1. 实验要求

（1）已知文法G[S']

(0) S'→E 

(1) E→aA

(2) E→bB

(3) A→cA 

(4) A→d

(5) B→cB 

(6) B→d

手工建立文法G[S']的LR(0)的项目集规范族DFA和LR(0)分析表。

（2） 根据清华大学版《编译原理（第3版）》教材上LR(0)语法分析的算法思想及算法流程，构造LR(0)语法分析程序。

（3）用该LR(0)语法分析程序对任意给定的键盘输入串进行语法分析，并根据栈的变化状态输出给定串的具体分析过程。如果分析成功，则输入输出串是给定文法的合法句子的结论；如果分析不成功，则输入输出串不是给定文法的句子的结论。

详细分析过程可以看看这篇：

LR(0)分析法 - ISGuXing - 博客园 (cnblogs.com)

2. 分析结果输出

 3. Python代码实现

import copy

class Stack():  # 定义类
    def __init__(self):  # 产生一个空的容器
        self.__list = []

    def size(self):  # 返回栈中元素个数
        return len(self.__list)

    def push(self, item):  # 入栈
        self.__list.append(item)

    def push_list(self, list):  # 末尾添加多个元素
        for i in range(len(list)):
            self.push(list[i])

    def pop(self):  # 出栈
        return self.__list.pop()

    def pop_list(self, n):  # 出栈n个元素
        for i in range(n):
            self.pop()

    def peek(self):  # 返回栈顶元素
        return self.__list[-1]

    def is_empty(self):  # 判断是否已为空
        return not self.__list

    def deep_copy(self):  # 深拷贝
        new_stack = Stack()
        for i in range(self.size()):
            new_stack.push(self.__list[i])
        return new_stack

    def bottom_output(self):  # 从栈底开始排列输出
        string = ""
        for i in range(self.size()):
            string += str(self.__list[i])
        return string

    def top_output(self):  # 从栈顶开始排列输出
        string = ""
        for i in range(self.size() - 1, -1, -1):
            string += str(self.__list[i])
        return string


# LR(0)分析表
LR0_table = {
    0: {'a': 'S2', 'b': 'S3', 'c': None, 'd': None, '#': None, 'E': 1, 'A': None, 'B': None},
    1: {'a': None, 'b': None, 'c': None, 'd': None, '#': 'acc', 'E': None, 'A': None, 'B': None},
    2: {'a': None, 'b': None, 'c': 'S4', 'd': 'S10', '#': None, 'E': None, 'A': 6, 'B': None},
    3: {'a': None, 'b': None, 'c': 'S5', 'd': 'S11', '#': None, 'E': None, 'A': None, 'B': 7},
    4: {'a': None, 'b': None, 'c': 'S4', 'd': 'S10', '#': None, 'E': None, 'A': 8, 'B': None},
    5: {'a': None, 'b': None, 'c': 'S5', 'd': 'S11', '#': None, 'E': None, 'A': None, 'B': 9},
    6: {'a': 'r1', 'b': 'r1', 'c': 'r1', 'd': 'r1', '#': 'r1', 'E': None, 'A': None, 'B': None},
    7: {'a': 'r2', 'b': 'r2', 'c': 'r2', 'd': 'r2', '#': 'r2', 'E': None, 'A': None, 'B': None},
    8: {'a': 'r3', 'b': 'r3', 'c': 'r3', 'd': 'r3', '#': 'r3', 'E': None, 'A': None, 'B': None},
    9: {'a': 'r5', 'b': 'r5', 'c': 'r5', 'd': 'r5', '#': 'r5', 'E': None, 'A': None, 'B': None},
    10: {'a': 'r4', 'b': 'r4', 'c': 'r4', 'd': 'r4', '#': 'r4', 'E': None, 'A': None, 'B': None},
    11: {'a': 'r6', 'b': 'r6', 'c': 'r6', 'd': 'r6', '#': 'r6', 'E': None, 'A': None, 'B': None},
}
# 产生式
Product = {
    0: {'S': 'E'},
    1: {'E': 'aA'},
    2: {'E': 'bB'},
    3: {'A': 'cA'},
    4: {'A': 'd'},
    5: {'B': 'cB'},
    6: {'B': 'd'},
}
# 终结符
VT = ['a', 'b', 'c', 'd', '#']
# 非终结符
VN = ['S', 'A', 'B', 'E']

# 记录分析结果
analyzeResult = False
# 记录分析步骤
analyzeStep = 0
# 状态栈、符号栈、字符串栈
stateStack = Stack()
symbolStack = Stack()
stringStack = Stack()


