对于任意的上下文无关文法，编写一个Python程序，读入该文法，判断该文法是否为LL (1)文法:如果是LL (1)文法，则构造并输出该文法的LL (1)分析表

以下是一个简单的Python程序实现：

# 输入文法
grammar = input("请输入文法（每个产生式一行，用->表示产生式）：\n")

# 分离非终结符和终结符
non_terminals = set()
terminals = set()
productions = []
for production in grammar.split('\n'):
    if not production:
        continue
    left, right = production.split('->')
    non_terminals.add(left.strip())
    for symbol in right.split():
        if symbol.isupper():
            non_terminals.add(symbol)
        elif symbol != 'ε':
            terminals.add(symbol)
    productions.append((left.strip(), right.split()))

# 计算FIRST集合
first = {}
for symbol in non_terminals | terminals:
    first[symbol] = set()
for symbol in terminals:
    first[symbol].add(symbol)
for symbol in non_terminals:
    first[symbol] = set()
while True:
    updated = False
    for left, right in productions:
        for symbol in right:
            if symbol in terminals:
                if symbol not in first[left]:
                    first[left].add(symbol)
                    updated = True
                break
            for f in first[symbol]:
                if f != 'ε' and f not in first[left]:
                    first[left].add(f)
                    updated = True
            if 'ε' not in first[symbol]:
                break
        else:
            if 'ε' not in first[left]:
                if 'ε' not in first.get('', set()):
                    first[''].add('ε')
                    updated = True
                if 'ε' not in first[left]:
                    first[left].add('ε')
                    updated = True
    if not updated:
        break

# 计算FOLLOW集合
follow = {symbol: set() for symbol in non_terminals}
follow[grammar[0]] = {'$'}
while True:
    updated = False
    for left, right in productions:
        for i, symbol in enumerate(right):
            if symbol in terminals:
                continue
            rest = set(right[i + 1:])
            if not rest or 'ε' in first[rest]:
                for f in follow[left]:
                    if f not in follow[symbol]:
                        follow[symbol].add(f)
                        updated = True
            for f in first[rest]:
                if f != 'ε' and f not in follow[symbol]:
                    follow[symbol].add(f)
                    updated = True
    if not updated:
        break

# 构造LL(1)分析表
table = {}
for left, right in productions:
    for symbol in first[right]:
        if symbol != 'ε':
            table[left, symbol] = right
    if 'ε' in first[right]:
        for symbol in follow[left]:
            table[left, symbol] = right
for symbol in terminals | {'$'}:
    table['', symbol] = [('synch',)]

# 判断是否为LL(1)文法
ll1 = True
for left1, right1 in productions:
    for left2, right2 in productions:
        if left1 != left2:
            continue
        for symbol1 in first[right1]:
            if symbol1 == 'ε':
                continue
            if (left1, symbol1) in table and table[left1, symbol1] != right1:
                ll1 = False
            elif (left1, symbol1) not in table:
                table[left1, symbol1] = ('synch',)
        for symbol2 in first[right2]:
            if symbol2 == 'ε':
                continue
            if (left1, symbol2) in table and table[left1, symbol2] != right2:
                ll1 = False
            elif (left1, symbol2) not in table:
                table[left1, symbol2] = ('synch',)

# 输出结果
if ll1:
    print("该文法是LL(1)文法，LL(1)分析表如下：")
    print(" " * 7, end='')
    for symbol in terminals | {'$'}:
        print(f"{symbol:^10}", end='')
    print()
    for symbol in non_terminals:
        print(f"{symbol:5} ->", end='')
        for t in terminals | {'$'}:
            if (symbol, t) in table:
                print(f" {symbol:5} -> {' '.join(table[symbol, t]):5}", end='')
            else:
                print(" " * 10, end='')
        print()
else:
    print("该文法不是LL(1)文法！")

该程序先读入文法，然后进行文法分析，得到非终结符集合、终结符集合、产生式集合等信息。接着，根据LL(1)文法的定义，依次计算FIRST集合和FOLLOW集合，并根据它们构造出LL(1)分析表。最后，判断该文法是否为LL(1)文法，并输出LL(1)分析表。