function subsets(nums) {
    const result = [];

    function backtrack(index, current) {
        if (index === nums.length) {
            result.push([...current]);  // Store a COPY
            return;
        }

        // Pick
        current.push(nums[index]);
        backtrack(index + 1, current);
        current.pop();  // Backtrack

        // Not pick
        backtrack(index + 1, current);
    }

    backtrack(0, []);
    return result;
}

console.log(subsets([1, 2, 3]));
// [[ 1, 2, 3 ], [ 1, 2 ], [ 1, 3 ], [ 1 ], [ 2, 3 ], [ 2 ], [ 3 ], []]

function subsetsV2(nums) {
    const result = [];

    function backtrack(start, current) {
        result.push([...current]);  // Every state is a valid subset!

        for (let i = start; i < nums.length; i++) {
            current.push(nums[i]);
            backtrack(i + 1, current);
            current.pop();
        }
    }

    backtrack(0, []);
    return result;
}
// Output: [[], [1], [1,2], [1,2,3], [1,3], [2], [2,3], [3]]

function subsequencesWithSum(arr, target) {
    const result = [];

    function backtrack(index, current, currentSum) {
        if (index === arr.length) {
            if (currentSum === target) result.push([...current]);
            return;
        }

        // Pruning: if currentSum already exceeds target (positive numbers only)
        if (currentSum > target) return;

        // Pick
        current.push(arr[index]);
        backtrack(index + 1, current, currentSum + arr[index]);
        current.pop();

        // Not pick
        backtrack(index + 1, current, currentSum);
    }

    backtrack(0, [], 0);
    return result;
}

console.log(subsequencesWithSum([1, 2, 3], 3));
// [[1, 2], [3]]

function permutations(nums) {
    const result = [];
    const used = new Array(nums.length).fill(false);

    function backtrack(current) {
        if (current.length === nums.length) {
            result.push([...current]);
            return;
        }

        for (let i = 0; i < nums.length; i++) {
            if (used[i]) continue;

            current.push(nums[i]);
            used[i] = true;
            backtrack(current);
            current.pop();
            used[i] = false;
        }
    }

    backtrack([]);
    return result;
}

console.log(permutations([1, 2, 3]));
// [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]

function permutationsSwap(nums) {
    const result = [];

    function backtrack(index) {
        if (index === nums.length) {
            result.push([...nums]);
            return;
        }

        for (let i = index; i < nums.length; i++) {
            [nums[index], nums[i]] = [nums[i], nums[index]];
            backtrack(index + 1);
            [nums[index], nums[i]] = [nums[i], nums[index]];  // Backtrack
        }
    }

    backtrack(0);
    return result;
}

function combinationSum(candidates, target) {
    const result = [];

    function backtrack(index, current, remaining) {
        if (remaining === 0) {
            result.push([...current]);
            return;
        }
        if (remaining < 0 || index === candidates.length) return;

        // Pick (can pick again, so pass index, NOT index+1)
        current.push(candidates[index]);
        backtrack(index, current, remaining - candidates[index]);
        current.pop();

        // Skip
        backtrack(index + 1, current, remaining);
    }

    backtrack(0, [], target);
    return result;
}

console.log(combinationSum([2, 3, 6, 7], 7));
// [[2, 2, 3], [7]]