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# 10.20 (Game: multiple Eight Queens solutions) Exercise 10.18 has you find one
# solution for the Eight Queens puzzle. Write a program to count all possible
# solutions for the Eight Queens problem and display all the solutions.
def main():
count = 0
# Queen positions
queens = 8 * [-1] # queens are placed at (i, queens[i])
# -1 indicates that no queen is currently placed in the ith row
queens[0] = 0 # Initially, place a queen at (0, 0) in the 0th row
# k - 1 indicates the number of queens placed so far
# We are looking for a position in the kth row to place a queen
k = 1
while k >= 0:
# Find a position to place a queen in the kth row
j = findPosition(k, queens)
if j < 0:
queens[k] = -1
k -= 1 # back track to the previous row
else:
queens[k] = j
if k == 7:
count += 1 # One more solution found
print("Solution" + str(count) + ":")
printResult(queens)
else:
k += 1
print("How many solutions?", count)
def findPosition(k, queens):
start = 0 if queens[k] == -1 else (queens[k] + 1)
for j in range(start, 8):
if isValid(k, j, queens):
return j # (k, j) is the place to put the queen now
return -1
# Return true if you a queen can be placed at (k, j)
def isValid(k, j, queens):
# See if (k, j) is a possible position
# Check jth column
for i in range(k):
if queens[i] == j:
return False
# Check major diagonal
row = k - 1
column = j - 1
while row >= 0 and column >= 0:
if queens[row] == column:
return False
row -= 1
column -= 1
# Check minor diagonal
row = k - 1
column = j + 1
while row >= 0 and column <= 7:
if queens[row] == column:
return False
row -= 1
column -= 1
return True
# Print a two-dimensional board to display the queens
def printResult(queens):
# Display the output
for i in range(8):
for j in range(queens[i]):
print("| ", end="")
print("|Q|", end="")
for j in range(queens[i] + 1, 8):
print(" |", end="")
print()
main()
