Implementation of a solver for the game Le Compte Est Bon

Le Compte Est Bon

var nums = new Array(6).fill(null).map(a => (Math.floor(Math.random()*9 + 1) * (Math.random()<.4?10:1)));
var goal = Math.floor(Math.random()*900 + 100);

console.log(`goal = ${goal}`);
console.log(`nums = ${nums}\n`);

const bag = [];
nums.forEach((num, index) => {
    bag.push(
        {
            num,
            mask: 1<<index,
            children: null,
        }
    );
});

const bagHash = {};

function checkBagHash(item) {
    if(item.num === goal) {
        found = true;
    }
    if  (!bagHash[item.num+","+item.mask]) {
        bagHash[item.num+","+item.mask] = item;
        return true;
    }
    return false;
}

var found = false;
for(var i=0; i<bag.length && !found; i++) {
    for(var j=0; j<bag.length && !found; j++) {
        if((bag[i].mask & bag[j].mask) === 0) {
            var item = {
                num: bag[i].num + bag[j].num,
                mask: bag[i].mask | bag[j].mask,
                operator: '+',
                children: [bag[i], bag[j]],
            };
            if(checkBagHash(item)) {
                bag.push(item);
            }
            var item = {
                num: Math.abs(bag[i].num - bag[j].num),
                mask: bag[i].mask | bag[j].mask,
                operator: '-',
                children: [bag[i], bag[j]],
            };
            if(checkBagHash(item)) {
                bag.push(item);
            }
            var item = {
                num: bag[i].num * bag[j].num,
                mask: bag[i].mask | bag[j].mask,
                operator: 'x',
                children: [bag[i], bag[j]],
            };
            if(checkBagHash(item)) {
                bag.push(item);
            }
            if(bag[i].num%bag[j].num===0 || bag[j].num%bag[i].num===0) {
                var item = {
                    num: Math.max(bag[i].num / bag[j].num, bag[j].num / bag[i].num),
                    mask: bag[i].mask | bag[j].mask,
                    operator: '/',
                    children: [bag[i], bag[j]],
                };
                if(checkBagHash(item)) {
                    bag.push(item);
                }
            }
        }
    }
}


const opLevel = {
    '+': 1, '-': 1, 'x':2, '/':2,
};

const orderMatter = {
    '-': true, '/': true,
};


function expression(item, parentOperator, left) {
    if(!item.children) {
        return item.num;
    }
    const a = item.children[0];
    const b = item.children[1];
    let exp = null;
    if(a.num>b.num) {
        exp = `${expression(a,item.operator, true)} ${item.operator} ${expression(b,item.operator, false)}`;
    } else {
        exp = `${expression(b,item.operator, true)} ${item.operator} ${expression(a,item.operator, false)}`;
    }
    if(opLevel[parentOperator] > opLevel[item.operator] || !left && orderMatter[parentOperator]) {
        exp = `(${exp})`;
    }
    return exp;
}

let best = bag[0];
for(let i=1; i<bag.length; i++) {
    if(Math.abs(goal-bag[i].num) < Math.abs(best.num-goal)) {
        best = bag[i]
    }
}
const exp = expression(best);
console.log(exp, "=", eval(exp.split("x").join("*")));