [[6, 3, 1], [1, 1, 1], [3, 2, 1]] // [[2, 2, 2, 2], [2, 4, 6, 8], [2, 6, 12, 20], [2, 8, 20, 40]] // [[40, 20, 8, 2], [20, 12, 6, 2], [8, 6, 4, 2], [2, 2, 2, 2]] // [[1, 5, 15, 34, 70], [1, 4, 10, 20, 34], [1, 3, 6, 10, 15], [1, 2, 3, 4, 5], [1, 1, 1, 1, 1]] // Main function to test square matrices to see if // they have valid Pascal triangle values in them. fun main(args: Array) { // Expanded function of the lambda providing // comments to explain it. fun process(matrix: List>): Boolean { // Declare the number of rows and columns in // the matrix, the row index, and the column // index. Declared prior to the nested // function so it can have access to them. val number = matrix.size var row = 0 var column = 0 // Function to return the current value of the // matrix by figuring out the bottom corner of // the unrotated matrix and adjusting the row // & column indices to get it. fun find() = if (matrix[0][0] != 1) matrix[number-row-1][number-column-1] else if (matrix[number-1][0] != 1) matrix[row][number-column-1] else if (matrix[0][number-1] != 1) matrix[number-row-1][column] else matrix[row][column] // Default the result to true. For each line // of the triangle that fits within the matrix, // process through that line. var good = 0 < 1 for (line in 0..number*2-2) { // Set up the row, column, and the first // value on the line. While there are values // for the line, process them. row = line column = 0 var value = 1 do { // If the row & column are within the matrix, // test it's value against the calculated // one and update the result. if (row < number && column < number) good = find() == value && good // The next value is calculated based on // f(line column) = f(line column-1)* // (line+1-column)/column. Both the column // must be increased and the row decreased // to prepare for the next value on the line. value = value*(line-column)/++column } while (--row >= 0) } // for return good } // process // Declare the lambda for the challenge see expanded // version above. val p = // 269 bytes {m:List>->val n=m.size var r=0 var c=0 fun f()=if(m[0][0]!=1)m[n-r-1][n-c-1] else if(m[n-1][0]!=1)m[r][n-c-1] else if(m[0][n-1]!=1)m[n-r-1][c] else m[r][c] var g=0<1 for(l in 0..n*2-2){r=l c=0 var v=1 do{if(r=0)} g} // Function to display the result of the processing // and the matrix we processed. fun display(matrix: List>) { println("\nIs this a Pascal Matrix? "+ "${p(matrix)}") for (row in matrix) { for (column in row) print("%3d".format(column)) println() } // for } // display // Try reading a user specified matrix and, if // successful, process it. try { // Default the matrix to empty and the size to // zero. While we have a valid line of integers // to process, do so. var data = mutableListOf>() var size = 0 while (true) { // Read the next input line breaking out of the // loop on end of file or getting an empty line. val input = readLine() ?: break if (input.isEmpty()) break // Convert the input line into a list of // integers (causing an exception when we can't) // and if it is our first line, update our size // to the lines size. data.add(input.split(" ").map { it.toInt() }) if (size == 0) size = data[0].size // Otherwise, this is the second or later line // so if this line's size is different from the // first line, throw an exception. else if (size != data[data.size-1].size) throw IllegalArgumentException( "Wrong size of row!") } // while // If the size is zero or the matrix is not // square, we do not have a valid square matrix // so throw an exception. if (size == 0 || size != data.size) throw IllegalArgumentException( "Matrix is not square!") // We got a valid square matrix so process it. display(data.toList()) // On exception, complain and run through the // various test cases from the challenge examples. } catch (error: Throwable) { println("Bad inputs using defaults!") for (test in listOf( listOf(listOf(1, 1, 1, 1), listOf(1, 2, 3, 4), listOf(1, 3, 6, 10), listOf(1, 4, 10, 20)), listOf(listOf(6, 3, 1), listOf(3, 2, 1), listOf(1, 1, 1)), listOf(listOf(1, 5, 15, 35, 70), listOf(1, 4, 10, 20, 35), listOf(1, 3, 6, 10, 15), listOf(1, 2, 3, 4, 5), listOf(1, 1, 1, 1, 1)), listOf(listOf(1)), listOf(listOf(1, 1), listOf(2, 1)), listOf(listOf(2)), listOf(listOf(1, 2), listOf(2, 1)), listOf(listOf(1, 1), listOf(3, 1)), listOf(listOf(1, 1, 1, 1), listOf(1, 2, 3, 4), listOf(1, 4, 6, 10), listOf(1, 4, 10, 20)), listOf(listOf(6, 3, 1), listOf(1, 1, 1), listOf(3, 2, 1)), listOf(listOf(2, 2, 2, 2), listOf(2, 4, 6, 8), listOf(2, 6, 12, 20), listOf(2, 8, 20, 40)), listOf(listOf(40, 20, 8, 2), listOf(20, 12, 6, 2), listOf(8, 6, 4, 2), listOf(2, 2, 2, 2)), listOf(listOf(1, 5, 15, 34, 70), listOf(1, 4, 10, 20, 34), listOf(1, 3, 6, 10, 15), listOf(1, 2, 3, 4, 5), listOf(1, 1, 1, 1, 1)))) display(test) } // try } // main

pascalMatrix cg