adding two linked lists efficiently in C

Question

I have two linked lists representing the digits of decimal numbers in order from most- to least-significant. for eg 4->7->9->6 and 5->7 The

Answer 1

This is how I would go about solving this:

Step 1: Make a pass on both linked lists, find lengths

say len(L1) = m and len(L2) = n

Step 2: Find difference of lengths

if ( m > n )
    d = m - n
else if ( n > m )
    d = n - m
else
    d = 0

Step 3: Move a temporary pointer d ahead of the larger list

Step 4: Now we have two linked lists to add whose lengths are same, so add them recursively, maintaining a carry.

Step 5: ( Note: if ( d == 0 ) don't perform this step )

After step 4, we've got partial output list, and now we have to put remaining of the larger list at the beginning of output list.

if ( d > 0 )
    -Travel larger list till d positions recursively
    -Append sum = value_at_end + carry (update carry if sum >= 10) to output list at beginning
    -Repeat until difference is consumed

Note: I'm solving the problem as its put before me, not by suggesting the change in underlying data structure.

Time complexity:

1. Making single passes on both the lists to find their lengths: O(m+n)
2. Summing two linked lists of equal size (m - d and n) recursively: O(n), assuming m > n
3. Appending remaining of larger list to output list: O(d)

Total: O( (m+n) + (n) + (d) ) OR O(m+n)

Space complexity:

1. step 2 of time complexity: O(n), run time stack space
2. step 3 of time complexity: O(d), run time stack space

Total: O(n + d) OR O(n)