You are given an integer n. We reorder the digits in any order (including the original order) such that the leading digit is not zero. Return true if and only if we can do this so that the resulting number is a power of two.

reorderedPowerOf2.js

/**
 * @param {number} n
 * @return {boolean}
 */
var reorderedPowerOf2 = function(n) {
    // Convert the number to an array of digit characters
    const digits = n.toString().split('');

    // Helper function to generate all unique permutations of the digits
    function getPermutations(arr) {
        const results = [];

        function backtrack(path, used) {
            // Base case: if path is complete, add to results
            if (path.length === arr.length) {
                // Skip permutations with leading zero
                if (path[0] !== '0') {
                    results.push([...path]);
                }
                return;
            }

            for (let i = 0; i < arr.length; i++) {
                // Skip used digits
                if (used[i]) continue;

                // Skip duplicates (important for repeated digits)
                if (i > 0 && arr[i] === arr[i - 1] && !used[i - 1]) continue;

                used[i] = true;
                path.push(arr[i]);
                backtrack(path, used);
                path.pop();
                used[i] = false;
            }
        }

        // Sort to handle duplicates properly
        arr.sort();
        backtrack([], Array(arr.length).fill(false));
        return results;
    }

    // Helper function to check if a number is a power of two
    function isPowerOfTwo(x) {
        // Bitwise trick: only powers of two have a single bit set
        return (x & (x - 1)) === 0 && x !== 0;
    }

    // Generate all valid permutations of the digits
    const validPermutations = getPermutations(digits);

    // Check each permutation to see if it's a power of two
    for (let perm of validPermutations) {
        const num = parseInt(perm.join(''), 10);
        if (isPowerOfTwo(num)) return true;
    }

    // If none match, return false
    return false;
};