Learning Journal

3/2/2024

Combination Sum - 3rd attempt

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

    backtrack(0);

    return result;

    function backtrack(start:number) {
        const total = sum(comb);

        if(total === target) {
            result.push([...comb]);
            return;
        }
        else if(total > target)
            return;

        for(let i = start; i < candidates.length; i++) {
            comb.push(candidates[i]);
            backtrack(i);
            comb.pop();
        }
    }


  
};

function sum(a:number[]) {
    let total = 0;

    for(let i = 0; i < a.length; i++) {
        total += a[i];
    }

    return total;
}function combinationSum(candidates: number[], target: number): number[][] {
    const comb:number[] = [];
    const result:number[][] = [];

    backtrack(0);

    return result;

    function backtrack(start:number) {
        const total = sum(comb);

        if(total === target) {
            result.push([...comb]);
            return;
        }
        else if(total > target)
            return;

        for(let i = start; i < candidates.length; i++) {
            comb.push(candidates[i]);
            backtrack(i);
            comb.pop();
        }
    }


  
};

function sum(a:number[]) {
    let total = 0;

    for(let i = 0; i < a.length; i++) {
        total += a[i];
    }

    return total;
}

THE PROBLEM

I learned from this attempt that it's important to understand what elements the comb array holds at any moment. At first, I mad a mistake by putting if(sum(comb) > target) break; to the for loop, right after comb.push(candidates[i]).

However, the core idea of the backtracking technique is that you try one possibility, then, you "backtrack", try another one.

The "backtrack" step in this case is the line comb.pop() inside the for loop. The for loop is for trying all possibilities, the backtrack call inside the for loop means that for each possibility, you need to recursively try all of the possibilities branching from that possibility. Then, when you finish for that possibility, you need to "backtrack", which means cleaning after yourself, make everything become back to before you consider that possibility, so that you're ready to consider the next one. In this case comb.pop() is used to pop out the last element, make the comb array back to the state before you consider the current possibility.

Revised by ChatGPT

In this attempt, I gained a deeper understanding of the backtracking technique, particularly the importance of maintaining the state of the comb array throughout the process. Initially, I made a mistake by adding a break condition if(sum(comb) > target) break; right after comb.push(candidates[i] in the for loop. This approach prematurely terminated the exploration of certain paths without properly backtracking.

The essence of backtracking is to explore a possibility and then revert to the previous state to explore another possibility. In this solution, the "backtrack" step is represented by comb.pop() inside the for loop. The for loop iterates through all possible candidates, and for each candidate, we recursively explore all subsequent combinations by calling backtrack(i). After exploring all combinations stemming from the current candidates, we need to backtrack by removing the last element added to comb (using comb.pop()). This action restores comb to its state before the current candidate was considered, allowing us to cleanly move on to the next candidate.

Understanding this mechanism is crucial for correctly implementing backtracking algorithms. It ensures that each recursive call explores a new path without interference from previous paths.