def solveSudoku(board):
cols = (
[ ("rc", j, i) for i in range(1,10) for j in range(1,10)] +
[ ("rn", i, j) for i in range(1,10) for j in range(1,10)] +
[ ("cn", i, j) for i in range(1,10) for j in range(1,10)] +
[ ("bn", i, j) for i in range(1,10) for j in range(1,10)])
rows = [ (j,i,k) for i in range(1,10) for j in range(1,10) for k in range(1,10) ]
Rows = {}
for x,y,n in rows:
Rows[(x,y,n)] = [("rc",x,y), ("rn", x,n), ("cn", y,n), ("bn", 1+(x-1)//3+(y-1)//3*3, n)]
Cols = {c:set() for c in cols}
for r, cols in Rows.items():
for c in cols:
Cols[c].add(r)
for y, line in enumerate(board):
for x, n in enumerate(line):
if n != '.':
select(Cols, Rows, (x+1,y+1,int(n)))
for s in solve(Cols, Rows, []):
for x,y,n in s:
board[y-1][x-1] = str(n)
break
def solveSudoku(board):
cols = ([("rc", j, i) for i in range(1, 10)
for j in range(1, 10)] + [("rn", i, j) for i in range(1, 10)
for j in range(1, 10)] +
[("cn", i, j) for i in range(1, 10)
for j in range(1, 10)] + [("bn", i, j) for i in range(1, 10)
for j in range(1, 10)])
rows = [(j, i, k) for i in range(1, 10) for j in range(1, 10)
for k in range(1, 10)]
Rows = {}
for x, y, n in rows:
Rows[(x, y, n)] = [("rc", x, y), ("rn", x, n), ("cn", y, n),
("bn", 1 + (x - 1) // 3 + (y - 1) // 3 * 3, n)]
Cols = {c: set() for c in cols}
for r, cols in Rows.items():
for c in cols:
Cols[c].add(r)
for y, line in enumerate(board):
for x, n in enumerate(line):
if n != '.':
select(Cols, Rows, (x + 1, y + 1, int(n)))
for s in solve(Cols, Rows, []):
for x, y, n in s:
board[y - 1][x - 1] = str(n)
break
def solveNQueens(n):
cols = ([("x", x) for x in range(n)] + [("y", y) for y in range(n)] +
[("c", c) for c in range(2 * n - 1)] + [("d", d)
for d in range(-n + 1, n)])
Cols = {c: set() for c in cols}
Rows = {(x, y): [("x", x), ("y", y), ("c", x + y), ("d", x - y)]
for x in range(n) for y in range(n)}
for r, cols in Rows.items():
for c in cols:
Cols[c].add(r)
return [make_chess_board(s, n) for s in solve(Cols, Rows, [], is_primary)]
def solveNQueens(n):
cols = (
[ ("x", x) for x in range(n) ] +
[ ("y", y) for y in range(n) ] +
[ ("c", c) for c in range(2*n-1) ] +
[ ("d", d) for d in range(-n+1,n) ]
)
Cols = {c:set() for c in cols}
Rows = {
(x,y): [("x", x), ("y", y), ("c", x+y), ("d", x-y)]
for x in range(n)
for y in range(n)}
for r, cols in Rows.items():
for c in cols:
Cols[c].add(r)
return [
make_chess_board(s, n)
for s in solve(Cols, Rows, [], is_primary)]