Python：检查对角线的 N-Queen 谜题的解决方案

Question

这里我要编写 N-Queens 问题，用户将输入棋盘的尺寸和皇后的位置。

Enter the dimension of the Chessboard: 4
Enter position of the Queen: 10
Enter position of the Queen: 31
Enter position of the Queen: 02
Enter position of the Queen: 23

并且根据用户输入，我制作了候选解决方案（这是一个列表），其中候选解决方案的索引代表皇后的列，值代表皇后的行位置。

候选解如下： [1, 3, 0, 2]

据此，我制作了一个矩阵来表示皇后的位置：

0, 0, 1, 0
1, 0, 0, 0
0, 0, 0, 1
0, 1, 0, 0

我的问题是我必须检查候选解是否为真，通过检查对角线并在解为真时打印一条消息。

到目前为止，这是我的代码，它将打印候选解决方案和显示皇后位置的矩阵：

#Ask the user to input the dimension of the Chessboard(N)
N=int(input("Enter the dimension of the Chessboard: "))

#Creating a list of list with zeros in the dimension N*N
list_0=[0 for m in range(N)]

#Iterating for the length of N
for t in range(N):

    #Creating a list for the input position values
    position=[int(i) for i in input("Enter position of the Queen: ")]

    x,y = position[0],position[1]

    #The y position is the index of the list_0, where x is the value at the index position
    list_0[y] = x

#Printing the list_0
print(list_0)

#Creating a list of list with zeros
list_matrix = [[0 for m in range(len(list_0))] for n in range(len(list_0))]

#Iterating through the list_0 to find the index and the value of the list_0
for element in range(len(list_0)):

    x,y = element, list_0[element]

    list_matrix[y][x] = 1

#Defining a list to print the candidate solution for N-Queen problen in matrix format
def printListInTableFormat(list_default):

    #Looping through length of the list_default
    for row in range(len(list_default)):

        new_row=''.join(str(list_matrix[row]))

        matrix=print(new_row.strip('[]'))

    return matrix

#Printing the matrix
matrix = printListInTableFormat(list_matrix)

由于我是 Python 新手，非常感谢任何帮助。提前致谢。

Answer 1

提示

(p, q) 的皇后与(r, s) 的皇后在同一对角线上，abs(p - r) == abs(q - s)。

Answer 2

请参阅@Raymond Hettinger 的提示了解这一点，但基本上，对于N = [1, 3, 0, 2] 的输入列表中的每个 x（列是 x 坐标以及 N 数组的索引值），检查所有其他棋子，看看它们的 x（列）和 y（行）坐标如何比较。

def is_valid(N):
    size = len(N)
    for x in range(size):
        for col in range(x + 1, size):
            if abs(x - col) == abs(N[x] - N[col]):
                return False
    return True

或 lil 更清洁，这会检查所有检查是否所有值都为真差异检查：

def is_valid(N):
    for x in range(size):
        return all(abs(x - row) != abs(N[x] - N[row]) for row in range(x + 1, size)

不过，对角线不应该是唯一的有效性测试。您还应该添加此检查，len(N) == len(set(N))。这样可以确保同一行中没有皇后。

Answer 3

一个简单的变体

import random

global maX
global maY
global mostAttacks
global posInVector
#1.
def GenM(N):
    p=[[" " for x in range(0,N)]for x in range(0,N)]
    #print(p)
    return p;

def fillPos():
    p=[[[] for x in range(0,2)]for x in range(0,N)]
    #print(p)
    return p;

N=4
matrix=GenM(N)
places = fillPos()
posInVector = 0

def randomPlace(N):
    for x in range(0,N):
        xpos = random.randint(0,N-1)
        ypos = random.randint(0,N-1)
        matrix[xpos][ypos]='R'
        places[x][0] = xpos
        places[x][1] = ypos

randomPlace(N)

print(places)

def printMatrix():
    print("---------------------------------\n")
    for i in matrix:
        print(i)
        print("\n")
printMatrix()

# == Generate random position , geterate random pos for N queens 
# and display the matrix and the array for the queen's positions

def VerifLine(L):
    queens = 0
    line=matrix[L]
    for element in line:
        if(element=='R'):
            queens+=1
        if(queens == 2):
            return 1;
    return 0;

#print(VerifLine(0))

def VerifCol(C):
    queens = 0
    for element in range(0,N):
        if(matrix[element][C]=='R'):
            queens+=1
        if(queens == 2):
            return 1;
    return 0;


def VerifDiagonalStg(L,C):
    #print("down left")
    j = C-1
    for i in range(L+1,N):
        if j < N and j >= 0:
            if matrix[i][j] == 'R':
                return 1
            j-=1      
    #print("---")

    #print("up right")
    j = C+1
    for i in range(L-1,-1,-1):
        if j < N and j >= 0:
            if matrix[i][j] == 'R':
                return 1
            j+=1
    #print("---")

    return 0

def VerifDiagonalDr(L,C):
    #print("down right")
    j = C+1
    for i in range(L+1,N):
        if j < N and j >= 0:
            if matrix[i][j] == 'R':
                return 1
            j+=1
    #print("---")

    #print("up left")
    j = C-1
    for i in range(L-1,-1,-1):
        if j < N and j >= 0:
            if matrix[i][j] == 'R':
                return 1
            j-=1
    #print("---")

    return 0


maX = -1
maY = -1
def countAttacks(qx, qy):
    '''print("queen: ", qx, " ", qy)
    print("pe line: ",VerifLine(qx))
    print("pe col: ", VerifCol(qy))
    print("pe diagonal: ", VerifDiagonalDr(qx,qy) + VerifDiagonalStg(qx,qy))
    print("\n=============\n")'''
    attacks = VerifLine(qx) + VerifCol(qy) + VerifDiagonalDr(qx,qy) + VerifDiagonalStg(qx,qy)
    return attacks

def findMostAttacked(places):
    global maX
    global maY
    global mostAttacks
    global posInVector
    mX = places[0][0]
    mY = places[0][1]
    maxAttacks = countAttacks(places[0][0], places[0][1])
    for i in range(1,N):
        if maxAttacks < countAttacks(places[i][0], places[i][1]):
            mX = places[i][0]
            mY = places[i][1]
            maxAttacks = countAttacks(places[i][0], places[i][1])
            posInVector = i
    print("most attacked: ", mX, " ", mY)
    maX = mX
    maY = mY
    mostAttacks = maxAttacks
    print("attacks: ", maxAttacks)
    if mostAttacks == 0:
        return 0
    else:
        return 1

def moveMostAttacked():
    global maX
    global maY
    global mostAttacks
    global posInVector
    for i in range(0,N):
        for j in range(0,N):
            if(matrix[i][j] == " "):
                attacksForThisPos = countAttacks(i,j)
                if(attacksForThisPos < mostAttacks):
                    matrix[maX][maY] = " "
                    matrix[i][j] = 'R'
                    places[posInVector][0] = i
                    places[posInVector][1] = j
                    print('poz in vector: ', posInVector)
                    print(matrix[maX][maY], "->", matrix[i][j])
                    print('mutata de pe ',maX, ' ',maY, ' pe ', i,' ',j)
                    print('nr vechi de atacuri: ', mostAttacks)
                    print('nr nou de atacuri: ', attacksForThisPos)
                    return 0

while(findMostAttacked(places) == 1):
    findMostAttacked(places)
    moveMostAttacked()
    printMatrix()
    input("Press Enter to continue...")


print(" ========== ")