JS解出网络疯传的“刑侦推理题”

题目如下：

解题方法：

    var arr = new Array(10).fill("A");
    var flag = true ;

    run(); // ["B", "C", "A", "C", "A", "C", "D", "A", "B", "A"]

    function run () {
        try {
            if(flag){
                flag = false ;
                recursion() ;
            }
        } catch (err) {
            flag = true;
            run();
        }
    }
    
    function a1 (){
        return true;
    }
    function a2 (){
        switch(arr[1])
        {
        case "A":
            return arr[4] === "C"
        case "B":
            return arr[4] === "D"
        case "C":
            return arr[4] === "A"
        case "D":
            return arr[4] === "B"
        default:
            return false;
        }
    }
    function a3 (){
        switch(arr[2])
        {
        case "A":
            return arr[5] === arr[1] && arr[5] === arr[3]
        case "B":
            return arr[2] === arr[1] && arr[2] === arr[3]
        case "C":
            return arr[5] === arr[2] && arr[5] === arr[3]
        case "D":
            return arr[5] === arr[1] && arr[5] === arr[2]
        default:
            return false;
        }
    }
    function a4 (){
        var f1 = arr[0] === arr[4] ,
            f2 = arr[1] === arr[6] ,
            f3 = arr[0] === arr[8] ,
            f4 = arr[5] === arr[9] ;
        switch(arr[3])
        {
        case "A":
            return f1 && !f2 && !f3 && !f4
        case "B":
            return !f1 && f2 && !f3 && !f4
        case "C":
            return !f1 && !f2 && f3 && !f4
        case "D":
            return !f1 && !f2 && !f3 && f4
        default:
            return false;
        }
    }
    function a5 (){
        switch(arr[4])
        {
        case "A":
            return arr[7] === "A"
        case "B":
            return arr[3] === "B"
        case "C":
            return arr[8] === "C"
        case "D":
            return arr[6] === "D"
        default:
            return false;
        }
    }
    function a6 (){
        var f1 = arr[7] === arr[1] && arr[7] === arr[3] ,
            f2 = arr[7] === arr[0] && arr[7] === arr[5] ,
            f3 = arr[7] === arr[2] && arr[7] === arr[9] ,
            f4 = arr[7] === arr[4] && arr[7] === arr[8] ;
        switch(arr[5])
        {
        case "A":
            return f1 && !f2 && !f3 && !f4
        case "B":
            return !f1 && f2 && !f3 && !f4
        case "C":
            return !f1 && !f2 && f3 && !f4
        case "D":
            return !f1 && !f2 && !f3 && f4
        default:
            return false;
        }
    }
    function a7 (){
        var c1 = arr.filter((i)=>{return i === "A"}).length ,
            c2 = arr.filter((i)=>{return i === "B"}).length ,
            c3 = arr.filter((i)=>{return i === "C"}).length ,
            c4 = arr.filter((i)=>{return i === "D"}).length ;
        switch(arr[6])
        {
        case "A":
            return Math.min(c1,c2,c3,c4) === c3
        case "B":
            return Math.min(c1,c2,c3,c4) === c2
        case "C":
            return Math.min(c1,c2,c3,c4) === c1
        case "D":
            return Math.min(c1,c2,c3,c4) === c4
        default:
            return false;
        }
    }
    function a8 (){
        switch(arr[7])
        {
        case "A":
            return Math.abs(arr[0].charCodeAt(0) - arr[6].charCodeAt(0))>=2
        case "B":
            return Math.abs(arr[0].charCodeAt(0) - arr[4].charCodeAt(0))>=2
        case "C":
            return Math.abs(arr[0].charCodeAt(0) - arr[1].charCodeAt(0))>=2
        case "D":
            return Math.abs(arr[0].charCodeAt(0) - arr[9].charCodeAt(0))>=2
        default:
            return false;
        }
    }
    function a9 (){
        var flag = arr[0] === arr[5],
            f1 = (arr[4] === arr[5]) === !flag ,
            f2 = (arr[4] === arr[9]) === !flag ,
            f3 = (arr[4] === arr[1]) === !flag ,
            f4 = (arr[4] === arr[8]) === !flag ;
        switch(arr[8])
        {
        case "A":
            return f1 && !f2 && !f3 && !f4
        case "B":
            return !f1 && f2 && !f3 && !f4
        case "C":
            return !f1 && !f2 && f3 && !f4
        case "D":
            return !f1 && !f2 && !f3 && f4
        default:
            return false;
        }
    }
    function a10 (){
        var c1 = arr.filter((i)=>{return i === "A"}).length ,
            c2 = arr.filter((i)=>{return i === "B"}).length ,
            c3 = arr.filter((i)=>{return i === "C"}).length ,
            c4 = arr.filter((i)=>{return i === "D"}).length ;
        switch(arr[9])
        {
        case "A":
            return Math.max(c1,c2,c3,c4) - Math.min(c1,c2,c3,c4) === 3
        case "B":
            return Math.max(c1,c2,c3,c4) - Math.min(c1,c2,c3,c4) === 2
        case "C":
            return Math.max(c1,c2,c3,c4) - Math.min(c1,c2,c3,c4) === 4
        case "D":
            return Math.max(c1,c2,c3,c4) - Math.min(c1,c2,c3,c4) === 1
        default:
            return false;
        }
    }

    function vali () {
        return a1() && a2() && a3() && a4() && a5() && a6() && a7() && a8() && a9() && a10() ;
    }
    
    //递归遍历arr的所有排列组合
    function recursion (){
        if(vali()){
            console.log(arr);
        }
        for(var x=0 ; x<arr.length ; x++){
            switch(arr[x])
            {
            case "A":
                arr[x] = "B" ;
                recursion () ;
                return ;
            case "B":
                arr[x] = "C" 
                recursion () ;
                return ;
            case "C":
                arr[x] = "D" ;
                recursion () ;
                return ;
            case "D":
                if(x===9) return ;
                arr[x] = "A" ;
                continue ;
            default:
                return ;
            }
        }
    }
    //原文：https://juejin.im/post/5aa94d57f265da237314284a