第一类是常见的有等级的抽奖活动,如一等、二等、三等奖等等
// 分别为一、二、三、四等将的奖品数量,最后一个为未中奖的数量。
private static final Integer[] lotteryList = {5, 10, 20, 40, 100};
private int getSum() {
int sum = 0;
for (int v : lotteryList) {
sum += v;
}
return sum;
}
private int getLotteryLevel() {
Random random = new Random(System.nanoTime());
int sum = getSum();
for (int i = 0; i < lotteryList.length; ++i) {
int randNum = Math.abs(random.nextInt()) % sum;
if (randNum <= lotteryList[i]) {
return i;
} else {
sum -= lotteryList[i];
}
}
return -1;
}
第二类是不分等级的抽奖活动,仅需要参与人数与奖品总数,各奖品中奖概率相等。
//另一种抽奖算法,用于公司抽奖,即总参与人数与奖品数固定。
private static final int lotteryNum = 75;
private static final int total = 175;
private static Set<Integer> lotterySet = new HashSet<Integer>();
static {
for (int i=1; i <= lotteryNum; ++i) {
lotterySet.add(total*i/lotteryNum);
}
}
private int getLotteryNum2() {
Random rand = new Random(System.nanoTime());
int randNum = Math.abs(rand.nextInt()) % total;
if (lotterySet.contains(randNum)) {
return randNum*lotteryNum/total;
}
return -1;
}
第三类 一个商场进行一场抽奖活动,其中有两个奖项,第一个奖项A抽中的概率是1/6,第二个奖项B抽中的概率是5/6;编码实现这个抽奖程序。
思路:
这题考察队随机函数的应用。
由于rand()函数产生的随机数的范围是0-65535,那么将该随机数对6求余,得到的数在0-5之间,且每个数出现概率相等。
[cpp]
- #include <iostream>
- #include <cstdio>
- #include <cstdlib>
- #include <ctime>
- #include <algorithm>
- using namespace std;
- char Draw()
- {
- int num = rand() % 6;
- if (num == 0) return 'A';
- else return 'B';
- }
- int main()
- {
- srand((unsigned int)time(0)); //注意:srand函数一定不能在循环里
- for (int i = 0; i < 36; i++)
- {
- cout << Draw() << endl;
- }
- return 0;
- }
第四类 : 不同概率抽奖
- VO类:Gift.java 具体对应就是上面表格里的内容
[java]
- <code class="hljs java" style=""><span class="hljs-keyword" style="">public</span> <span class="hljs-class" style=""><span class="hljs-keyword" style=""><span class="hljs-class" style=""><span class="hljs-keyword" style="">class</span></span></span><span class="hljs-class" style=""> </span><span class="hljs-title" style=""><span class="hljs-class" style=""><span class="hljs-title" style="">Gift</span></span></span><span class="hljs-class" style=""> </span></span>{
- <span class="hljs-keyword" style="">private</span> <span class="hljs-keyword" style="">int</span> index;
- <span class="hljs-keyword" style="">private</span> String gitfId;
- <span class="hljs-keyword" style="">private</span> String giftName;
- <span class="hljs-keyword" style="">private</span> <span class="hljs-keyword" style="">double</span> probability;
- <span class="hljs-function" style=""><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">public</span></span></span><span class="hljs-function" style=""> </span><span class="hljs-title" style=""><span class="hljs-function" style=""><span class="hljs-title" style="">Gift</span></span></span><span class="hljs-params" style=""><span class="hljs-function" style=""><span class="hljs-params" style="">(</span></span><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-params" style=""><span class="hljs-keyword" style="">int</span></span></span></span><span class="hljs-function" style=""><span class="hljs-params" style=""> index, String gitfId, String giftName, </span></span><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-params" style=""><span class="hljs-keyword" style="">double</span></span></span></span><span class="hljs-function" style=""><span class="hljs-params" style=""> probability)</span></span></span><span class="hljs-function" style=""> </span></span>{
- <span class="hljs-keyword" style="">this</span>.index = index;
- <span class="hljs-keyword" style="">this</span>.gitfId = gitfId;
- <span class="hljs-keyword" style="">this</span>.giftName = giftName;
- <span class="hljs-keyword" style="">this</span>.probability = probability;
- }
