redis存储空间复杂度和时间复杂度的平衡

// 精度范围（rateRange）决定了数组大小
rateRange = 10000      // 万分位 (0.0001)
rateRange = 100000     // 十万分位 (0.00001)
rateRange = 1000000    // 百万分位 (0.000001)

rateRange = 10000
awardCount = 100
slotsPerAward = 100  // 每个奖品100个槽位

内存占用 = 10000 × 4 bytes = 40 KB
✅ 可接受

rateRange = 100000
awardCount = 100
slotsPerAward = 1000  // 每个奖品1000个槽位

内存占用 = 100000 × 4 bytes = 400 KB
✅ 可接受，但增长明显

rateRange = 1000000
awardCount = 100
slotsPerAward = 10000  // 每个奖品10000个槽位

内存占用 = 1000000 × 4 bytes = 4 MB
⚠️ 开始需要注意

rateRange = 100000
awardCount = 1000
slotsPerAward = 100  // 每个奖品100个槽位

内存占用 = 100000 × 4 bytes = 400 KB
✅ 可接受

rateRange = 1000000
awardCount = 1000
slotsPerAward = 1000  // 每个奖品1000个槽位

内存占用 = 1000000 × 4 bytes = 4 MB
⚠️ 内存占用较大

// 存储随机数到奖品的映射
int[] awardMappingArray = new int[rateRange];  // 固定大小数组

// 例如：rateRange = 1000000
// 内存 = 1000000 × 4 bytes = 4 MB

// 存储奖品信息和前缀和
List<StrategyAwardEntity> awards = new ArrayList<>();  // 奖品列表
double[] prefixSums = new double[awardCount];          // 前缀和数组

// 例如：awardCount = 1000
// 内存 = 1000 × (award对象大小 + 8 bytes) ≈ 100 KB

rateRange >> awardCount 时，O(logn) 更节省内存
rateRange ≈ awardCount 时，两者内存相近

/**
 * O(1)抽奖算法 - 预热时生成固定大小数组
 * 优点：查询时间O(1)
 * 缺点：内存占用与rateRange成正比
 */
public Integer raffleStrategyO1(Long strategyId, 
        List<StrategyAwardEntity> strategyAwardEntities) {
    
    // 1. 获取精度范围
    BigDecimal minAwardRate = minAwardRate(strategyAwardEntities);
    int rateRange = convert(minAwardRate);  // 例如：10000, 100000, 1000000
    
    // 2. 分配数组（内存占用 = rateRange × 4 bytes）
    int[] strategyAwardRateRandom = new int[rateRange];
    
    // 3. 填充数组
    int currentIndex = 0;
    for (StrategyAwardEntity award : strategyAwardEntities) {
        // 计算该奖品应该占用的槽位数
        int awardSlots = (int) (award.getAwardRate() * rateRange);
        
        // 填充槽位
        for (int i = 0; i < awardSlots; i++) {
            if (currentIndex >= rateRange) break;
            strategyAwardAwardRateRandom[currentIndex++] = award.getAwardId();
        }
    }
    
    // 4. 随机打乱（消除初始顺序偏差）
    shuffle(strategyAwardAwardRateRandom);
    
    // 5. 抽奖（O(1)时间复杂度）
    int randomIndex = ThreadLocalRandom.current().nextInt(rateRange);
    return strategyAwardAwardRateRandom[randomIndex];
}

/**
 * O(logn)抽奖算法 - 实时计算前缀和
 * 优点：内存占用与awardCount成正比，与rateRange无关
 * 缺点：查询时间O(logn)，需要每次计算
 */
public Integer raffleStrategyLogn(Long strategyId, 
        List<StrategyAwardEntity> strategyAwardEntities) {
    
    // 1. 计算最小精度（用于确定随机数范围）
    BigDecimal minAwardRate = minAwardRate(strategyAwardEntities);
    int rateRange = convert(minAwardRate);  // 例如：100000, 1000000
    
    // 2. 构建前缀和数组（内存占用 = awardCount × 8 bytes）
    double[] awardRates = new double[strategyAwardEntities.size()];
    double[] prefixSums = new double[strategyAwardEntities.size()];
    
    for (int i = 0; i < strategyAwardEntities.size(); i++) {
        StrategyAwardEntity award = strategyAwardEntities.get(i);
        awardRates[i] = award.getAwardRate();
        
        if (i == 0) {
            prefixSums[i] = awardRates[i];
        } else {
            prefixSums[i] = prefixSums[i - 1] + awardRates[i];
        }
    }
    
    // 3. 生成随机数
    int randomValue = ThreadLocalRandom.current().nextInt(rateRange);
    double randomRate = (double) randomValue / rateRange;
    
