Write a recursive function max_sum that accepts a list of integers L and an integer limit n as its parameters and uses backtracking to find the maximum sum that can be generated by adding elements of L that does not exceed n.
For example, if you are given the list of integers [7, 30, 8, 22, 6, 1, 14] and the limit of 19, the maximum sum that can be generated that does not exceed is 16, achieved by adding 7, 8, and 1.
If the list L is empty, or if the limit is not a positive integer, or all of L's values exceed the limit, return 0.
Each index's element in the list can be added to the sum only once, but the same number value might occur more than once in a list, in which case each occurrence might be added to the sum.
For example, if the list is [6, 2, 6, 1] you may use up to two sixes in the sum.
Here are several example calls to your function and their expected return values:
| List L |
Limit n |
max_sum(L, n) returns |
[7, 30, 8, 22, 6, 1, 14]
|
19
|
16
|
[5, 30, 15, 13, 8]
|
42
|
41
|
[30, 15, 20]
|
40
|
35
|
[6, 2, 6, 9, 1]
|
30
|
24
|
[11, 5, 3, 7, 2]
|
14
|
14
|
[10, 20, 30]
|
7
|
0
|
[10, 20, 30]
|
20
|
20
|
[]
|
10
|
0
|
You may assume that all values in the list are non-negative.
Your function may alter the contents of the list L as it executes, but L should be restored to its original state before your function returns.
Do not use any loops in solving this problem.
