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def max_happiness(n, k, ai):
    # 動態規劃表格,dp[i]表示前i天的最大幸福值
    dp = [0] * (n + 1)
    
    # 追蹤連續抱蘿莉的天數
    continuous_days = 0
    
    for i in range(1, n + 1):
        # 選擇該天不抱蘿利
        dp[i] = dp[i - 1]
        
        # 如果可以吃蘋果且不會連續超過k+1天
        if continuous_days < k:
            dp[i] = max(dp[i], dp[i - 1] + ai*k)
            continuous_days += 1
        else:
            continuous_days = 0
    
    return dp[n]

# 範例使用
n = 10  # 設定最近n天
k = 3   # 設定一天最多能抱蘿莉數量
ai = 5   # 抱蘿莉增加ai的幸福值

result = max_happiness(n, k, ai)
print(f"在不出事的情形下,最大化的幸福值是: {result}")
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