- <span class="hljs-function" style=""><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">public</span></span></span><span class="hljs-function" style=""> </span><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">int</span></span></span><span class="hljs-function" style=""> </span><span class="hljs-title" style=""><span class="hljs-function" style=""><span class="hljs-title" style="">getIndex</span></span></span><span class="hljs-params" style=""><span class="hljs-function" style=""><span class="hljs-params" style="">()</span></span></span><span class="hljs-function" style=""> </span></span>{
- <span class="hljs-keyword" style="">return</span> index;
- }
- <span class="hljs-function" style=""><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">public</span></span></span><span class="hljs-function" style=""> </span><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">void</span></span></span><span class="hljs-function" style=""> </span><span class="hljs-title" style=""><span class="hljs-function" style=""><span class="hljs-title" style="">setIndex</span></span></span><span class="hljs-params" style=""><span class="hljs-function" style=""><span class="hljs-params" style="">(</span></span><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-params" style=""><span class="hljs-keyword" style="">int</span></span></span></span><span class="hljs-function" style=""><span class="hljs-params" style=""> index)</span></span></span><span class="hljs-function" style=""> </span></span>{
- <span class="hljs-keyword" style="">this</span>.index = index;
- }
- <span class="hljs-function" style=""><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">public</span></span></span><span class="hljs-function" style=""> String </span><span class="hljs-title" style=""><span class="hljs-function" style=""><span class="hljs-title" style="">getGitfId</span></span></span><span class="hljs-params" style=""><span class="hljs-function" style=""><span class="hljs-params" style="">()</span></span></span><span class="hljs-function" style=""> </span></span>{
- <span class="hljs-keyword" style="">return</span> gitfId;
- }
- <span class="hljs-function" style=""><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">public</span></span></span><span class="hljs-function" style=""> </span><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">void</span></span></span><span class="hljs-function" style=""> </span><span class="hljs-title" style=""><span class="hljs-function" style=""><span class="hljs-title" style="">setGitfId</span></span></span><span class="hljs-params" style=""><span class="hljs-function" style=""><span class="hljs-params" style="">(String gitfId)</span></span></span><span class="hljs-function" style=""> </span></span>{
- <span class="hljs-keyword" style="">this</span>.gitfId = gitfId;
- }
- <span class="hljs-function" style=""><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">public</span></span></span><span class="hljs-function" style=""> String </span><span class="hljs-title" style=""><span class="hljs-function" style=""><span class="hljs-title" style="">getGiftName</span></span></span><span class="hljs-params" style=""><span class="hljs-function" style=""><span class="hljs-params" style="">()</span></span></span><span class="hljs-function" style=""> </span></span>{
- <span class="hljs-keyword" style="">return</span> giftName;
- }
- <span class="hljs-function" style=""><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">public</span></span></span><span class="hljs-function" style=""> </span><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">void</span></span></span><span class="hljs-function" style=""> </span><span class="hljs-title" style=""><span class="hljs-function" style=""><span class="hljs-title" style="">setGiftName</span></span></span><span class="hljs-params" style=""><span class="hljs-function" style=""><span class="hljs-params" style="">(String giftName)</span></span></span><span class="hljs-function" style=""> </span></span>{
