N皇后问题 -Python

import time
"""
N 皇后问题，不同皇后不能放置在同一直线或对角线上

"""
def Nqueen(n):
    # arr[i] 表示每行皇后放置的第几列
    arr = [0 for i in range(n)] 
    cnt = 0
    i = 0
    resume_flag = False      # 回溯标志
    while i >= 0 and i <n:
        if arr[i] > n-1:
            i = i-1
            resume_flag = True
            continue
        
        if resume_flag:       # 回溯，重置未放置皇后的行的值
            for k in range(i+1, n):
                arr[k] = 0
            resume_flag = False
            arr[i] += 1
            if arr[i] > n-1:
                continue

        attack_flag = False
        for j in range(i):
            if  nearby([i,arr[i]], [j, arr[j]]):
                attack_flag = True
                break
        if attack_flag:
            arr[i] += 1
        else:
            if i == n-1:
                cnt += 1
                # print("arr:", arr) # 当前可能的皇后放置方法
                arr[i] += 1
            elif i< n-1:
                i = i+1
    return cnt
        


def nearby(a, b):
    if a[0] == b[0] or a[1] == b[1]:
        return True

    if abs(a[0] - b[0]) == abs(a[1] - b[1]):
        return True
    return False

def test_nqueen():
    for i in range(12):
        start_time = time.time()
        ret = Nqueen(i)
        print("{:<4d} {:>10d} {:>10.3f}".format(i, ret, time.time()-start_time))

if __name__ == "__main__":
   test_nqueen()

运行结果：

0             0      0.000
1             1      0.000
2             0      0.000
3             0      0.000
4             2      0.000
5            10      0.001
6             4      0.003
7            40      0.011
8            92      0.063
9           352      0.225
10          724      1.348
11         2680      7.262