Finding the maximum sum in a field of numbers - c++

Question

I have to write a program that sums up sequential elements of an array and outputs the maximum sum. As you will see my algorithm won't work if all elements are negative.
#include <iostream>
int main()
{
int nums[1000] = {-1,-3,-4,-2,-5,-1,-9,-4,-2,-2};
int sums[100][100];
int n = 9;
for(int i = 0; i <= n; i++) {
for(int j = n; j >= i; j--) {
for(int k = j; k >= i; k--) {
sums[i][j] += nums[k];
}
}
}
int max_sum = 0;
int max_begin;
int max_end;
for(int i = 0; i <= n; i++) {
for(int j = i+1; j <= n; j++){
std::cout << "i = " << i << " j = " << j << ": " << sums[i][j] << "\n";
if(max_sum < sums[i][j]) {
max_sum = sums[i][j];
max_begin = i;
max_end = j;
}
}
}
std::cout << "Maximum: " << max_sum << " bei i = " << max_begin << " bis j = " << max_end;
return 0;
}
I already tried this solution
#include <climits>
...
int max_sum = INT_MIN;
...
While this works perfectly fine we didn't have climits in our lecture yet so I'm looking for another way.

Answer 1

Change to:
int max_sum = sums[0][0];
This way you will never have to worry about the range of numbers.

Answer 2

This is one of the main motivations for a std::optional type (when all values in a range are valid). If you cannot use it, we can imitate it for our purposes with a simple boolean:
bool max_set = false;
int max_sum = 0;
// ...
if (!max_set || max_sum < sums[i][j]){
max_set = true;
max_sum = sums[i][j];
}
We can make a simple class to further imitate it if we'd like (untested code):
class optional_int{
bool is_set = false;
int value = 0;
public:
bool operator()() const{return is_set;}
int& operator=(int _value){value = _value; is_set=true; return value;}
int& get(){
if (!is_set){throw std::logic_error("attempting to access unset optional");}
return value;
};
optional_int max_sum;
//...
if (!max_sum || max_sum.get() < sums[i][j]){
max_sum = sums[i][j];
}
We can continue to make this type more and more generic, but we'd only be re-implementing std::optional