What's going on with this backtracking problem?

Question

class Solution {
    List<List<Integer>> res = new ArrayList<>();
    public List<List<Integer>> combine(int n, int k) {
    
         List<Integer> list = new ArrayList<>();
         helper(k, n, list, 1);
         return res;
    }
    private void helper(int k, int n, List<Integer> list, int index){
        if(list.size() == k){
            res.add(new ArrayList<>(list));
            return;
        }
        for(int i=index; i<=n; i++){
            list.add(i);
            helper(k, n, list, index+1);
            list.remove(list.size()-1);
        }
        return;
    }
}

When I do this, the output is as follows: [[1,2],[1,3],[1,4],[2,2],[2,3],[2,4],[3,2],[3,3],[3,4],[4,2],[4,3],[4,4]]. And the expected output is: [[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]].

But when I change this line helper(k, n, list, index+1); to helper(k, n, list, i+1);, the output becomes correct.

I want to know the difference between the two, but so far I'm not getting an answer (isn't it supposed to be the same value every time for both index+1 and i+1?).

your for loop increments i, not index. So i and index will have different values. You can observe this by printing i and index above your call to the helper function. — Zico
– Zico, Commented Oct 21, 2024 at 21:29

Stephen C · Accepted Answer · 2024-10-22 04:53:36Z

But when I change this line helper(k, n, list, index+1); to helper(k, n, list, i+1);, the output becomes correct.

As expected.

I want to know the difference between the two, but so far I'm not getting an answer (isn't it supposed to be the same value every time for both index+1 and i+1?).

No it isn't.

The difference is that i is changed in the loop, but not index.

for (int i = index; i <= n; i++) {

means (in English):

"start with i set to the value of index, increment i by one on each iteration, and keep going while i is less or equal to n".

Nothing changes index. In fact index and i will only have the same value on the first iteration.

As the comment says, you can verify this by adding some trace print statements to print out i and index at the start of the loop body.

In Java, = denotes some form of assignment; i.e. i = index means the value of index is assigned to the variable i. It doesn't mean that i and index are the same thing. They were and are two distinct variable. They have the same value immediately after the assignment ... but when i is incremented by the i++ expression the values of the two variables will be different.

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