    // 4. 二分查找（O(logn)时间复杂度）
    int left = 0;
    int right = prefixSums.length - 1;
    
    while (left < right) {
        int mid = (left + right) / 2;
        if (prefixSums[mid] < randomRate) {
            left = mid + 1;
        } else {
            right = mid;
        }
    }
    
    return strategyAwardEntities.get(left).getAwardId();
}

/**
 * 综合考虑槽位数和内存占用的算法选择
 */
public Integer raffleStrategy(Long strategyId, 
        List<StrategyAwardEntity> strategyAwardEntities) {
    
    // 1. 计算精度范围
    BigDecimal minAwardRate = minAwardRate(strategyAwardEntities);
    int rateRange = convert(minAwardRate);  // 10000, 100000, 1000000...
    
    int awardCount = strategyAwardEntities.size();
    int slotsPerAward = rateRange / awardCount;
    
    // 2. 计算内存占用
    long o1MemoryBytes = (long) rateRange * 4;  // O(1)数组内存
    long lognMemoryBytes = (long) awardCount * 40;  // O(logn)奖品对象内存估算
    
    // 3. 算法选择条件
    // 条件1：槽位数 >= 10（保证公平性）
    // 条件2：内存占用可接受（O(1)算法不超过10MB）
    if (slotsPerAward >= 10 && o1MemoryBytes <= 10 * 1024 * 1024) {
        // 使用O(1)算法
        return raffleStrategyO1(strategyId, strategyAwardEntities);
    } else {
        // 使用O(logn)算法
        return raffleStrategyLogn(strategyId, strategyAwardEntities);
    }
}

/**
 * 内存优化：如果rateRange非常大，使用压缩算法
 */
public Integer raffleStrategyCompressed(Long strategyId, 
        List<StrategyAwardEntity> strategyAwardEntities) {
    
    BigDecimal minAwardRate = minAwardRate(strategyAwardEntities);
    int rateRange = convert(minAwardRate);
    
    // 如果rateRange > 1000000，使用Run-Length Encoding压缩
    if (rateRange > 1000000) {
        return raffleStrategyCompressed(strategyId, strategyAwardEntities);
    }
    
    // 正常O(1)算法
    return raffleStrategyO1(strategyId, strategyAwardEntities);
}

/**
 * Run-Length Encoding压缩存储
 * 例如：[A,A,A,B,B,C,C,C,C] → [(A,3), (B,2), (C,4)]
 */
class CompressedArray {
    int[] awardIds;     // 奖品ID数组（去重后的）
    int[] runLengths;   // 每个奖品连续出现的次数
    
    // 随机抽奖
    public int raffle() {
        // 1. 计算总长度
        int totalLength = Arrays.stream(runLengths).sum();
        
        // 2. 生成随机位置
        int randomPosition = ThreadLocalRandom.current().nextInt(totalLength);
        
        // 3. 查找对应的奖品
        int currentPosition = 0;
        for (int i = 0; i < runLengths.length; i++) {
            currentPosition += runLengths[i];
            if (randomPosition < currentPosition) {
                return awardIds[i];
            }
        }
        
        return awardIds[awardIds.length - 1];
    }
}

/**
 * 分级缓存策略：根据访问频率选择不同的存储方式
 */
public class TieredStrategyCache {
    
    // 热数据：高频访问的奖品，使用O(1)数组
    private int[] hotAwardsArray;
    
    // 冷数据：低频访问的奖品，使用O(logn)列表
    private List<StrategyAwardEntity> coldAwardsList;
    
    // 访问统计
    private Map<Long, AtomicInteger> accessCountMap = new ConcurrentHashMap<>();
    
    // 定期调整热冷数据
    public void rebalance() {
        // 统计访问频率
        Map<Long, Integer> sortedAwards = accessCountMap.entrySet().stream()
            .sorted(Map.Entry.comparingByValue())
            .limit(100)  // 取访问最多的100个奖品
            .collect(Collectors.toMap(
                Map.Entry::getKey,
                Map.Entry::getValue,
                (e1, e2) -> e1,
                LinkedHashMap::new
            ));
        
        // 将高频奖品放入热数据
        rebuildHotAwardsArray(sortedAwards.keySet());
    }
}

/**
 * 懒加载策略：只有首次访问时才加载数据
 */
public class LazyStrategyCache {
    
    private volatile int[] cachedArray = null;
    private volatile List<StrategyAwardEntity> cachedAwards = null;
    
    // 懒加载O(1)数组
    public int[] getO1Array(List<StrategyAwardEntity> awards) {
        if (cachedArray == null) {
            synchronized (this) {
                if (cachedArray == null) {
                    // 只在首次访问时计算
                    cachedArray = buildStrategyArray(awards);
                }
            }
        }
        return cachedArray;
    }
    
    // 懒加载O(logn)列表
    public List<StrategyAwardEntity> getAwardsList() {
        if (cachedAwards == null) {
            synchronized (this) {
                if (cachedAwards == null) {
                    cachedAwards = loadAwardsFromDB();
                }
            }
        }
        return cachedAwards;
    }
}