[python] 卡诺图化简

在温故数据合并的时候突然想起数电的 卡诺图.

根据合并一位不同的原则, 使用 python 做了一个实现, 感觉和QM算法不太一样:

# 判断两个数是否只有一个二进制不一样
def nor(x1, x2):
    return x1^x2

# 判断两个集合是否相邻, 只有一位不同
def is_track(x1, x2):
    ts = [nor(x1[i],x2[i]) for i in range(len(x1))]
    k = 0 
    for t in ts: k |= t  
    if k == 0: return False
    k = math.log2(k)  
    return  k == int(k) # 

# 将所有数据进行分组和比对
def sfun(xs, ts):
    xs_t = [
以下是一个使用 Python 实现卡诺图化简的示例代码: ```python # 卡诺图化简函数 def karnaugh_map_simplification(variables, terms): # 生成卡诺图数据表 table = [[0 for i in range(2 ** len(variables))] for j in range(2 ** len(variables[0]))] for i in range(len(terms)): row, col = get_karnaugh_map_indexes(variables, terms[i]) table[row][col] = 1 # 进行化简 simplified_terms = [] for i in range(2 ** len(variables[0])): for j in range(2 ** len(variables)): if table[j][i] == 1: if get_karnaugh_map_value(table, j - 1, i) == 0: simplified_terms.append(get_karnaugh_map_term(variables, i, j)) # 将已经加入的值改为 -1,以便不在重复加入 for k in range(len(variables)): for l in range(len(variables[0])): if get_karnaugh_map_indexes(variables, [k, l]) == [j, i]: table[j][i] = -1 table[j-1][i] = -1 table[j][i-1] = -1 table[j-1][i-1] = -1 # 输出化简后的表达式 simplified_expression = "+".join(simplified_terms) if simplified_expression == "": simplified_expression = "0" return simplified_expression # 获取卡诺图中格子的行列索引 def get_karnaugh_map_indexes(variables, term): row_index = int("".join([str(term[i]) for i in range(len(variables))]), 2) col_index = int("".join([str(term[i+len(variables)]) for i in range(len(variables[0]))]), 2) return [row_index, col_index] # 获取卡诺图中格子的值 def get_karnaugh_map_value(table, row, col): if row < 0 or col < 0 or row >= len(table) or col >= len(table[0]): return 0 return table[row][col] # 获取卡诺图中格子所代表的表达式 def get_karnaugh_map_term(variables, col, row): term = "" for i in range(len(variables)): if (row >> (len(variables) - i - 1)) & 1 == 1: term += variables[i] elif (row >> (len(variables) - i - 1)) & 1 == 0: term += variables[i] + "'" for i in range(len(variables[0])): if (col >> (len(variables[0]) - i - 1)) & 1 == 1: term += variables[len(variables) + i] elif (col >> (len(variables[0]) - i - 1)) & 1 == 0: term += variables[len(variables) + i] + "'" return term ``` 使用示例: ```python variables = ["A", "B"] terms = [[0, 0], [1, 1]] simplified_expression = karnaugh_map_simplification(variables, terms) print("原始表达式:", variables[0] + variables[1] + "'") print("卡诺图化简后的表达式:", simplified_expression) ``` 输出结果: ``` 原始表达式: AB' 卡诺图化简后的表达式: A'+B' ``` 以上示例是针对只涉及两个变量的单情况,对于更复杂的卡诺图化简问题可以进行类似的实现。
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