Data commit

Task/Cramers-rule/C-sharp/cramers-rule.cs

@@ -0,0 +1,102 @@
+using System;
+using System.Collections.Generic;
+using static System.Linq.Enumerable;
+
+public static class CramersRule
+{
+    public static void Main() {
+        var equations = new [] {
+            new [] { 2, -1,  5,  1,  -3 },
+            new [] { 3,  2,  2, -6, -32 },
+            new [] { 1,  3,  3, -1, -47 },
+            new [] { 5, -2, -3,  3,  49 }
+        };
+        var solution = SolveCramer(equations);
+        Console.WriteLine(solution.DelimitWith(", "));
+    }
+
+    public static int[] SolveCramer(int[][] equations) {
+        int size = equations.Length;
+        if (equations.Any(eq => eq.Length != size + 1)) throw new ArgumentException($"Each equation must have {size+1} terms.");
+        int[,] matrix = new int[size, size];
+        int[] column = new int[size];
+        for (int r = 0; r < size; r++) {
+            column[r] = equations[r][size];
+            for (int c = 0; c < size; c++) {
+                matrix[r, c] = equations[r][c];
+            }
+        }
+        return Solve(new SubMatrix(matrix, column));
+    }
+
+    private static int[] Solve(SubMatrix matrix) {
+        int det = matrix.Det();
+        if (det == 0) throw new ArgumentException("The determinant is zero.");
+
+        int[] answer = new int[matrix.Size];
+        for (int i = 0; i < matrix.Size; i++) {
+            matrix.ColumnIndex = i;
+            answer[i] = matrix.Det() / det;
+        }
+        return answer;
+    }
+
+    //Extension method from library.
+    static string DelimitWith<T>(this IEnumerable<T> source, string separator = " ") =>
+        string.Join(separator ?? " ", source ?? Empty<T>());
+
+    private class SubMatrix
+    {
+        private int[,] source;
+        private SubMatrix prev;
+        private int[] replaceColumn;
+
+        public SubMatrix(int[,] source, int[] replaceColumn) {
+            this.source = source;
+            this.replaceColumn = replaceColumn;
+            this.prev = null;
+            this.ColumnIndex = -1;
+            Size = replaceColumn.Length;
+        }
+
+        private SubMatrix(SubMatrix prev, int deletedColumnIndex = -1) {
+            this.source = null;
+            this.prev = prev;
+            this.ColumnIndex = deletedColumnIndex;
+            Size = prev.Size - 1;
+        }
+
+        public int ColumnIndex { get; set; }
+        public int Size { get; }
+
+        public int this[int row, int column] {
+            get {
+                if (source != null) return column == ColumnIndex ? replaceColumn[row] : source[row, column];
+                return prev[row + 1, column < ColumnIndex ? column : column + 1];
+            }
+        }
+
+        public int Det() {
+            if (Size == 1) return this[0, 0];
+            if (Size == 2) return this[0, 0] * this[1, 1] - this[0, 1] * this[1, 0];
+            SubMatrix m = new SubMatrix(this);
+            int det = 0;
+            int sign = 1;
+            for (int c = 0; c < Size; c++) {
+                m.ColumnIndex = c;
+                int d = m.Det();
+                det += this[0, c] * d * sign;
+                sign = -sign;
+            }
+            return det;
+        }
+
+        public void Print() {
+            for (int r = 0; r < Size; r++) {
+                Console.WriteLine(Range(0, Size).Select(c => this[r, c]).DelimitWith(", "));
+            }
+            Console.WriteLine();
+        }
+    }
+
+}