[60] 排列序列

/**
 * @param {number} n
 * @param {number} k
 * @return {string}
 */
const getPermutation = function (n, k) {
    const list = new Array(n).fill(1).map((v, i) => ++i);
    let num = 1;
    const numList = [];
    for (let i = 1; i < n; i++) {
        num *= i;
        numList[i] = num;
    }
    const ans = [];
    const dfs = p => {
        if (p === 1) {
            return [...ans, ...list].join('');
        }
        const len = list.length - 1;
        if (p > numList[len]) {
            const newP = p % numList[len];
            const t = (p - newP) / numList[len];
            if (newP === 0) {
                ans.push(list.splice(t - 1, 1)[0]);
                return [...ans, ...list.reverse()].join('');
            } else {
                ans.push(list.splice(t, 1)[0]);
                return dfs(newP);
            }
        } else {
            ans.push(list.splice(0, 1)[0]);
            return dfs(p);
        }
    };
    return dfs(k);
};