8-queens problem in Python.
Hi! I only start teaching Python, so could someone explain the code written below (found in the Internet)? Some pieces of the code are compli
Your code is wrong (cut and paste error?), but here's the gist:
You want a list of possible solutions. Each solution is a list of queens. Every queen is a tuple - a row (integer) and column (integer). For example, the solution for BOARD_SIZE=1
is [[(1,1)]]
- a single solution - [(1,1)]
containing a single queen - (1,1)
placed on row 1 and column 1.
There are 8 smaller_solutions
for BOARD_SIZE=8
, and n=1
- [[(1,1)],[(1,2)],[(1,3)],[(1,4)],[(1,5)],[(1,6)],[(1,7)],[(1,8)]] - a single queen placed in every column in the first row.
You understand recursion? If not, google it NOW.
Basically, you start by adding 0 queens to a size 0 board - this has one trivial solution - no queens. Then you find the solutions that place one queen the first row of the board. Then you look for solutions which add a second queen to the 2nd row - somewhere that it's not under attack. And so on.
def solve(n):
if n == 0: return [[]] # No RECURSION if n=0.
smaller_solutions = solve(n-1) # RECURSION!!!!!!!!!!!!!!
solutions = []
for solution in smaller_solutions:# I moved this around, so it makes more sense
for column in range(1,BOARD_SIZE+1): # I changed this, so it makes more sense
# try adding a new queen to row = n, column = column
if not under_attack(column , solution):
solutions.append(solution + [(n,column)])
return solutions
That explains the general strategy, but not under_attack
.
under_attack
could be re-written, to make it easier to understand (for me, you, and your students):
def under_attack(column, existing_queens):
# ASSUMES that row = len(existing_queens) + 1
row = len(existing_queens)+1
for queen in existing_queens:
r,c = queen
if r == row: return True # Check row
if c == column: return True # Check column
if (column-c) == (row-r): return True # Check left diagonal
if (column-c) == -(row-r): return True # Check right diagonal
return False
My method is a little slower, but not much.
The old under_attack
is basically the same, but it speeds thing up a bit. It looks through existing_queens
in reverse order (because it knows that the row position of the existing queens will keep counting down), keeping track of the left and right diagonal.