# 字符串翻转
def reverseString(string):
    return string[::-1]

# 检查输入串
def checkString(string):
    stringLegal = True
    if (len(string) == 0):
        print("输入出错：输入串不能为空！")
        stringLegal = False
    if (string[-1] != "#"):
        print("输入出错：输入串缺少结束符'#'！")
        stringLegal = False
    for i in range(len(string)):
        if (string[i] not in VT):
            print("输入出错：存在不是终结符的字符！")
            stringLegal = False
            break
    return stringLegal


# 初始化三个栈
def initStack(string):
    # 状态栈，入栈0
    stateStack.push(0)
    # 符号栈，入栈#
    symbolStack.push('#')
    # 输入串入栈，即string逆序入栈
    stringStack.push_list(reverseString(string))
    # 调用分析函数
    toAnalyze()

# 根据栈中内容进行分析
def toAnalyze():
    global analyzeResult
    global analyzeStep
    analyzeStep += 1
    stateStack_top = stateStack.peek()
    stringStack_top = stringStack.peek()
    curren = LR0_table[stateStack_top][stringStack_top]

    # LR(0)分析表中查到None
    if (curren == None):
        print(
            "|{:^5}|{:^20}|{:^20}|{:^20}|{:^10}|{:^10}|".format(analyzeStep, stateStack.bottom_output(),
                                                               symbolStack.bottom_output(), stringStack.top_output(),
                                                               'None', ''))
        print("错误：Action值为None!")
        analyzeResult = False
        return

    # LR(0)分析表中查到acc
    if (curren == 'acc'):
        print(
            "|{:^5}|{:^20}|{:^20}|{:^20}|{:^10}|{:^10}|".format(analyzeStep, stateStack.bottom_output(),
                                                               symbolStack.bottom_output(), stringStack.top_output(),
                                                               'acc', ''))
        analyzeResult = True
        return

    # LR(0)分析表中查到S
    elif (curren[0] == 'S' ):
        print(
            "|{:^5}|{:^20}|{:^20}|{:^20}|{:^10}|{:^10}|".format(analyzeStep, stateStack.bottom_output(),
                                                               symbolStack.bottom_output(), stringStack.top_output(),
                                                               curren, ''))
        # 状态栈进S下标
        curren = curren.replace('S', '')
        stateStack.push(int(curren))
        # 字符栈弹栈顶部元素进符号栈
        symbolStack.push(stringStack.pop())
        # 接着分析
        toAnalyze()

    # LR(0)分析表中查到r
    elif (curren[0] == 'r' ):
        # 保存一下curren, stateStack和symbolStack,，以便后续打印出来
        save_curren = curren
        save_stateStack = stateStack.deep_copy()
        save_symbolStack = symbolStack.deep_copy()
        # 根据r下标，寻找归约所用的产生式的key和value
        curren = curren.replace('r', '')
        key = list(Product[int(curren)].keys())[0]
        value = list(Product[int(curren)].values())[0]
        # 根据产生式左部value的长度，对状态站和符号栈进行退栈操作
        val_len = len(value)
        stateStack.pop_list(val_len)
        symbolStack.pop_list(val_len)
        # 根据状态站当前栈顶元素和产生式左部key，寻找GOTO值
        state_top = stateStack.peek()
        tmp_GOTO = LR0_table[state_top][key]
        # GOTO值为None，打印错误信息
        if (tmp_GOTO == None):
            print(
                "|{:^5}|{:^20}|{:^20}|{:^20}|{:^10}|{:^10}|".format(analyzeStep, save_stateStack.bottom_output(),
                                                                   save_symbolStack.bottom_output(),
                                                                   stringStack.top_output(),
                                                                   save_curren, 'None'))
            print("错误：GOTO值为None!")
            analyzeResult = False
            return
        # GOTO值不为None,将GOTO值入状态栈，产生式左部key入符号栈
        else:
            print(
                "|{:^5}|{:^20}|{:^20}|{:^20}|{:^10}|{:^10}|".format(analyzeStep, save_stateStack.bottom_output(),
                                                                   save_symbolStack.bottom_output(),
                                                                   stringStack.top_output(),
                                                                   save_curren, tmp_GOTO))
            stateStack.push(tmp_GOTO)
            symbolStack.push(key)
            toAnalyze()

if __name__ == '__main__':
    print("请输入待分析的字符串：")
    string = input()
    # 滤空格
    string = string.replace(" ", "")
    if (checkString(string)):
        print(
            "|{:^4}|{:^18}|{:^18}|{:^18}|{:^10}|{:^10}|".format('步骤', '状态栈', '符号栈', '输入串', 'Action', 'GOTO'))
        initStack(string)
        if (analyzeResult):
            print("由以上分析可知，该串是文法的合法句子。\n")
        else:
            print("由以上分析可知，该串不是文法的合法句子。\n")