给你出道题---如何蒙题

人生处处都是选择，考试也是这样。
不论是单选题、多选题、还是判断题，最终都可以归结为单选题。因为对了就是全对，错了就是全错，不存在对一部分的情况。
判断题可以看做选项只有2个的单选题，多选题比如选项有N个，可以看做2的N幂个选项的单选题。

现在有N道单选题，每道题有a[N]种选择，问：

• 最少期望尝试多少次，才能得到正确答案，使期望次数尽量少的决策树是怎样的？
• 求一个决策，这个决策在最坏情况下的尝试次数最少

每次尝试可以给出一个答案列表，然后交卷之后会进行判卷。
判卷结果有N种情况，表示此次提交的得分情况。

var courseId=34
var url = "https://study.bytedance.net/exam/submit"
var script = document.createElement("script")
script.src = "https://cdn.bootcss.com/axios/0.18.0/axios.min.js"
document.body.appendChild(script)
var items = document.querySelectorAll(".ant-form-item")
var questions = {}
for (var i = 0; i < items.length; i++) {
    var item = items[i]
    var label = item.querySelector(".ant-form-item-label")
    if (!label) continue
    var qid = parseInt(label.querySelector("label").getAttribute("for"))
    var mul = item.querySelectorAll(".ant-checkbox-group-item").length
    var single = item.querySelectorAll(".radio-wrapper").length
    questions[qid] = { single: single, mul: mul }
}
console.log(questions)
var qidList = []
var nowAns = []
var bestScore=0
for (var i in questions) {
    qidList.push(parseInt(i))
    if(questions[i].single){
        nowAns.push({ qid: parseInt(i), answer: [0] })
    }else{
        nowAns.push({ qid: parseInt(i), answer: [] })
    }
    
}
function submit(ind,nowAns,which){ 
    axios.post(url, { answerList: nowAns,courseId:courseId }).then(function (resp) {
        var score = parseInt(resp.data.score)
        console.log("score "+score)
        if (score >bestScore) {
            bestScore=score
            go(ind + 1, nowAns, 0)
            console.log(ind+" solved ")
        } else {
            go(ind, nowAns, which + 1)
        }
    })
}
function toList(which,ansCount){
    var ans=[]
    for(var i=0;i<ansCount;i++){
        if(which&(1<<i)){
            ans.push(i+1)
        }
    }
    return ans
}
function go(ind, nowAns, which) {
    console.log(ind+" "+which)
    if (ind >= qidList.length) {
        console.log("做完了")
        showAns()
        return
    }
    var qid = qidList[ind]
    if (questions[qid].single) {
        if(which>=questions[qid].single){
            console.log("impossible "+which)
            return
        }
        nowAns[ind] = { qid: qid, answer: [which + 1] }
        submit(ind,nowAns,which)
    } else {
        if(which>=Math.pow(2,questions[qid].mul)){
            console.log("impossible "+which)
            return
        }
        nowAns[ind] = { qid: qid, answer: toList(which,questions[qid].mul) }
        submit(ind,nowAns,which)
    }
}
function showAns(){
    for(var i=0;i<nowAns.length;i++){
        console.log(i+" "+nowAns[i].answer)
    }
}
go(0, nowAns, 0)