61 lines
1.8 KiB
Markdown
61 lines
1.8 KiB
Markdown
## 权重抽奖
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### 轮盘赌
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适合奖品数量较少，一次性抽奖的场景
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核心顺序遍历，逐个减权重：是用一个随机数 `r`，依次减去每个奖品的权重，当 `r` 变成负数的那一刻，说明它“落入了”当前奖品的权重区间。时间复杂度 **O(n)**，空间复杂度**O(1)**
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```go
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func Draw(rewards []*Reward) *Reward {
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totalWeight := 0
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for _, r := range rewards {
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totalWeight += r.Weight
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}
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r := rand.Intn(totalWeight) // [0, totalWeight)
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for _, reward := range rewards {
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r -= reward.Weight
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if r < 0 {
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return reward
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}
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}
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return rewards[len(rewards)-1] // 兜底，理论上不会走到
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}
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```
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### 前缀和 + 二分查找
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适合奖品数量较多，需要频繁抽奖的通用场景
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核心是构建前缀和数组，二分查找：把权重想象成一条线段，每个奖品占据一段，生成 `[0, 100)` 的随机数，落在哪个区间就中哪个奖品。二分查找快速定位区间，时间复杂度 **O(log n)**，空间复杂度**O(n)**
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```
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权重: 50 25 15 7 2 1
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├─────────┼────────┼──────┼────┼──┼──┤
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0 50 75 90 97 99 100
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← 谢谢参与 →←5元券→←10元券→←月卡→←年卡→←大奖→
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```
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```go
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type Reward struct {
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Name string
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Weight int
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}
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func Draw(rewards []*Reward) *Reward {
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prefixSumArray := make([]int, len(rewards)) // 前缀和数组
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totalWeight := 0 // 总权重
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for i, p := range rewards {
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totalWeight += p.Weight
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prefixSumArray[i] = totalWeight
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fmt.Println(totalWeight)
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}
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r := rand.Intn(totalWeight) // r ∈ [0, totalWeight-1]
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idx := sort.SearchInts(prefixSumArray, r+1) // 查找目标 ∈ [1, totalWeight]
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return rewards[idx]
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}
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```
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