- <span class="hljs-keyword" style="">this</span>.giftName = giftName;
- }
- <span class="hljs-function" style=""><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">public</span></span></span><span class="hljs-function" style=""> </span><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">double</span></span></span><span class="hljs-function" style=""> </span><span class="hljs-title" style=""><span class="hljs-function" style=""><span class="hljs-title" style="">getProbability</span></span></span><span class="hljs-params" style=""><span class="hljs-function" style=""><span class="hljs-params" style="">()</span></span></span><span class="hljs-function" style=""> </span></span>{
- <span class="hljs-keyword" style="">return</span> probability;
- }
- <span class="hljs-function" style=""><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">public</span></span></span><span class="hljs-function" style=""> </span><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">void</span></span></span><span class="hljs-function" style=""> </span><span class="hljs-title" style=""><span class="hljs-function" style=""><span class="hljs-title" style="">setProbability</span></span></span><span class="hljs-params" style=""><span class="hljs-function" style=""><span class="hljs-params" style="">(</span></span><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-params" style=""><span class="hljs-keyword" style="">double</span></span></span></span><span class="hljs-function" style=""><span class="hljs-params" style=""> probability)</span></span></span><span class="hljs-function" style=""> </span></span>{
- <span class="hljs-keyword" style="">this</span>.probability = probability;
- }
- <span class="hljs-meta" style="">@Override</span>
- <span class="hljs-function" style=""><span class="hljs-keyword" style=""><span class="hljs-function" style=""><span class="hljs-keyword" style="">public</span></span></span><span class="hljs-function" style=""> String </span><span class="hljs-title" style=""><span class="hljs-function" style=""><span class="hljs-title" style="">toString</span></span></span><span class="hljs-params" style=""><span class="hljs-function" style=""><span class="hljs-params" style="">()</span></span></span><span class="hljs-function" style=""> </span></span>{
- <span class="hljs-keyword" style="">return</span> <span class="hljs-string" style="">"Gift [index="</span> + index + <span class="hljs-string" style="">", gitfId="</span> + gitfId + <span class="hljs-string" style="">", giftName="</span> + giftName + <span class="hljs-string" style="">", probability="</span> + probability + <span class="hljs-string" style="">"]"</span>;
- }
- }</code>
- Util类:LotteryUtil.java 真正的不同概率的抽奖工具类
[java]
- <code class="hljs groovy" style=""><span class="hljs-keyword" style="">import</span> java.util.ArrayList;
- <span class="hljs-keyword" style="">import</span> java.util.Collections;
- <span class="hljs-keyword" style="">import</span> java.util.List;
- <span class="hljs-comment" style=""><span class="hljs-comment" style="">/**
- * 不同概率抽奖工具包
- *
- * </span><span class="hljs-doctag" style=""><span class="hljs-comment" style=""><span class="hljs-doctag" style="">@author</span></span></span><span class="hljs-comment" style=""> Shunli
- */</span></span>
- <span class="hljs-keyword" style="">public</span> <span class="hljs-class" style=""><span class="hljs-keyword" style=""><span class="hljs-class" style=""><span class="hljs-keyword" style="">class</span></span></span><span class="hljs-class" style=""> </span><span class="hljs-title" style=""><span class="hljs-class" style=""><span class="hljs-title" style="">LotteryUtil</span></span></span><span class="hljs-class" style=""> {</span></span>
