题目详细如下：
源代码
import torch
import torch.nn as nn
import torch.optim as optim
import random#数据准备与预处理
def generate_data(num_samples, max_n=5):data = []for _ in range(num_samples):n = random.randint(1, max_n)seq = '0' * n + '1' * n data.append(seq)return datadef encode_seq(seq, max_len):encoded = [0 if c == '0' else 1 for c in seq]padded = encoded + [2] * (max_len - len(encoded)) #2为填充符return torch.tensor(padded, dtype=torch.long)max_n = 5
max_seq_len = 2 * max_n
train_data = generate_data(1000, max_n)#定义LSTM模型
class SeqGenerate(nn.Module):def __init__(self, vocab_size=3, embed_dim=8, hidden_dim=16):super().__init__()self.embedding = nn.Embedding(vocab_size, embed_dim)self.lstm = nn.LSTM(embed_dim, hidden_dim, batch_first=True)self.fc = nn.Linear(hidden_dim, vocab_size)def forward(self, x, hidden=None):# x形状：（batch_size, seq_len）x = self.embedding(x)x, hidden = self.lstm(x, hidden)logits = self.fc(x)return logits, hidden#训练模型
model = SeqGenerate()
criterion = nn.CrossEntropyLoss(ignore_index=2)
optimizer = optim.Adam(model.parameters(), lr=0.001)
#训练循环
epochs = 50
batch_size = 32
for epoch in range(epochs):total_loss = 0random.shuffle(train_data)for i in range(0, len(train_data), batch_size):batch = train_data[i: (i+batch_size)]inputs = [encode_seq(seq[:-1], max_seq_len-1) for seq in batch]labels = [encode_seq(seq[1:], max_seq_len-1) for seq in batch]inputs = torch.stack(inputs)labels = torch.stack(labels)optimizer.zero_grad()logits, _ = model(inputs)loss = criterion(logits.reshape(-1, 3), labels.reshape(-1))loss.backward()optimizer.step()total_loss += loss.item()if (epoch + 1) % 10 == 0:print(f"Epoch {epoch+1}, Loss:{total_loss / len(train_data):.4f}")#生成 0n 1n序列
def generate_seq(model, start_char='0', target_n=3):model.eval()seq = [start_char]hidden = Nonefor _ in range(target_n - 1):input_tensor = torch.tensor([[0]], dtype=torch.long)logits, hidden = model(input_tensor, hidden)next_char = torch.argmax(logits, dim=-1).item()seq.append('0' if next_char == 0 else '1')for _ in range(target_n):nput_tensor = torch.tensor([[1]], dtype=torch.long)logits, hidden = model(input_tensor, hidden)next_char = torch.argmax(logits, dim=-1).item()seq.append('0' if next_char == 0 else '1')return ''.join(seq)generate_seq = generate_seq(model, target_n=3)
print(f"生成的0^n 1^n序列：{generate_seq}")输出结果：
