Recursive function to check all pairs in an array - c++

Question

an int vector is given, and I need to find the maximum sum of number sequences that are more than 3 positions away from each other. So an example:
Input: 10, 5, 6, 7, 16, 18, 12
Output: 29
Explanation:
candidate "routes":
10-7-12 = 29
10-16 = 26
10-18 = 28
5-16 = 21
5-18 = 23
5-12 = 17
...
16
18
12
I want to solve this problem using recursion and I have gotten to the point where the program tests all paths with numbers that are more than 3 positions away. However, it fails to test all the paths starting from the same digit.
Here my code:
#include <iostream>
using namespace std;
const int n = 7;
int sum = 0;
int temp=0;
void rec(int (*arr), int ind){
if (ind > n-3){
if(temp > sum)
sum = temp;
temp=0;
return;
}
temp += arr[ind];
cout<<arr[ind]<<" ";
for(int i=3;i<n;i++)
rec(arr, ind+i);
cout<<endl;
}
int main(){
int arr[n] = {10, 9, 9, 9, 8, 8, 7};
for(int i=0;i<n;i++)
rec(arr, i);
cout<<endl<<endl<<"Max: "<<sum;
return 0;}
Output:
10 9 7
8
8
7
9 8
8
7
9 8
7
9 7
8
8
7
Max: 26
Even though in this case the output is correct, you can see that it tests only 10-9-7 and not the other 10-8, 10-8 and 10-7. It seems it doesn´t even go in the first for-loop I called the function recursively.
Am I understanding something wrong or how do I accomplish that it tests all pairs that are more than 3 positions away?

Answer 1

There are 3 problems here:
Based on your output:
10 9 7
8
8
⋮
Your code actually loops through all the possible routes. Instead of thinking your second line 8 and third line 8 as two complete routes, they were actually derived from your first rout 10 9 7. So really think of it like this:
10 --- 9 --- 7
`- 8
`- 8
`- 7
9 --- 8
`- 8
`- 7
⋮
That's actually not your output. Plugged your code in, I got my output:
10 9
8
9 8
9
9
8
Max: 19
The reason that it didn't go through all routes is because your line:
if (ind > n-3)
{
⋮
return;
}
You are terminating your loop way too early. Instead, you should only end it right before it goes out of index. So it should be:
if (ind > n - 1)
{
⋮
}
Your logic actually has flaws.
Because you always set your temp back to 0 once reached the last possible number inside the array, you actually lost some part of your previous sums. You can easily create a sequence that makes it fails, such as: 10, 9, 9, 7, 8, 20, 7.
Instead of having temp as a global, it would be better to set it local, and being passed to each recursions.
To do that, you would need to add the temp as a parameter of your rec function, and call it like:
void rec(int (*arr), int ind, int temp)
{
⋮
rec(arr, i, temp);
⋮
}
int main()
{
⋮
rec(arr, i, 0);
⋮
}
Or if you want to keep the signature the same in your main, you could also add a default argument in your rec:
void rec(int (*arr), int ind, int temp = 0)
Side note, I would considering using std::array or std::vector instead of c-style array, to avoid having a global size n or passing int (*arr) in your function. Plus you can easily make your arr as a longer sequence.