Path Sum II

Unlike Path Sum I, we need to return every root-to-leaf path whose values add up to targetSum, not just whether one exists.

Since we need the paths themselves, we keep one path list that always holds the nodes from the root down to the current call. When we reach a leaf that completes the sum, we add a copy of path to result.

We use DFS with backtracking.

1. State: one shared path list, and remaining, what is still needed.
2. Action: entering a node, append node.val to path.
3. Check: at a leaf whose value is exactly remaining, save a copy of path.
4. Recurse: otherwise call the left and right children with remaining - node.val.
5. Backtrack: pop node.val off path before returning, so the parent’s other branch starts from the right path.

The outlined nodes are path itself: a node joins when its call starts and leaves just before its call returns. Each visited node shows what was still needed below it, and a leaf whose path is saved turns green.