BOTH CHAINS START AT THE ONES PLACE, SO THE TWO HEADS MOVE TOGETHER. EACH COLUMN ADDS TWO DIGITS PLUS THE CARRY INTO ONE SUM DIGIT AND A NEXT CARRY. A DUMMY NODE GIVES THE TAIL SOMETHING TO BUILD ON.

BLUE L1 AND MAGENTA L2 MARK THE TWO FRONTIERS. EACH STEP WRITES ONE TAN NODE ONTO THE SUM CHAIN AND THE GREEN TAIL FOLLOWS. THE GOLD CARRY FEEDS THE NEXT COLUMN. A LEFTOVER CARRY CREATES ONE FINAL NODE. THE GOLD TILE IS THE RETURNED HEAD.

1def addTwoNumbers(l1, l2):2    dummy = ListNode()3    tail = dummy4    carry = 05    while l1 or l2 or carry:6        v1 = l1.val if l1 else 07        v2 = l2.val if l2 else 08        total = v1 + v2 + carry9        carry = total // 1010        tail.next = ListNode(total % 10)11        tail = tail.next12        if l1:13            l1 = l1.next14        if l2:15            l2 = l2.next16    return dummy.next