Learning Journal

2/22/2024

Subset

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

    backtrack(0);

    function backtrack(start) {
        if(start === nums.length) {
            return;
        }

        for(let i = start; i < nums.length; i++) {
            comb.push(nums[i]);
            result.push([...comb]);

            backtrack(i + 1);
            comb.pop();
        }

    }

    return result;
};function subsets(nums: number[]): number[][] {
    const result:number[][] = [[]];
    const comb = [];

    backtrack(0);

    function backtrack(start) {
        if(start === nums.length) {
            return;
        }

        for(let i = start; i < nums.length; i++) {
            comb.push(nums[i]);
            result.push([...comb]);

            backtrack(i + 1);
            comb.pop();
        }

    }

    return result;
};

THE PROBLEM

This problem can be solved using the backtracking approach.

We need an array comb to save all the current combination and an array result to store all the combinations.

The backtracking algorithm works by consider all combination of the elements and push them to result. The catch here is not include the same element twice and not include two sets that have the same elements but in different order. To achieve this, you can use the pointer start so that each time you call the backtrack function, the pointer will advance 1 step so that we do not need to consider the previous elements anymore.

Revised by ChatGPT

This problem asks us to generate all possible subsets of a given set of numbers. A subset is a collection of elements from the set, and it can be of any size, from zero elements (the empty set) to the full set.

To solve this problem, we use a backtracking approach. Backtracking is a methodical way to iterate through all possible configurations of a search space. In this case, our search space is the set of all possible subsets.

Here's how the algorithm works:

Initialization: We start with an empty array comb to hold the current combination of elements we are considering, and an array result to store all the combinations we find. We also start with an empty subset in result.
Backtracking Function: We define a function backtrack(start) that will recursively explore the search space. The start parameter is used to control which elements are considered in the current recursive call, ensuring that we do not revisit elements we have already included in the current combination.
Exploring Combinations: For each element in the array staring from start, we do the following:

Add the element to the current combination (comb).
Add a copy of the current combination to the result.
Recursively call backtrack with the next start index (i + 1) to explore further combinations that include the current element.
Remove the last element from comb (backtrack) to explore combinations that do not include the current element.

Termination: The recursion terminates when start equals the length of the input array, meaning we have considered all elements.

By following this approach, we ensure that we explore all possible subsets without duplicating any set or including the same element multiple times in a single set. The result is a complete list of all possible subsets.