- <span class="hljs-comment" style=""><span class="hljs-comment" style="">/**
- * 抽奖
- *
- * </span><span class="hljs-doctag" style=""><span class="hljs-comment" style=""><span class="hljs-doctag" style="">@param</span></span></span><span class="hljs-comment" style=""> orignalRates
- * 原始的概率列表,保证顺序和实际物品对应
- * </span><span class="hljs-doctag" style=""><span class="hljs-comment" style=""><span class="hljs-doctag" style="">@return</span></span></span><span class="hljs-comment" style="">
- * 物品的索引
- */</span></span>
- <span class="hljs-keyword" style="">public</span> <span class="hljs-keyword" style="">static</span> <span class="hljs-keyword" style="">int</span> lottery(List<Double> orignalRates) {
- <span class="hljs-keyword" style="">if</span> (orignalRates == <span class="hljs-literal" style="">null</span> || orignalRates.isEmpty()) {
- <span class="hljs-keyword" style="">return</span> <span class="hljs-number" style="">-1</span>;
- }
- <span class="hljs-keyword" style="">int</span> size = orignalRates.size();
- <span class="hljs-comment" style="">// 计算总概率,这样可以保证不一定总概率是1</span>
- <span class="hljs-keyword" style="">double</span> sumRate = <span class="hljs-number" style="">0</span>d;
- <span class="hljs-keyword" style="">for</span> (<span class="hljs-keyword" style="">double</span> <span class="hljs-string" style="">rate :</span> orignalRates) {
- sumRate += rate;
- }
- <span class="hljs-comment" style="">// 计算每个物品在总概率的基础下的概率情况</span>
- List<Double> sortOrignalRates = <span class="hljs-keyword" style="">new</span> ArrayList<Double>(size);
- Double tempSumRate = <span class="hljs-number" style="">0</span>d;
- <span class="hljs-keyword" style="">for</span> (<span class="hljs-keyword" style="">double</span> <span class="hljs-string" style="">rate :</span> orignalRates) {
- tempSumRate += rate;
- sortOrignalRates.add(tempSumRate / sumRate);
- }
- <span class="hljs-comment" style="">// 根据区块值来获取抽取到的物品索引</span>
- <span class="hljs-keyword" style="">double</span> nextDouble = Math.random();
- sortOrignalRates.add(nextDouble);
- Collections.sort(sortOrignalRates);
- <span class="hljs-keyword" style="">return</span> sortOrignalRates.indexOf(nextDouble);
- }
- }</code>
- Test类:Test.java
[java]
- <code class="hljs groovy" style=""><span class="hljs-keyword" style="">import</span> java.util.ArrayList;
- <span class="hljs-keyword" style="">import</span> java.util.HashMap;
- <span class="hljs-keyword" style="">import</span> java.util.List;
- <span class="hljs-keyword" style="">import</span> java.util.Map;
- <span class="hljs-keyword" style="">import</span> java.util.Map.Entry;
- <span class="hljs-comment" style=""><span class="hljs-comment" style="">/**
- * 不同概率抽奖
- *
- * </span><span class="hljs-doctag" style=""><span class="hljs-comment" style=""><span class="hljs-doctag" style="">@author</span></span></span><span class="hljs-comment" style=""> ShunLi
- */</span></span>
- <span class="hljs-keyword" style="">public</span> <span class="hljs-class" style=""><span class="hljs-keyword" style=""><span class="hljs-class" style=""><span class="hljs-keyword" style="">class</span></span></span><span class="hljs-class" style=""> </span><span class="hljs-title" style=""><span class="hljs-class" style=""><span class="hljs-title" style="">LotteryTest</span></span></span><span class="hljs-class" style=""> {</span></span>
- <span class="hljs-keyword" style="">public</span> <span class="hljs-keyword" style="">static</span> <span class="hljs-keyword" style="">void</span> main(String[] args) {
- List<Gift> gifts = <span class="hljs-keyword" style="">new</span> ArrayList<Gift>();
- <span class="hljs-comment" style="">// 序号==物品Id==物品名称==概率</span>
