我正在尝试为n皇后问题实现Sosic和Gu算法-它提供了一个称为initial_search（）的初始化阶段。
该算法首先在有限的尝试次数内将皇后分配到棋盘上的随机位置（由int（3.08 * n）迭代的循环控制）。对于每次皇后放置尝试，它使用partial_collision函数检查是否存在与先前放置的皇后的任何立即冲突。如果检测到冲突，算法会在不同的随机位置重新尝试放置，直到找到一个有效的放置。这一步的目的是在最小化初始冲突的同时将皇后分布在整个板上。我发现partial_collision（）的实现存在问题：在文章中，他们说它应该花费O（1），但是我找不到一种方法来使用对角数组只检查左边的列（实际上函数total_collision（）是O（1））。

import random
def queen_search(queens):
    while True:
        nd, pd = initialize_diagonal_arrays(len(queens))
        k = initial_search(queens, nd, pd)
        if len(queens) > 200:
            final_search(queens, k, nd, pd)
            break
        else:
            final_search_reduced(queens, k, nd, pd)
            if board_collision(queens) == 0:
                break
def initial_search(queens, nd, pd):
    n = len(queens)
    queens[:] = list(range(n))
    update_diagonal_arrays(queens, nd, pd)
    j = 0
    # place queens without collisions
    for i in range(int(3.08 * n)):
        if j == n:
            break
        m = random.randint(j, n - 1)
        swap(queens, j, m, nd, pd)
        if partial_collision(queens, j) == 0:
            j += 1
        else:
            swap(queens, j, m, nd, pd)
    # place queens with possible collisions
    for i in range(j, n):
        m = random.randint(i, n - 1)
        swap(queens, i, m, nd, pd)
    # return the number of queens with possible collisions
    return n - j
def final_search(queens, k, nd, pd):
    n = len(queens)
    it = 0
    for i in range(n - k, n):
        if total_collisions(queens, i, nd, pd) > 0:
            while it < 7000:
                j = random.randint(0, n - 1)
                swap(queens, i, j, nd, pd)
                b = (total_collisions(queens, i, nd, pd) > 0) or (total_collisions(queens, j, nd, pd) > 0)
                if b:
                    swap(queens, i, j, nd, pd)
                    it += 1
                else:
                    break
def final_search_reduced(queens, k, nd, pd):
    n = len(queens)
    for i in range(n - k, n):
        if total_collisions(queens, i, nd, pd) > 0:
            for j in range(n):
                swap(queens, i, j, nd, pd)
                b = (total_collisions(queens, i, nd, pd) > 0) or (total_collisions(queens, j, nd, pd) > 0)
                if b:
                    swap(queens, i, j, nd, pd)
                else:
                    break
# auxiliary functions
def initialize_diagonal_arrays(n):
    neg_diagonal = [0] * (2 * n - 1)
    pos_diagonal = [0] * (2 * n - 1)
    return neg_diagonal, pos_diagonal
def update_diagonal_arrays(queens, neg_diagonal, pos_diagonal):
    n = len(queens)
    for i in range(len(queens)):
        neg_diagonal[i + queens[i]] += 1
        pos_diagonal[i - queens[i] + n - 1] += 1
def swap(queens, a, b, neg_diagonal, pos_diagonal):
    original_a, original_b = queens[a], queens[b]
    queens[a], queens[b] = queens[b], queens[a]
    neg_diagonal[a + original_a] -= 1
    neg_diagonal[b + original_b] -= 1
    pos_diagonal[a - original_a + len(queens) - 1] -= 1
    pos_diagonal[b - original_b + len(queens) - 1] -= 1
    neg_diagonal[a + queens[a]] += 1
    neg_diagonal[b + queens[b]] += 1
    pos_diagonal[a - queens[a] + len(queens) - 1] += 1
    pos_diagonal[b - queens[b] + len(queens) - 1] += 1
def partial_collision(queens, i):
    return sum(1 for j in range(i) if (i - j) == abs(queens[i] - queens[j]))
def total_collisions(queens, i, neg_diagonal, pos_diagonal):
    n = len(queens)
    return neg_diagonal[i + queens[i]] + pos_diagonal[i - queens[i] + n - 1] - 2  # Exclude self-collision
def board_collision(queens):
    return sum(partial_collision(queens, i) for i in range(len(queens)))

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