add a backtracking sudoku solver

sudoku.py

@@ -0,0 +1,79 @@
+#!/usr/bin/python
+# vim:set fileencoding=utf-8:
+
+"""
+A backtracking Sudoku solver.
+"""
+
+from __future__ import division, print_function
+import numpy as np
+import time
+
+
+puzzle = [3,  7,  0,  0,  0,  4,  9,  5,  1,
+          0,  0,  2,  5,  0,  0,  0,  0,  8,
+          0,  0,  0,  0,  0,  0,  0,  0,  7,
+          0,  0,  0,  0,  0,  3,  0,  2,  0,
+          0,  1,  0,  0,  2,  0,  0,  4,  0,
+          0,  5,  0,  9,  0,  0,  0,  0,  0,
+          8,  0,  0,  0,  0,  0,  0,  0,  0,
+          7,  0,  0,  0,  0,  5,  3,  0,  0,
+          5,  9,  4,  6,  0,  0,  0,  7,  2]
+puzzle = np.array(puzzle).reshape(9, 9)
+
+visual = True
+
+
+def valid():
+    rows = np.vsplit(puzzle, 9)
+    cols = np.hsplit(puzzle, 9)
+    grids = [grid for h in np.hsplit(puzzle, 3) for grid in np.vsplit(h, 3)]
+
+    units = rows + cols + grids
+    return all(np.max(np.bincount(unit[unit != 0])) == 1 for unit in units)
+
+
+def print_puzzle(clear=True):
+    ANSI_CPL = "\033[%dF"  # CPL = Cursor Previous Line
+
+    if clear:
+        print(ANSI_CPL % 10)
+
+    for row in np.vsplit(puzzle, 9):
+        for element in row[0]:
+            if element != 0:
+                print(element, end=' ')
+            else:
+                print('_', end=' ')
+        print()
+
+
+def set_next_number():
+    position = find_first(puzzle == 0)
+    for number in range(1, 10):
+        puzzle[position] = number
+        if valid():
+            if visual:
+                print_puzzle()
+                time.sleep(0.005)
+            if 0 not in puzzle:
+                # Solved
+                return True
+            else:
+                if set_next_number():
+                    return True
+
+    # dead end ⇒ backtrack
+    puzzle[position] = 0
+    return False
+
+
+def find_first(condition):
+    return tuple(p[0] for p in np.where(condition))
+
+
+print(__doc__)
+print_puzzle(clear=False)
+
+if set_next_number():
+    print_puzzle()