lua实现游戏抽奖的几种方法

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---

 假设配置如下：

 local reward_pool = {
     {weight = , item = {, num = }},
     {weight = , item = {, num = }},
     {weight = , item = {, num = }},
     {weight = , item = {, num = }},
     {weight = , item = {, num = }},
     {weight = , item = {, num = }},
 }

1.顺序查找，预处理时间复杂度O(n)，抽奖最坏情况O(n)

 --预处理
 local N = #reward_pool
 
 for _, v in ipairs(reward_pool) do
     total_weight = total_weight + v.weight
 end
 
 --实现
 local rand_weight = math.random(total_weight)
 local reward_index
 
 for k, v in ipairs(reward_pool) do
     _total_weight = _total_weight + v.weight
     if _total_weight >= rand_weight then
         reward_index = k
         break
     end
 end

---

2.按照离散思路进行分割，二分查找，预处理时间复杂度O(n)，抽奖最坏情况O(logn)

 --预处理
 local N = #reward_pool
 
 for _, v in ipairs(reward_pool) do
     com_weight = com_weight + v.weight
     v.weight = com_weight
 end
 
 --实现
 , #reward_pool
 while right >= left then
     )
     local mid_weight = reward_pool[mid].weight
     if value == mid_weight then
         right = right -
         break
     elseif value < mid_weight then
         right = mid -
     else
         left = mid +
     end
 end
 right = right +  --此时right为reward_pool中抽到的索引

这种方法在实际上是对第一种方法的优化，在大多数情况下都可以取代第一种方法，但取舍还要看实际情况，一个极端且明显的例子如下：

 local reward_pool = {
     {weight = , item = {, num = }}, {weight = , item = {, num = }},
     {weight = , item = {, num = }}, {weight = , item = {, num = }},
     {weight = , item = {, num = }}, {weight = , item = {, num = }},
     {weight = , item = {, num = }}, {weight = , item = {, num = }},
     {weight = , item = {, num = }}, {weight = , item = {, num = }},
 }

---

3.AliasMethod，个人实现的预处理O(3n)，抽奖时间复杂度O(1)，下面是实现过程，证明日后有时间再整理给出

 queue = {}
 
 function queue:new()
     , last = -}
     self.__index = self
     setmetatable(res, self)
     return res
 end
 
 function queue:push(value)
     self.last = self.last +
     self[self.last] = value
 end
 
 function queue:pop()
     local first = self.first
     if first > self.last then
         self.first =
         self.last = -
         return nil
     end
     local value = self[first]
     self[first] = nil
     self.first = self.first +
     return value
 end
 
 function queue:front()
     return self[self.first]
 end
 
 --预处理
 local N = #reward_pool
 
 for _, v in ipairs(reward_pool) do
     total_weight = total_weight + v.weight
 end
 
 local Prob = {}
 local Alias = {}
 local weightN_queue_L = queue:new()
 local weightN_queue_U = queue:new()
 for k, v in ipairs(reward_pool) do
     local weight_N = v.weight * N
     if weight_N == total_weight then
         Prob[k] = weight_N
     else
         local tb = {index = k, value = weight_N}
         local qu = weight_N > total_weight and weightN_queue_U or weightN_queue_L
         qu:push(tb)
     end
 end
 
 while true do
     local l_qu = weightN_queue_L:pop()
     if not l_qu then
         break
     end
     local u_qu = weightN_queue_U:front() --或直接pop，比total_weight大再push回去
     Prob[l_qu.index] = l_qu.value
     Alias[l_qu.index] = u_qu.index
     u_qu.value = u_qu.value + l_qu.value - total_weight
     if u_qu.value < total_weight then
         weightN_queue_U:pop()
         weightN_queue_L:push(u_qu)
     elseif u_qu.value == total_weight then
         weightN_queue_U:pop()
         Prob[u_qu.index] = total_weight
     end
 end
 weightN_queue_U = nil
 weightN_queue_L = nil
 
 --实现
 local n = math.random(N)
 local weight = math.random(total_weight)
 local reward_index = weight > Prob[n] and Alias[n] or n