Data commit

Task/Random-Latin-squares/Python/random-latin-squares.py

@@ -0,0 +1,61 @@
+from random import choice, shuffle
+from copy import deepcopy
+
+def rls(n):
+    if n <= 0:
+        return []
+    else:
+        symbols = list(range(n))
+        square = _rls(symbols)
+        return _shuffle_transpose_shuffle(square)
+
+
+def _shuffle_transpose_shuffle(matrix):
+    square = deepcopy(matrix)
+    shuffle(square)
+    trans = list(zip(*square))
+    shuffle(trans)
+    return trans
+
+
+def _rls(symbols):
+    n = len(symbols)
+    if n == 1:
+        return [symbols]
+    else:
+        sym = choice(symbols)
+        symbols.remove(sym)
+        square = _rls(symbols)
+        square.append(square[0].copy())
+        for i in range(n):
+            square[i].insert(i, sym)
+        return square
+
+def _to_text(square):
+    if square:
+        width = max(len(str(sym)) for row in square for sym in row)
+        txt = '\n'.join(' '.join(f"{sym:>{width}}" for sym in row)
+                        for row in square)
+    else:
+        txt = ''
+    return txt
+
+def _check(square):
+    transpose = list(zip(*square))
+    assert _check_rows(square) and _check_rows(transpose), \
+        "Not a Latin square"
+
+def _check_rows(square):
+    if not square:
+        return True
+    set_row0 = set(square[0])
+    return all(len(row) == len(set(row)) and set(row) == set_row0
+               for row in square)
+
+
+if __name__ == '__main__':
+    for i in [3, 3,  5, 5, 12]:
+        square = rls(i)
+        print(_to_text(square))
+        _check(square)
+        print()