Answer
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# 10.18 (Game: Eight Queens) The classic Eight Queens puzzle is to place eight
# queens on a chessboard such that no two queens can attack each other (i.e., no
# two queens are in the same row, same column, or same diagonal). There are
# many possible solutions. Write a program that displays one such solution. A
# sample output is shown below:
def main():
# 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 and k <= 7:
# 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
k += 1
printResult(queens)
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):
for i in range(8):
print(str(i) + ", " + str(queens[i]))
print()
# 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()