- gifts.add(<span class="hljs-keyword" style="">new</span> Gift(<span class="hljs-number" style="">1</span>, <span class="hljs-string" style="">"P1"</span>, <span class="hljs-string" style="">"物品1"</span>, <span class="hljs-number" style="">0.2</span>d));
- gifts.add(<span class="hljs-keyword" style="">new</span> Gift(<span class="hljs-number" style="">2</span>, <span class="hljs-string" style="">"P2"</span>, <span class="hljs-string" style="">"物品2"</span>, <span class="hljs-number" style="">0.2</span>d));
- gifts.add(<span class="hljs-keyword" style="">new</span> Gift(<span class="hljs-number" style="">3</span>, <span class="hljs-string" style="">"P3"</span>, <span class="hljs-string" style="">"物品3"</span>, <span class="hljs-number" style="">0.4</span>d));
- gifts.add(<span class="hljs-keyword" style="">new</span> Gift(<span class="hljs-number" style="">4</span>, <span class="hljs-string" style="">"P4"</span>, <span class="hljs-string" style="">"物品4"</span>, <span class="hljs-number" style="">0.3</span>d));
- gifts.add(<span class="hljs-keyword" style="">new</span> Gift(<span class="hljs-number" style="">5</span>, <span class="hljs-string" style="">"P5"</span>, <span class="hljs-string" style="">"物品5"</span>, <span class="hljs-number" style="">0</span>d));
- gifts.add(<span class="hljs-keyword" style="">new</span> Gift(<span class="hljs-number" style="">6</span>, <span class="hljs-string" style="">"P6"</span>, <span class="hljs-string" style="">"物品6"</span>, <span class="hljs-number" style="">-0.1</span>d));
- gifts.add(<span class="hljs-keyword" style="">new</span> Gift(<span class="hljs-number" style="">7</span>, <span class="hljs-string" style="">"P7"</span>, <span class="hljs-string" style="">"物品7"</span>, <span class="hljs-number" style="">0.008</span>d));
- List<Double> orignalRates = <span class="hljs-keyword" style="">new</span> ArrayList<Double>(gifts.size());
- <span class="hljs-keyword" style="">for</span> (Gift <span class="hljs-string" style="">gift :</span> gifts) {
- <span class="hljs-keyword" style="">double</span> probability = gift.getProbability();
- <span class="hljs-keyword" style="">if</span> (probability < <span class="hljs-number" style="">0</span>) {
- probability = <span class="hljs-number" style="">0</span>;
- }
- orignalRates.add(probability);
- }
- <span class="hljs-comment" style="">// statistics</span>
- Map<Integer, Integer> count = <span class="hljs-keyword" style="">new</span> HashMap<Integer, Integer>();
- <span class="hljs-keyword" style="">double</span> num = <span class="hljs-number" style="">1000000</span>;
- <span class="hljs-keyword" style="">for</span> (<span class="hljs-keyword" style="">int</span> i = <span class="hljs-number" style="">0</span>; i < num; i++) {
- <span class="hljs-keyword" style="">int</span> orignalIndex = LotteryUtil.lottery(orignalRates);
- Integer value = count.get(orignalIndex);
- count.put(orignalIndex, value == <span class="hljs-literal" style="">null</span> ? 1 : value + <span class="hljs-number" style="">1</span>);
- }
- <span class="hljs-keyword" style="">for</span> (Entry<Integer, Integer> <span class="hljs-string" style="">entry :</span> count.entrySet()) {
- System.out.println(gifts.get(entry.getKey()) + <span class="hljs-string" style="">", count="</span> + entry.getValue() + <span class="hljs-string" style="">", probability="</span> + entry.getValue() / num);
- }
- }
- }</code>
不同概率的抽奖原理很简单
就是把0到1的区间分块,而分块的依据就是物品占整个的比重,再根据随机数种子来产生0-1中间的某个数,来判断这个数是落在哪个区间上,而对应的就是抽到了那个物品。随机数理论上是概率均等的,产生的每个数理论上也应该概率均等,那么相应的区间所含数的多少就体现了抽奖物品概率的不同。(p.s. 当然数目是数不清楚的,具体抽象话了点)
这个实例的数据可以说明
1. 概率可以是负数和0,当然实际上中应该不会(p.s. 正常情况下可能真的有0,比如抽个iphone5,当然是抽不到的了,这个时候,构建礼物(List gifts)的时候最好就不要加这个进去),还有可以把负数的处理放到抽奖工具类(LotteryUtil)中;
2. 所有礼物加起来的概率可以不是1,可以认为这里的概率是一个权重;
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